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Vehicle routing problems (VRP) are a kind of typical combinational optimization problem, particularly in the logistics industry. This paper proposes a constrained evolutionary optimization algorithm, called CEOA, for solving many-objective VRP with simultaneous delivery, pickup, and time windows (VRPSDPTW). Specifically, we first define the weight value vectors based on the constraint satisfaction situation, which can adaptively adjust according to the feedback of population solutions during the search process. Subsequently, based on the feedback from the weight value vectors, the environmental selection strategy is employed to identify promising solutions for both infeasible and feasible situations. Furthermore, considering the data characteristics of the problem at hand, the crossover and mutation operations are tailored to better align with the VRPSDPTW, which is further explained and illustrated in detail regarding solution construction. The experimental results demonstrate the effectiveness of the proposed algorithm for VRPSDPTW in comparison with other state-of-the-art methods. • This paper designs an adapting weight value vector to indicate infeasible solutions, which cannot compare together. • We use a constrained satisfaction strategy to select feasible solutions and select infeasible solutions, respectively. • The crossover and mutation operations are redesigned to make it more fit the real problem. [ABSTRACT FROM AUTHOR]

Dynamic Constrained Multiobjective Optimization Problems (DCMOPs) are very difficult to solve because both of the objectives and constraints may change over time. The existing approaches for solving DCMOPs mainly develop dynamic response techniques and constraint handling techniques. But they do not focus on the search capability of the static optimizer in each environment, which ignores the intrinsic requirement of quickly locating Pareto-optimal Front (PF) in each environment when solving DCMOPs. To this end, this paper proposes a dual-population evolutionary algorithm for solving DCMOPs, called as DpEA, which maintains a population without considering constraints (called UP) for exploration and a population with considering constraints (called CP) for exploitation in each environment. In each iteration of a new environment, UP firstly adopts a stratified mutation strategy (SMS) and a dominated solution repairment strategy (DSR) to enhance the exploration ability of finding promising regions where the PF may reside. SMS uses solutions from different nondominated fronts to generate offspring, while DSR repairs the single-optimal variables of the dominated solutions by sampling from the distribution of those variables of nondominated solutions. Secondly, this paper uses an adaptive offspring ratio adjustment strategy to control the offspring number generated by UP and CP according to the normalized Hausdorff distance between nondominated solution sets from the two latest generations of UP. This strategy is helpful to balance the intensity between exploration and exploitation and thereby ensures efficient search. Experimental results on CEC 2023 DCF test suite show that DpEA has a superior performance over six state-of-the-art algorithms. • First EA that focuses on the search capability of static optimizer in solving DCMOPs. • Two offspring generation strategies to enhance the exploration ability. • An adaptive strategy to balance the intensity between exploration and exploitation. [ABSTRACT FROM AUTHOR]

Nature- and society-inspired metaheuristic algorithms have recently become the most promising technological model. To solve more complex optimization problems and complicated engineering applications, this paper proposes a new people duality psychological tendency and feedback mechanism-based Inherited Optimization Algorithm(IOA), which is inspired by people showing positive-negative duality cognitive tendency and adaptive feedback behavior when selecting information resources with different identity attributes. The IOA algorithm contains the symmetric two exploration phases. The exploitation phase adaptively regulates the dualistic psychological balance of people in inheriting the information resources with better existence value through a feedback regulation mechanism controlled by the profitability awareness to increase population diversity. This paper qualitatively and quantitatively evaluates the optimization performance of IOA on 84 benchmarks, including swarm convergence behavior, effectiveness, convergence, robustness, and significance. The scalability of the IOA is investigated using the CEC2017 suites. The algorithm performance in solving constrained optimization is verified on 8 engineering problems. All statistical results of the IOA are compared with the most promising 12 metaheuristics, which shows that the absolute computational efficiency of IOA on four types of functions is 95%, 96.67%, 80.95%, and 76.92%, respectively, the average rank (rank sum ratio) of IOA is 1.08 (1.19%) among the 13 algorithms, ranking first. The Wilcoxon signed rank test results on the CEC2017 suites show that IOA contains 1437 significance indicators out of 1440 comparisons, with the proportion of significant differences 99.79%, which suggests the proposed IOA maintains efficient search efficiency. [ABSTRACT FROM AUTHOR]

Dynamic constrained optimization problems (DCOPs) are common and important optimization problems in real-world, which have great difficulty to solve. Dynamic constrained evolutionary algorithms (DCEAs) are widely used methods for solving DCOPs. However, existing DCEAs often struggle with convergence, particularly for DCOPs with drastic dynamic changes or intricate constraints. To address this issue, this paper proposes a novel DCEA called DCEA-DQN, which leverages the powerful perception and decision-making capabilities of Deep Q-Network (DQN). DCEA-DQN integrates two DQNs to enhance its performance. The first DQN is designed to adaptively respond to dynamic changes, enabling effective handling of DCOPs with various types and degrees of changes. It provides a high-quality re-initialized population for subsequent static optimization, resulting in faster and improved convergence. The second DQN is introduced to guide the mutation direction during offspring generation. It steers the population towards better feasible regions or directs it towards the optimal individual within the current feasible region. Moreover, a penalty mechanism is employed to handle constraints during offspring generation. To evaluate the performance of DCEA-DQN, comprehensive empirical studies are conducted using a new test suite called C-GMPB and a dynamic flexible job-shop scheduling problem. The experimental results, using two commonly used metrics E B and E O in the field of DCOPs, demonstrate that DCEA-DQN outperforms six state-of-the-art DCEAs and achieved optimal performance on 80% and 75% of all 24 test problems, respectively. The source code for DCEA-DQN is available at https://github.com/CIA-SZU/YRT. • A change response strategy based on DQN is proposed for complex DCOPs. • An offspring generation strategy based on penalty and DQN is proposed for complex DCOPs. • A new complex dynamic constrained test suite C-GMPB is proposed. [ABSTRACT FROM AUTHOR]

When dealing with Constrained Multi-objective Optimization Problems (CMOPs) and struggling to enhance feasibility, convergence and diversity, the researchers of Constrained Multi-objective Optimization Evolutionary Algorithms (CMOEAs) gravitate toward feasibility or take precedence to preserve well-converged solutions ignoring diversity in the past. To compensate for the defects, the paper proposes CMOEA-MSWA to guide the search of infeasible regions by coordinated strategy of archive and weight vectors. Firstly, the archive carrying the information of population diversity updates the weight vectors. Secondly, the updated weight vectors perpetuate the diversity information to the search of infeasible regions. The circular effects between strategies promote the detection of infeasible solutions with good objectives and exhibit competitive performance in terms of spread and evenness. To testify the versatility the CMOEA-MSWA in enhancing diversity, the comprehensive performance is evaluated firstly and the diversity analysis of the CMOEA-MSWA is carried out on four benchmark suites with 34 test instances, where the number of objectives for some of test problems is scaled from three to five. In comparison with five state-of-the-art CMOEAs, the proposed algorithm yields highly competitive performance in diversity on different types of CMOPs. In addition, the effectiveness of collaboration between archive and weight vectors on handling infeasible solutions is also verified. [ABSTRACT FROM AUTHOR]

