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This paper aims to develop a new axiomatic design-based mathematical programming method for heterogeneous multi-criteria group decision making (HMCGDM) problems with linguistic fuzzy truth degrees (LFTDs). The main contributions of this paper are summarized in five aspects: (1) The information content definitions for six types of fuzzy numbers are initially provided according to axiomatic design . (2) Considering the authority of experts on different criteria and group consensus, a bi-objective programming model is constructed to derive experts’ weights by maximizing individual deviation and minimizing group discordance. (3) Each alternative is assessed on the basis of its information content to a fuzzy positive ideal solution. Information content is firstly used to define the linguistic fuzzy consistency and inconsistency indices. (4) A bi-objective linguistic fuzzy mathematic programming model is built to determine the criteria weights, which considers consistency and inconsistency indices simultaneously. This model can be dexterously transformed into a crisp linear programming model for resolution by the linguistic scale function. (5) The group information content of each alternative to fuzzy positive ideal solution is calculated to determine the ranking order of alternatives. Finally, an example of blockchain service provider selection is given to validate the proposed method.

In this paper, we propose a new fuzzy best-worst method (BWM) based on triangular fuzzy numbers for multi-criteria decision-making (MCDM). Aimed at the Best-to-Others vector and the Others-to-Worst vector in the form of triangular fuzzy numbers, this paper regards consistency equations as fuzzy equations. The derivation of optimal fuzzy weights of criteria is formulated as a fuzzy decision-making problem, where a mathematical programming model is constructed to derive optimal fuzzy weights of criteria to build a normalized triangular fuzzy weight vector. Then, we propose four linear programming models based on the obtained mathematical programming model for the optimistic decision maker, the pessimistic decision maker and the neutral decision maker, respectively. Through a proper selection of the values of tolerance parameters, each of the linear programming models certainly has a unique global optimal solution. Moreover, this paper proposes the concept of fuzzy consistency index and the concept of fuzzy consistency ratio. Several application examples are used to validate the proposed fuzzy BWM. The proposed fuzzy BWM provides us with a very useful way for MCDM in fuzzy environments.

The paper introduces a novel many-objective evolutionary method, with a diversity-based selection operator and aims to fill the “gaps” in the Pareto Front approximation and to increase its spread. It shows, that guiding the evolution process towards the least explored parts of a space increases overall diversity, but can also lead to increased convergence. A set of experiments is carried out on a many-objective Multi-Skill Resource-Constrained Project Scheduling Problem and a bi-objective Travelling Thief Problem. Both of those problems comprise two interwoven subproblems. Separate optimal solutions to the subproblems do not guarantee the optimal solution to the entire problem