This paper introduces the Human Evolutionary Optimization Algorithm (HEOA), a metaheuristic algorithm inspired by human evolution. HEOA divides the global search process into two distinct phases: human exploration and human development. Logistic Chaos Mapping is employed for initialization. In the human exploration phase, an initial global search is conducted, followed by the human development phase, in which the population is categorized into leaders, explorers, followers, and losers, each utilizing distinct search strategies. The convergence speed and search accuracy of HEOA are evaluated using 23 well-established test functions. Furthermore, the algorithm's applicability in engineering optimization is assessed with four engineering problems. A comparative analysis with ten other algorithms highlights HEOA's effectiveness, as evidenced by various performance metrics and statistical measures. Consistently, the results demonstrate that HEOA surpasses most current state-of-the-art algorithms in approximating optimal solutions for complex global optimization problems. The MATLAB code for HEOA is available at https://github.com/junbolian/HEOA.git. [ABSTRACT FROM AUTHOR]

How to balance the satisfaction of constraints and the optimization of objective functions is one of the key issues to solve constrained multi-objective optimization problems (CMOPs), especially when the constraints are complex. Although many algorithms have been designed to handle this, most of them are still unable to effectively handle CMOPs with complex constraints. Based on the above issue, this paper proposes a framework for bi-directional search, which evolves two populations (P 1 and P 2). P 1 aims to search the constrained Pareto front (CPF) from the infeasible side of the objective space, and P 2 from the feasible side, aiming to achieve a more efficient and comprehensive bi-directional search for the CPF. To ensure the diversity, we adopt a preferred weight vector selection strategy to choose potential mating parents, which improves the search capability for the marginal CPF. Furthermore, to coordinate the interaction between the two populations, we propose an environmental selection strategy to select the offspring generated by P 1 and P 2 under the same weight vector with the better fitness to update the populations respectively, and the fitness is evaluated based on the different constraint relaxations of the two populations, to update them respectively. Extensive experiments indicate that our proposed algorithm has significantly better results or was at least competitive when compared to eight state-of-the-art methods. [ABSTRACT FROM AUTHOR]

• This paper proposes an enhanced SCA algorithm variant, called ARSCA. • ARSCA improves the convergence accuracy and avoids premature convergence. • This paper compares ARSCA with classical algorithms, variations of other algorithms. • ARSCA is applied to six engineering design problems and its results are satisfactory. The sine cosine algorithm (SCA) is a well-known meta-heuristic optimization algorithm. SCA has received much attention in various optimization fields due to its simple structure and excellent optimization capabilities. However, the dimension of objective function also increases with the increasing complexity of optimization tasks. This makes the original SCA appear to have insufficient optimization capability and likely to fall into premature convergence. A multi-mechanism acting variant of SCA, called ARSCA, is proposed to address the above deficiencies. ARSCA is an enhanced SCA algorithm based on the adaptive quadratic interpolation mechanism (AQIM) and Rounding mechanism (RM). RM enables a more balanced state between exploration and exploitation of the ARSCA. AQIM enhances local exploitation capabilities. To verify the performance of ARSCA, we compared ARSCA with some advanced traditional optimization algorithms and variants of algorithms for 30 consecutive benchmark functions of IEEE CEC2014. In addition, ARSCA was applied to 6 constrained engineering optimization problems. These six algorithms include the tension–compression spring design problem, the welded beam design problem, the pressure vessel design problem, the I-beam design problem, the speed reducer design problem, and the three-bar design problem. Experimental results show that ARSCA outperforms its competitors in both the solution quality and the ability to jump out of the local optimum. The relevant codes for the paper are publicly available at https://github.com/YangXiao9799/paper_ARSCA. [ABSTRACT FROM AUTHOR]

Most multiple unmanned aerial vehicle (UAV) path planning problems are often treated as constrained single-objective optimization problems. How to consider them as constrained multi-objective optimization problems (CMOPs) have seldom been explored in this field. To fill this gap, this paper firstly constructs multiple UAV path planning problem as a CMOP with two objectives and five constraints. Then a novel multi-objective evolutionary algorithm with a two-fold constraint-handling mechanism is proposed for multiple UAV path planning. To cope with constraints effectively, a constraint-handling technique based on a progressive weight vector strategy is proposed. Besides, a constraint repair technique that considers the flying environment is designed to further guide the algorithm to find feasible promising regions. Eight multiple UAV path planning test instances with different solving difficulties are constructed. Subsequently, they are used to validate the performance of the proposed algorithm. The experimental results demonstrate that the proposed algorithm is superior over four compared algorithms in terms of obtaining a set of better-distributed Pareto optimal solutions. [ABSTRACT FROM AUTHOR]

Despite the inherent stability of Quadratic Approximation based Jaya (JaQA) in solving constrained optimization problems, its effectiveness in exploring the search space is limited. Furthermore, the user-defined penalty parameter utilized to mitigate constraint violation poses another impediment to the efficiency of JaQA. In light of these drawbacks, this paper introduces a new meta-heuristic algorithm, namely Self-adaptive Multi-population Quadratic Approximation guided Jaya (SMP-JaQA). The three additional key features of the SMP-JaQA over JaQA are (i) the inclusion of a multi-population technique to ensure sufficient diversity in the search process (to address the exploration), (ii) a self-adaptation strategy to make it more user-friendly for complex problems in various domains (to address the exploration further), and (iii) a dynamic penalty factor (to automate the penalty parameter). These novel changes help strike a balance between exploration and exploitation too by identifying potential areas in the search space and reduces the likelihood of getting stuck in a local optima. The validity of SMP-JaQA is tested over 18 and 28 benchmark functions of varying dimensions from the CEC-2010 and CEC-2017 test suites, respectively. In order to justify the wide applicability of the proposed algorithm, a set of four real-life constrained problems (includes two mechanical design problems, an electronics design problem and an agricultural problem) are being solved through SMP-JaQA. A thorough analysis of computational outcomes, exploration–exploitation phases, and scalability are presented to shed light on the efficacy and stability levels of SMP-JaQA. The results are compared with those of other state-of-the-art meta-heuristics using Friedman's and Wilcoxon Signed-Rank tests. The outcomes indicate that SMP-JaQA produces reasonable solutions in terms of global optimality and solution quality. [ABSTRACT FROM AUTHOR]

Traditional differential evolution (DE) algorithms have functional limitations in effectively addressing increasingly intricate numerical optimization problems. The key to responding to this challenge is to strike a suitable balance between exploration and exploitation. Exploration is used to find the global optimal solution, and exploitation is used to improve the accuracy of the global optimal solution. Therefore, this study introduces a novel differential evolution algorithm with a stage stratification method and a dual balanced mutation strategy framework, named SbmDE. To enhance the balance between convergence and diversity, the population is stratified into exploration and exploitation layers based on the size of the fitness value and evolutionary period. In the exploitation layer, a hybridization mutation is applied as the first mutation. A novel dual improved mutation operation is proposed and applied to the exploration layer. For the first mutation, the hybridization mutation is used in the same manner as for the exploitation layer. For the secondary mutation, two improved mutation strategies are proposed to alleviate premature convergence at the early stage of evolution and to enhance the local neighborhood search at a later stage, named DE/ranking-to-rand/1 and DE/best-current-dev/1. Experiments were conducted on the CEC2017 benchmark suite, which contains 29 single-objective real-parameter numerical optimization problems, to evaluate the performance of the proposed algorithm. Compared with 11 state-of-the-art algorithms, the results demonstrate the superiority of the proposed algorithm, which does not increase the time complexity. Additionally, based on the four engineering design problems, the proposed algorithm is fully competent in solving practical constrained optimization problems. • A stage stratification method is proposed to divide population. • Dual mutation is proposed and applied to the exploration layer. • Proposed two improved mutation strategies applied to the secondary mutation. • SbmDE obtains better values than the other algorithms in the paper. • SbmDE is applied to four engineering design problems. [ABSTRACT FROM AUTHOR]

The main challenge in addressing constrained multi-objective optimization problems (CMOPs) lies in achieving a balance among convergence, diversity, and feasibility. To address this issue, this paper proposes a constrained multi-objective evolutionary algorithm with Pareto estimation via neural network named CMOEA-PeNN. In order to exploit and explore the decision space, the proposed algorithm employs a dual-population mechanism, which is trained with a self-organizing map (SOM). Firstly, the population distribution structure in decision space is mapped to objective space while preserving neighborhood information, and then the neuron weight is utilized to estimate the Pareto front (PF). Secondly, a novel approach is devised to preserve the feasibility of the population and enhance the estimation of the Pareto front by SOM. The achievement scalarizing function (ASF) is employed to choose promising solutions. This strategy could guide the population toward the optimal solution while exploring the small feasible regions. Finally, the performance of CMOEA-PeNN is compared with five state-of-the-art constrained multi-objective evolutionary algorithms (CMOEAs) on three widely used benchmark problems and a real-world problem. The experimental results show that CMOEA-PeNN could archive competitive performance in solving CMOPs. [ABSTRACT FROM AUTHOR]

The fuzzy analytic hierarchy process (FAHP) is a widely implemented approach for determining the weights of criteria and alternatives from pairwise comparison matrices. FAHP methodology uses triangular fuzzy as a tool for the decision-maker to arrange judgments expressed as the pairwise comparison matrix elements. FAHP is then modeled into a nonlinear constrained optimization problem to increase the decision maker's satisfaction. However, in some cases, this model would yield multiple optimal solutions. Logarithmic fuzzy preference programming (LFPP) is offered to overcome this unfavorable situation. Nevertheless, LFPP includes a parameter in its model for which no specific method is available to determine. Meanwhile, the differences in parameter values will affect the solution. In the worst case, the weights obtained will be inaccurate. As a result, the decision taken based on the weights will be biased and unreliable. This issue is particularly important when it requires high accuracy. It includes the decisions on the portfolio investment, economic, human capital measurements, and shipping registry. Another crucial thing is that the use of the natural logarithm function in the LFPP method has the potential for an overflow effect at the computational stage when it is implemented to derive the weights. Therefore, in the application context, it is significant to improve the shortcomings of the LFPP method in terms of parameter involvement and the use of the logarithmic function. For this purpose, this paper proposes a non-parameter transcendental fuzzy preference programming (TFPP) model for deriving the optimal weights from fuzzy pairwise comparison matrices. The TFPP is obtained by investigating different functions' effects on fuzzy preference programming (FPP). The proposed method has a more general form. One of the specific forms of the TFPP is chosen in a computational implementation. The numerical results confirm that the TFPP optimization model is reliable in obtaining the optimum global weights. The comparison with the LFPP method also shows that the TFPP is more efficient. • Logarithmic fuzzy preference programming (LFPP) includes a parameter in its model. • The parameter incorporated in LFPP affects the optimality of the solution. • Some transcendental functions employed to replace the logarithmic function in LFPP. • Transcendental fuzzy preference programming performs better than the LFPP. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a meerkat optimization algorithm(MOA) by simulating the behavior pattern of meerkats in nature. MOA is mainly inspired by the survival strategies of meerkat populations, whose sentinel mechanism controls meerkats to switch between different behavior patterns. Some mathematical properties of meerkat optimization algorithm are proved, and the advantages of MOA are verified with classical optimization test functions. MOA is applied to solve real-world engineering problems with constraints, which proves the effectiveness and superiority of MOA in solving such problems. • A new optimization algorithm is proposed based on the meerkat survival strategy. • The algorithm is called MOA and is used to solve constrained optimization problems. • The convergent property of MOA is proved strictly in theory. • It proves the effectiveness and superiority of MOA compared with other algorithms. [ABSTRACT FROM AUTHOR]

A formation tracking control problem for uncertainty traffic cone robots (TCRs) is considered. In this paper, the TCRs can not only perform formation behaviors but also track placement targets under environmental constraints (i.e., the position constraints in the y -direction.). To deal with the environmental constraints, a differential homeomorphism transformation is selected to eliminate the constraints. Moreover, the uncertainty of the TCRs is bounded, including matching portions and mismatching portions. For the matching uncertainty, a series of adaptive parameters are introduced to estimate the real-time information of the uncertainty. The mismatching uncertainty is tackled by a geometric decomposition, which is orthogonal to the range space of the formation. At the same time, a fuzzy uncertainty optimization design problem is presented. The global solution to the resulting optimization problem always exists and is unique. Using adaptive robust control, TCRs' performance is deterministically and fuzzy-optimized. The system performance is demonstrated by a range of numerical simulations and real experiments with three TCRs. • An adaptive robust formation tracking control design method is proposed. • The artificial potential field function has the property of "repulsion at near and attraction at far". • The uncertainty of the TCR system is divided into a matching part and a mismatching part. • A constrained optimization problem based on uncertain fuzzy information is presented. [ABSTRACT FROM AUTHOR]

The paper intends to propose an enhanced Harris hawk optimizer (EHHO) to solve the highly constrained and non-linear multiobjective hydrothermal generation scheduling (MOHGS) optimization problem. Hydrothermal generation scheduling aims to minimize thermal unit fuel costs and environmental consequences while utilizing available water during the optimization time horizon. A multi-chain and cascaded hydro system are taken for hydropower generation. A non-linear relationship between water discharge rate and power generation is established for a multichain-linked hydro system. Water movement between linked reservoirs accounts for the time delay. A fuzzy decision-making approach solves the conflicting objectives of the MOHGS problem. The two-step proportional sharing heuristic method handles the complicated constraints imposed on hydrothermal units instead of indirect constraint handling methods. Harris Hawk Optimization (HHO) is a swarm-based optimizer that works on the natural hunting behavior of hawks. Despite having good adaptability, scalability, flexibility, and robustness, it tends to get stuck in the local search region and gives immature convergence for confined engineering optimization problems. The proposed EHHO speeds up the global search phase of the HHO by utilizing opposition-based learning, keeping it out of the stagnated local search region, and avoiding untimely convergence. Compared to the existing heuristic methods, the EHHO gives better results while solving thirteen unconstrained benchmarks, thirteen constrained benchmarks, and minimum cost and emission for three MOHGS problems. The convergence curves, box plots, and Wilcoxon signed-rank test justify the robustness of the EHHO. The results revealed that EHHO supports its efficacy in applications of non-linear, discontinuous, highly constrained optimization problems. [ABSTRACT FROM AUTHOR]

To address constrained optimization problems (COPs), there are two crucial trade-offs in preeminent constrained evolutionary algorithms: (1) the trade-off between exploration and exploitation, and (2) the one between the constraints and the objectives. Moreover, the problem of inaccurate diversity regulation in constrained optimization evolutionary algorithms has yet to be completely solved. To achieve the first trade-off, this paper designs a diversity controller (DC) based on a small-world network. Then, the fitness distance correlation information is applied to adjust the reconnection probability of the small-world network to dynamically control the diversity. To achieve the second trade-off, we propose an infeasible–feasible regions constraint handling method (IF). There are two stages in the IF method. The first stage is to search the boundary between the infeasible and feasible regions, while the second stage adopts the self-adaptive Epsilon constraint handling method. Furthermore, combining the DC and IF constraint handing methods into the success-history-based parameter adaptive differential evolution (SHADE) algorithm, a DC-SHADE-IF algorithm is proposed. Twenty-eight constrained optimization problems provided in the CEC2017 competition on constrained real parameter optimization are employed to compare the performance between the proposed DC-SHADE-IF and seven state-of-the-art algorithms. Besides that, two real-world constrained optimization problems are employed to examine the performance of the proposed DC-SHADE-IF in real-world problems. Experimental results show the superior performance of the proposed algorithm in terms of accuracy and convergence. • A diversity controller is proposed to control population diversity. • An infeasible–feasible regions constraint handling method. • Experiments were outperform in CEC 2017 and real-world problems. [ABSTRACT FROM AUTHOR]

The balance between multiple objectives and various constraints is the key to solving constrained multi-objective optimization problems (CMOPs). When dealing with CMOPs with complex feasible regions, some evolutionary algorithms suffer from great challenges in converging to the constrained Pareto front (CPF) with well-distributed feasible solutions. To address this issue, this paper proposes a dual-population based bidirectional coevolution algorithm, called DBC-CMOEA, which aims to converge to the CPF using promising solutions explored from both feasible and infeasible regions. To do so, DBC-CMOEA maintains two populations and an archive, where the dual-population is complementary in the search process and the archive is used to retain promising feasible and infeasible solutions, thus facilitating information exchange between these two populations. For updating the archive, a nondominated sorting procedure and an angle-based selected scheme are conducted to store infeasible and feasible solutions, as they can help to maintain the diversity of the search and find more feasible regions. To evolve the CPF from the bidirectional side of the feasible region, a novel mating selection strategy is used to choose appropriate mating parents. In comparison with some related constraint multi-objective optimization algorithms on a number of benchmark problems, experimental results show that the proposed algorithm performs better than the state-of-the-art constrained multi-objective evolutionary optimizers. • A cooperative dual-population algorithm is proposed for solving CMOPs. • Constraints are handled in three different ways to explore the search space. • A brand-new selection strategy is applied to select the mating parents. • A novel archive update strategy is designed to retain the promising information. [ABSTRACT FROM AUTHOR]

Most of the existing methods for solving fully fuzzy mathematical programs are based on the standard fuzzy arithmetic operations and/or Zadeh's extension principle. These methods may produce questionable results for many real-life applications. Due to this fact, this paper presents a novel method based on the constrained fuzzy arithmetic concept to solve fully fuzzy balanced/unbalanced transportation problems in which all of the parameters (source capacities, demands of destinations, transportation costs etc.) as well as the decision variables (transportation quantities) are considered as fuzzy numbers. In the proposed method, the requisite crisp and/or fuzzy constraints between the base variables of the fuzzy components are provided from the decision maker according to his/her exact or vague judgments. Thereafter, fuzzy arithmetic operations are performed under these requisite constraints by taking into account the additional information while transforming the fuzzy transportation model into crisp equivalent form. Therefore, various fuzzy efficient solutions can be generated by making use of the proposed method according to the decision maker's risk attitude. In order to present the efficiency/applicability of the proposed method, different types of fully fuzzy transportation problems are generated and solved as illustrative examples. A detailed comparative study is also performed with other methods available in the literature. The computational analysis have shown that relatively more precise solutions are obtained from the proposed method for “risk-averse” and “partially risk-averse” decision makers. The proposed method also successfully provided fuzzy acceptable solutions for “risk seekers” with high degree of uncertainty similar to the other existing methods in the literature. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) algorithm is popular to tackle real-world optimization problems. The standard DE, however, is not able to solve constrained optimization problems (COPs) for their complicated linear or nonlinear constraints. The transformation of constraints, which is realized via constraint handling technique, has a great impact on dealing with constrained algorithms. In this paper, a lightweight and efficient variant of DE named C ε -LDE is proposed to solve constrained single-objective optimization problems. This study firstly introduces a combined constraint handling method, which is designed based on the difference and relationship between two different ε constrained methods and balances infeasible solution and feasible solution with rules from the perspective of probability allocation. In addition, an extra control parameter is redefined in terms of different initial ε level in consideration of the complexity and diversity of COPs. On the other hand, DE evolves by opposition-based learning initialization and modifications on mutation operator and crossover rate selection, respectively. Mutation strategies frequently named rand/1 and best/1 are adopted and Lévy flight is added to the mutation strategy as a multiplier with scale factor F for a long jump. The crossover rate CR tends to be a larger or smaller stochastic value according to the pros and cons of the selected vector. A set of 28 problems under different dimension settings (D = 10, 30, 50 and 100) used for the CEC 2017 Competition is employed to evaluate the performance of the proposed C ε -LDE. The computational results demonstrate the effectiveness and superiority of the proposed combined ε constrained method. A comparative study of C ε -LDE with state-of-art algorithms is conducted on the obtained experimental results under the rules of CEC 2017 Competition. The ranking outcomes reveal that C ε -LDE is equipped with high competitiveness. Furthermore, the applications in several standard real-life engineering problems verify the effectiveness and practicability of the proposed scheme. [ABSTRACT FROM AUTHOR]

This study considers a constrained huge-scale optimization problem over networks where the objective is to minimize the sum of nonsmooth local loss functions. To solve this problem, many optimization algorithms have been proposed by employing (sub)gradient descent methods to handle high-dimensional data, but the computation of the entire sub(gradient) becomes a computational bottleneck. To reduce the computational burden of each agent and preserve privacy of data in time-varying networks, we propose a privacy-preserving decentralized randomized block-coordinate subgradient projection algorithm over time-varying networks, in which the coordinates of the subgradient vector is randomly chosen to update the optimized parameter and the partially homomorphic cryptography is used to protect the privacy of data. Further, we prove that our algorithm is convergent asymptotically. Moreover, the rates of convergence are also established by choosing appropriate step sizes, i.e., O (log K / K) under local strong convexity and O (log K / K) under local convexity, in which K represents the number of iterations. Meanwhile, we show that the privacy of data can be protected by the proposed algorithm. The results of experiments demonstrate the computational benefit of our algorithm on two real-world datasets. The theoretical results are also verified by different experiments. • This paper proposes a privacy-preserving decentralized randomized block-coordinate subgradient projection algorithm. • It proves that the proposed algorithm is asymptotically convergent. • It proves that the proposed algorithm can protect the privacy of data. • It proves that the rate of convergence is achieved, i.e., O (log K / K) and O (log K / K). [ABSTRACT FROM AUTHOR]

• A search algorithm is investigated as an optimization method. • The proposed approach covers static, constrained, and dynamic problems. • The search algorithm is based on random solutions in all generations. • Proof of stochastic mechanisms of the method's core algorithm is provided. In this work, the application of an optimization algorithm is investigated to optimize static and dynamic engineering problems. The methodology of the approach is to generate random solutions and find a zone for the initial answer and keep reducing the zones. The generated solution in each loop is independent of the previous answer that creates a powerful method. Simplicity as its main advantage and the interlaced use of intensification and diversification mechanisms--to refine the solution and avoid local minima/maxima--enable the users to apply that for a variety of problems. The proposed approach has been validated by several previously solved examples in structural optimization and scored good results. The method is also employed for dynamic problems in vibration and control. A modification has also been done on the method for high-dimensional test functions (functions with very large search domains) to converge fast to the global minimum or maximum; simulated for several well-known benchmarks successfully. For validation, a number of 9 static and 4 dynamic constrained optimization benchmark applications and 32 benchmark test functions are solved and provided, 45 in total. All the codes of this work are available as supplementary material in the online version of the paper on the journal website. [ABSTRACT FROM AUTHOR]

When solving constrained optimization problems by constraint-handling techniques, the core idea is to balance constraint violation and objective function during the search process. Although many constraint-handling techniques have proposed to deal with this problem, it is difficult to reduce the risk of falling into the local optimums and maintain good population diversity. To tackle these issues, this paper proposes an evolutionary algorithm using multiple dynamic penalties based on decomposition for constrained optimization. Specifically, a constrained optimization problem is decomposed into a number of unconstrained optimization subproblems, and each subproblem is assigned a penalty coefficient to balance constraint and objective function. Then, these subproblems are solved simultaneously, which can improve global search ability and population diversity. In order to generate proper penalty coefficients, a penalty coefficient adjusting strategy is designed, and the penalty coefficient value increases with the number of evolutionary generations to balance the exploration and exploitation. The experimental results on two benchmark test suites and six real-world application problems demonstrate the proposed algorithm is efficient and competitive. • Multiple dynamic penalties based on decomposition are proposed for constrained optimization. • We convert a constrained optimization problem into a set of unconstrained optimization problems by assigning a penalty coefficient to each subproblem. • We design a penalty coefficient adjusting strategy to balance the exploration and exploitation. [ABSTRACT FROM AUTHOR]

• Optimal foraging algorithm with direction prediction & Gaussian oscillation is built. • New algorithm includes two update methods: prediction model and random model. • Prediction model mends exploitation ability by predicting the evolutionary direction. • Random model mends exploration by exploring the space with Gaussian distribution. • The superiority of algorithm is verified on benchmark set and engineering problems. Optimal foraging algorithm (OFA) is a newly stochastic optimization technique and is famous for its computational accuracy. However, the high computational accuracy leads to slow convergence speed. Experimental results demonstrate that OFA is good at unimodal functions but poor at multimodal functions. To improve these drawbacks, in this paper a novel modified OFA with direction prediction and Gaussian oscillation, named OFA/P&G is introduced. In OFA/P&G, a transition matrix is constructed when a new global optimum is found to generate the candidate individuals. If the current global optimum does not change, the Gaussian oscillation is employed in a low probability and OFA update method is used in a high probability to generate the candidate individuals. The superior performance of OFA/P&G is verified on the 12 CEC2017 benchmark functions, 13 constrained benchmark functions and 5 engineering problems. Experimental results demonstrate that OFA/P&G outperforms other comparative algorithms. Finally, a real-world problem, drilling path optimization, is solved by OFA/P&G. [ABSTRACT FROM AUTHOR]

• New method to improve satisfaction of hard constraints in operations engineering optimization. • Hard constraints are represented as quantum entanglement circuit and circuit parameters. • A quantum entanglement inspired GA is developed to solve the optimization problem. • Constraints satisfied with less computation efforts & better exploration-exploitation balance. • A real-world case study of an airport shift planning demonstrates the improved performance. Constraint handling, especially hard constraint handling, is a critical issue for discrete constrained optimization problem solving in operations engineering. The performance of conventional constraint handling techniques, such as penalty functions and repair operators, are susceptible to problem complexity and scale. The recent dawning of quantum computation has been recognized as a very promising direction in the paradigm of optimization. This paper presents a quantum entanglement inspired hard constraint handling approach, to efficiently solve discrete constrained optimization problems. We propose a quantum entanglement inspired representation method of hard constraints, which uses a series of qubits and quantum circuit to coherently represent the hard constraints in the posterior quantum states. A quantum entanglement inspired genetic algorithm (QEI-GA) is proposed by embedding the quantum entanglement inspired representation into classical genetic algorithm optimization strategy. The proposed method is applied to solve a real-world airport workforce shift planning problem to validate the algorithm's effectiveness and robustness. The results of the case study show that the proposed method can consistently reach better solutions for the discrete constrained optimization problem, even with a much smaller population size, compared to the conventional genetic algorithms with penalty function based and multi-objective concept-based strategies. [ABSTRACT FROM AUTHOR]

In many real-world optimization problems, several conflicting objectives must be achieved and optimized simultaneously and the solutions are often required to satisfy certain restrictions or constraints. Moreover, in some applications, the numerical values of the objectives and constraints are obtained from computationally expensive simulations. Many multi-objective optimization algorithms for continuous optimization have been proposed in the literature and some have been incorporated or used in conjunction with expert and intelligent systems. However, relatively few of these multi-objective algorithms handle constraints, and even fewer, use surrogates to approximate the objective or constraint functions when these functions are computationally expensive. This paper proposes a surrogate-assisted evolution strategy (ES) that can be used for constrained multi-objective optimization of expensive black-box objective functions subject to expensive black-box inequality constraints. Such an algorithm can be incorporated into an intelligent system that finds approximate Pareto optimal solutions to simulation-based constrained multi-objective optimization problems in various applications including engineering design optimization, production management and manufacturing. The main idea in the proposed algorithm is to generate a large number of trial offspring in each generation and use the surrogates to predict the objective and constraint function values of these trial offspring. Then the algorithm performs an approximate non-dominated sort of the trial offspring based on the predicted objective and constraint function values, and then it selects the most promising offspring (those with the smallest predicted ranks from the non-dominated sort) to become the actual offspring for the current generation that will be evaluated using the expensive objective and constraint functions. The proposed method is implemented using cubic radial basis function (RBF) surrogate models to assist the ES. The resulting RBF-assisted ES is compared with the original ES and to NSGA-II on 20 test problems involving 2–15 decision variables, 2–5 objectives and up to 13 inequality constraints. These problems include well-known benchmark problems and application problems in manufacturing and robotics. The numerical results showed that the RBF-assisted ES generally outperformed the original ES and NSGA-II on the problems used when the computational budget is relatively limited. These results suggest that the proposed surrogate-assisted ES is promising for computationally expensive constrained multi-objective optimization. [ABSTRACT FROM AUTHOR]

When planning a new development (facility/service site), location decisions are always the major issue. In this paper we introduce a novel query capacity constraint MaxBRNN, which can solve the facility location selection problem efficiently. The MaxBRNN (maximizing BRNN) query is based on bichromatic reverse nearest neighbor (BRNN) query which uses the number of reverse nearest customers to model the influence of a facility location. The MaxBRNN query has been appreciated extensively in spatial database studies because of its great potential in real life applications, such as, markets decision, sensor network clustering and the design of GSM (global system for mobile communication). The existing researches mostly suppose that the service facility's capacity is unlimited. However, in real cases, facilities are inevitably constrained by designed capacities. For example, if the government wants to select a new place to set up an emergency center to share the existing centers’ patients, they need to know the current emergency centers’ capacity so that they can estimate the new center's scale. Thus, the capacity constrained MaxBRNN query is significantly important in planning a new development. As far as we know, the capacity constrained MaxBRNN query has not been studied yet, so, we formulate this problem, propose a basic solution and develop some efficient algorithms for the query. Our major contributions are as follows: (1) we propose a novel query capacity constraint MaxBRNN which can solve the facility location selection problem effectively and efficiently; (2) we develop a basic algorithm CCMB and two improved algorithms which can find out the optimal region in terms of building a new facility, maximize its impact and deal with the complicated reassignment when adding new facilities into the dataset; (3) we prove the algorithms’ effectiveness and efficiency by extensive experiments using both real and synthetic data sets. [ABSTRACT FROM AUTHOR]

• Applying the Niching concept to ChOA (NChOA). • The NChOA proposes a novel constraint handling technique. • The NChOA's performance was evaluated on 37 numerical functions. • The NChOAs' performance was tested on twelve real-world constraint problems. Two significant concerns need to be addressed to handle multimodal problems: classifying various local/global optima and preserving these optimum values until the termination. Besides, a comprehensive local search ability is also a need to achieve the exact global optima. Chimp Optimization Algorithm (ChOA) is a recently swarm intelligence algorithm that needs less parameter tuning. The ChOA, on the other hand, is prone to early convergence and fails to strike a balance between exploration and exploitation when it comes to resolving multimodal challenges. In order to overcome these concerns, this paper embeds the niching technique in ChOA (NChOA) that includes the personal best qualities of PSO and a local search technique. To evaluate the NChOA's performance, we analyze it against fifteen frequently utilized multimodal numerical test functions, ten complex IEEE CEC06-2019 suit tests, and twelve constrained real-world optimization problems in a variety of engineering fields, including industrial chemical producer, process design and synthesis, mechanical design, power system, power-electronic, and livestock teed ration problems. The results indicate that the NChOA outperforms several benchmark algorithms and sixteen out of eighteen state-of-the-art algorithms by an average rank of Friedman test greater than 81% for 25 numerical functions and twelve engineering problems while outperforming jDE100 and DISHchain1e + 12 by 22% and 41%, respectively. The Bonferroni-Dunn and Holm tests demonstrated that NChOA outperforms all benchmark and state-of-the-art algorithms for all numerical functions and engineering tasks while performing comparably to jDE100 and DISHchain1e + 12. The proposed NChOA, we believe, can be used to address difficulties involving multimodal search spaces. Additionally, NChOA is more broadly applicable than rival benchmarks to a broader range of engineering applications. [ABSTRACT FROM AUTHOR]

In the last decades, a number of novel meta-heuristics and hybrid algorithms have been proposed to solve a great variety of optimization problems. Among these, constrained optimization problems are considered of particular interest in applications from many different domains. The presence of multiple constraints can make optimization problems particularly hard to solve, thus imposing the use of specific techniques to handle fitness landscapes which generally show complex properties. In this paper, we introduce a modified Covariance Matrix Adaptation Evolution Strategy (CMA-ES) specifically designed for solving constrained optimization problems. The proposed method makes use of the restart mechanism typical of most modern variants of CMA-ES, and handles constraints by means of an adaptive penalty function. This novel CMA-ES scheme presents competitive results on a broad set of benchmark functions and engineering problems, outperforming most state-of-the-art algorithms as for both efficiency and constraint handling. [ABSTRACT FROM AUTHOR]

One of the key issues in solving constrained multi-objective optimization problems (CMOPs) is balancing the three indicators of convergence, diversity, and feasibility. We believe at different stages of the evolution, different indicators should be emphasized. This paper proposes a two-stage constrained multi-objective evolutionary algorithm (CMOEA) with different emphases on the three indicators. In Stage-I, the Pareto nondominated sorting and the unbiased two-objective model are used to evaluate the three indicators. The purpose of Stage-I is to obtain solutions with good distribution and to prevent the population from falling into local optima. After Stage-I, almost all of the individuals in the population are distributed in the vicinity of all feasible areas. The goal of Stage-II is to quickly converge the population to the Pareto front (PF). Thirty benchmark CMOPs and four real-world problems were used to evaluate the performance of our algorithm. Experimental results indicate that our approach achieved significantly better results or was at least competitive to the compared eight state-of-the-art CMOEAs on most of the benchmark problems. • A TSTI method is proposed for the CMOPs. • Two stages are used in TSTI with different goals. • TSTI obtains better results compared with six related methods. [ABSTRACT FROM AUTHOR]

• A hybrid Harris hawks optimization named CLHHEO is presented for constrained optimization. • Comprehensive learning and equilibrium optimizer are added to enhance convergence. • Terminal replacement mechanism is also adopted to avoid local convergence. • CLHHEO is tested over 15 benchmark functions and 10 real-world problems. • The superior performance of CLHHEO is confirmed over advanced algorithms. Harris hawks optimization (HHO) is a novel metaheuristic algorithm which has strong convergence for unconstrained optimization problems. However, HHO may encounter premature or local stagnation for constrained optimization problems. In this paper, a hybrid HHO algorithm named comprehensive learning harris hawks-equilibrium optimization (CLHHEO) is presented for solving constrained optimization problems, with the help of three operators: comprehensive learning, equilibrium optimizer, and terminal replacement mechanism. In the proposed algorithm, comprehensive learning strategy is incorporated with HHO to make search agents share their knowledge to enhance the convergence capacity. The operator of equilibrium optimizer is utilized to improve the exploration capacity of HHO. Besides, the terminal replacement mechanism is incorporated in the proposed algorithm to avoid local stagnation. The proposed CLHHEO is tested on 15 unconstrained and 10 real-world constrained optimization problems, and compared with 10 state-of-the-art metaheuristic algorithms, including PSO, CLPSO, BBBC, GWO, DA, WOA, SSA, HHO, SOA and AOA. From the experimental results, it is observed that CLHHEO outperforms HHO and other comparing metaheuristic algorithms in terms of solution quality. The results also demonstrate that the ensemble strategies of CLHHEO can enhance the performance of HHO for constrained optimization problems. [ABSTRACT FROM AUTHOR]

Highlights: [•] In this paper, a novel swarm algorithm called the Social Spider Optimization (SSO-C) is proposed for solving constrained optimization tasks. [•] In the proposed method, individuals emulate a group of spiders which interact to each other based on the biological laws of the cooperative colony. [•] For constraint handling, the approach incorporates the combination of two different paradigms: a penalty function and a feasibility criterion. [•] Comparisons based on several well-studied benchmarks functions demonstrate the effectiveness, efficiency and stability of the proposed method. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to develop design scheme based on an easy-to-use meta-heuristic approach with superior reliability and validity for fixed-structure robust controllers, satisfying both multiple control specifications and system stability conditions. For this purpose, a particle swarm optimizer is first developed, which reduces the probability of premature convergence to local optima in the PSO (particle swarm optimization) by exploiting the particle’s local social learning based on the idea of cyclic-network topology. Next, it is shown how to obtain a fixed-structure robust controller with constraints on multiple H ∞ specifications and system stability based on the developed PSO technique incorporated with a simple constraint handling method. Finally, typical numerical examples are studied to show the applicability of the proposed methodology to the synthesis of fixed-structure robust controllers. These examples clearly verify that the developed design scheme gives a novel and powerful impetus with remarkable reliability to fixed-structure robust controller syntheses. [Copyright &y& Elsevier]

Abstract: Several constrained and unconstrained optimization problems have been adequately solved over the years thanks to advances in the metaheuristics area. In the last decades, different metaheuristics have been proposed employing new ideas, and hybrid algorithms that improve the original metaheuristics have been developed. One of the most successfully employed metaheuristics is the Differential Evolution. In this paper it is proposed a Multi-View Differential Evolution algorithm (MVDE) in which several mutation strategies are applied to the current population to generate different views at each iteration. The views are then merged according to the winner-takes-all paradigm, resulting in automatic exploration/exploitation balance. MVDE was tested to solve a set of well-known constrained engineering design problems and the obtained results were compared to those from many state-of-the-art metaheuristics. Results show that MVDE was very competitive in the considered problems, largely outperforming several of the compared algorithms. [Copyright &y& Elsevier]

Abstract: This paper proposes a novel Bayesian kernel model that can forecast the non-negative distribution of target option prices, which are constrained to be positive. The method utilizes a new transform measure that guarantees the non-negativity of option prices, and can be applied to Bayesian kernel models to provide predictive distributions of option prices. Simulations conducted on the model-generated option data and KOSPI 200 index option data show that the proposed method not only provide a predictive distribution of non-negative option prices, but also preserves the probabilistic distribution of large deviations. We also perform a very extensive empirical study on a large-scale time series of option prices to assess the prediction performance of the proposed method. We find that the method outperforms other state of the arts non-parametric methods in prediction accuracy and is statistically different. [Copyright &y& Elsevier]

Abstract: The generation of priority vectors from pairwise comparison matrices is an essential part of the Analytic Hierarchy Process. Perhaps the most popular approach for deriving the priority weights is the right eigenvalue method (REV) which was proposed by Saaty. Despite its popularity some shortcomings of the REV have been reported in literature. Among the alternative approaches one can find the statistical estimation techniques, methods founded on constrained optimization models and models based on fuzzy description of decision maker preferences. In this paper new optimization techniques for deriving priority weights are introduced. In the proposed approach, the constrained optimization models are based on the same idea which underlies the REV. The properties of the resulting prioritization techniques are studied via computer simulations. This study demonstrates that the new methods perform very well in comparison with other popular techniques known from literature. What is especially important, the new approach provides the decision maker with a meaningful index that can be used to measure consistency of his/her judgments. The new index is closely related to the well-known Saaty’s consistency index CI, but in difference to the latter, it can be applied to both reciprocal as well as nonreciprocal comparison matrices. Hence the new index can be considered as a natural extension of the CI to all types of matrices. Some additional advantages resulting from the new approach are discussed and illustrated by numerical examples. [Copyright &y& Elsevier]

Abstract: In today’s globalization, the success of an industry is dependent on cost effective supply chain management under various markets, logistics and production uncertainties. Uncertainties in the supply chain usually decrease profit, i.e. increase total supply chain cost. Demand uncertainty and constraints posed by the every echelon are important factors to be considered in the supply chain design operations. Optimization is no longer a luxury but has become the order of the day. This paper specifically deals with the modeling and optimization of a three echelon supply chain network using the particle swarm optimization/intelligence algorithms. [Copyright &y& Elsevier]

Abstract: Over the years, several metaheuristics have been developed to solve hard constrained and unconstrained optimization problems. In general, a metaheuristic is proposed and following researches are made to improve the original algorithm. In this paper, we evaluate a not so new metaheuristic called differential evolution (DE) to solve constrained engineering design problems and compare the results with some recent metaheuristics. Results show that the classical DE with a very simple penalty function to handle constraints is still very competitive in the tested problems. [Copyright &y& Elsevier]

Abstract: The multivariate exponentially weighted moving average, MEWMA, control chart is an effective statistical tool for detecting small shifts in process mean vectors. On the one hand, the economic design process of a MEWMA control chart involves determining the main parameters of the chart, namely, the sample size n, the sampling interval h, the smoothing constant r, and the control limit L such that a quality cost function is minimized. On the other hand, the statistically constrained economic design of MEWMA chart is to determine the chart parameters such that a cost function is minimized while the statistical performance of the chart is maintained at a desire level. In this paper, the statistically constrained economic design model of the MEWMA control chart is first extended by the Taguchi loss function to improve its effectiveness. Next, an ant-colony optimization algorithm is proposed to solve the model in which a Markov chain approach is developed to calculate the average run lengths, ARLs. Then, the main parameters of the employed ant colony algorithm are tuned by means of a response surface methodology, RSM, approach. Finally, a sensitivity analysis on the main parameters of both the cost function and the control chart is performed using experimental design approach. The results show that augmenting a proper statistical nonlinear constraint to the model will improve the effectiveness of the model without a significant increase in the cost. [Copyright &y& Elsevier]

Abstract: Unconstrained binary quadratic programming problem (UBQP) consists in maximizing a quadratic 0–1 function. It is a well known NP-hard problem and is considered as a unified model for a variety of combinatorial optimization problems. This paper combines a tabu Hopfield neural network (HNN) (THNN) with estimation of distribution algorithm (EDA), and thus a THNN–EDA is proposed for the UBQP. In the THNN, the tabu rule, instead of the original updating rule of the HNN, is used to govern the state transition or updating of neurons to search for the global minimum of the energy function. A probability vector in EDA model is built to characterize the distribution of promising solutions in the search space, and then the THNN is guided by the global search information in EDA model to search better solution in the promising region. Thus, the short term memory of the tabu mechanism in the THNN cooperates with the long term memory mechanism in the EDA to help the network escape from local minima. The THNN–EDA is tested on 21 UBQP benchmark problems with the size ranging from 3000 to 7000, and 48 maximum cut benchmark problems, a special case of the UBQP, with the size ranging from 512 to 3375. Simulation results show that the THNN–EDA is better than the other HNN based algorithms, and is better than or competitive with metaheuristic algorithms and state-of-the-art algorithms. [Copyright &y& Elsevier]

Abstract: The RFM model provides an effective measure for customers’ consumption behavior analysis, where three variables, namely, consumption interval, frequency, and money amount are used to quantify a customer’s loyalty and contribution. Based on the RFM value, customers can be clustered into different groups and the group information is very useful in market decision making. However, most previous works completely left out important characteristics of purchased products, such as their prices and lifetimes, and apply the RFM measure on all of a customer’s purchased products. This renders the calculation of the RFM value unreasonable or insignificant for customer analysis. In this paper, we propose a new framework called GRFM (for group RFM) analysis to alleviate the problem. The new measure method takes into account the characteristics of the purchased items so that the calculated the RFM value for the customers are strongly related to their purchased items and can correctly reflect their actual consumption behavior. Moreover, GRFM employs a constrained clustering method PICC (for Purchased Items-Constrained Clustering) that could base on a cleverly designed purchase pattern table to adjust original purchase records to satisfy various clustering constraints as well as to decrease re-clustering time. The GRFM allows a customer to belong to different clusters, and thus to be associated with different loyalties and contributions with respect to different characteristics of purchased items. Finally, the clustering result of PICC contains extra information about the distribution status inside each cluster that could help the manager to decide when is most proper to launch a specific sales promotion campaign. Our experiments have confirmed the above observations and suggest that GRFM can play an important role in building a personalized purchasing management system and an inventory management system. [Copyright &y& Elsevier]

Abstract: The updating rule of the original discrete Hopfield neural network (DHNN) is based on gradient descent dynamics, which always leads to the local minima problem. In this paper, by introducing the idea of the simulated annealing (SA) into the DHNN, we first propose an annealing HNN (AHNN) that permits temporary energy ascent to help the DHNN escape from local minima. Then, from a cooperative perspective, a population of the AHNN processes are simultaneously implemented and coupled by their acceptance probabilities, and thus a cooperative AHNN (CoAHNN) is proposed. The primary objective of the coupling in the CoAHNN is to create cooperative behavior via information exchange among neural networks. This objective helps in the decision of whether uphill moves will be accepted. In addition, coupling can provide information used online to guide the networks toward the global optimum. The CoAHNN is tested on 21 unconstrained binary quadratic programming problems (UBQP) with the size ranging from 3000 to 7000, and 48 maximum cut benchmark problems, a special case of the UBQP, with the size ranging from 512 to 3375. The UBQP consists in maximizing a quadratic 0–1 function. It is a well known NP-hard problem and is considered as a unified model for a variety of combinatorial optimization problems. Simulation results show that the CoAHNN is better than or competitive with other HNN based algorithms, metaheuristic algorithms and state-of-the-art algorithms. [Copyright &y& Elsevier]

Abstract: This paper compares the effectiveness of five state-of-the-art multiobjective evolutionary algorithms (MOEAs) together with a steady state evolutionary algorithm on the mean–variance cardinality constrained portfolio optimization problem (MVCCPO). The main computational challenges of the model are due to the presence of a nonlinear objective function and the discrete constraints. The MOEAs considered are the Niched Pareto genetic algorithm 2 (NPGA2), non-dominated sorting genetic algorithm II (NSGA-II), Pareto envelope-based selection algorithm (PESA), strength Pareto evolutionary algorithm 2 (SPEA2), and e-multiobjective evolutionary algorithm (e-MOEA). The computational comparison was performed using formal metrics proposed by the evolutionary multiobjective optimization community on publicly available data sets which contain up to 2196 assets. [Copyright &y& Elsevier]

Abstract: Overcurrent relays (OCR) are the major protection devices in a distribution system. To reduce the power outages, mal-operation of the backup relays should be avoided, and therefore, OCR time coordination in power distribution network is a major concern of protection engineer. The OCR time coordination in ring fed distribution networks is a highly constrained optimization problem. The purpose is to find an optimum relay setting to minimize the time of operation of relays and at the same time, to avoid the mal-operation of relays. This paper presents continuous genetic algorithm (CGA) technique for optimum coordination of OCR in a ring fed distribution system. Constraints are incorporated in the fitness function making use of the penalty method. The CGA is inherently faster than binary genetic algorithm (GA) because the chromosomes do not have to be decoded. Also the CGA gives an advantage of requiring less storage than binary GA. [Copyright &y& Elsevier]

Abstract: A directed searching optimization algorithm (DSO) is proposed to solve constrained optimization problems in this paper. The proposed algorithm includes two important operations — position updating and genetic mutation. Position updating enables the non-best solution vectors to mimic the best one, which is beneficial to the convergence of the DSO; genetic mutation can increase the diversity of individuals, which is beneficial to preventing the premature convergence of the DSO. In addition, we adopt the penalty function method to balance objective and constraint violations. We can obtain satisfactory solutions for constrained optimization problems by combining the DSO and the penalty function method. Experimental results indicate that the proposed algorithm can be an efficient alternative on solving constrained optimization problems. [Copyright &y& Elsevier]

Abstract: This paper addresses a new uncertainty set – interval random uncertainty set for worst-case value-at-risk and robust portfolio optimization. The form of interval random uncertainty set makes it suitable for capturing the downside and upside deviations of real-world data. These deviation measures capture distributional asymmetry and lead to better optimization results. We also apply our interval random chance-constrained programming to robust worst-case value-at-risk optimization under interval random uncertainty sets in the elements of mean vector and covariance matrix. Numerical experiments with real market data indicate that our approach results in better portfolio performance. [Copyright &y& Elsevier]

Abstract: The dynamic economic dispatch (DED) is a complicated nonlinear dynamic constrained problem which occupies an important role in the economic operation of power system. An adaptive hybrid differential evolution algorithm (AHDE) is proposed in this paper to solve DED problem. In the proposed algorithm, an adaptive dynamic parameter control mechanism is adopted to obtain parameter settings in differential evolution algorithm (DE). Moreover, a local random search (LRS) operator is integrated with DE to avoid premature convergence. In view of the difficulties of handling the complicated constraints of DED problem, a new heuristic constraints handling method which does not require penalty factor settings is presented. The feasibility and effectiveness of the proposed method is demonstrated for an application example. Compared with other algorithms, AHDE can find the global optimum dispatch result with a shorter computational time along with higher effectiveness and robustness. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a parallelized Dual Projected Pseudo Quasi-Newton (parallelized DPPQN) based Expert System method to solve a kind of distributed constrained optimization problem. The proposed parallelized DPPQN based Expert System method differs from the conventional Lagrange method by treating the inequality constraints as the domain of the original variable in the dual function and uses projection theory to process the inequality constraints. The proposed algorithm was implemented in a n +1 processors network. We also demonstrated the efficiency in solving a typical constrained weighted least squares problem in power system. The parallelized DPPQN based Expert System method associated with a projected Jacobi method can be applied to general large scale nonlinear network optimization problems in large distributed interconnected systems. [Copyright &y& Elsevier]

In this paper, we present a parallel dual-type (PDT) algorithm for solving a strictly convex quadratic programming problem with equality and box constraints. The PDT algorithm is suitable for distributed implementation and can be used as a basic optimization module for handling optimization problems of large distributed systems. Besides, combining the proposed algorithm with a successive quadratic programming (SQP) method, we can solve constrained nonlinear programming problems such as power-system state estimation with power-flow balance constraints on no generation and no-load buses. We have demonstrated the computational efficiency of our method, by comparing with the benchmark commercial NCONF and QPROG routines and the state-of-the-art parallel algorithm through the implementation in the sequential version of Sparc workstation and the parallel version of PC network in solving constrained state estimation problems within IEEE 30-bus and IEEE 118-bus systems. [Copyright &y& Elsevier]

Abstract: Constrained optimization problems are very important in that they frequently appear in the real world. A constrained optimization problem consists of the optimization of a function subject to constraints, in which both the function and constraints may be nonlinear. Constraint handling is one of the major concerns when solving constrained optimization problems by hybrid Nelder–Mead simplex search method and particle swarm optimization, denoted as NM–PSO. This paper proposes embedding constraint handling methods, which include the gradient repair method and constraint fitness priority-based ranking method, in NM–PSO as a special operator to deal with satisfying constraints. Experiments using three benchmark function and three engineering design problems are presented and compared with the best known solutions reported in the literature. The comparison results with other evolutionary optimization methods demonstrate that NM–PSO with the embedded constraint operator proves to be extremely effective and efficient at locating optimal solutions. [Copyright &y& Elsevier]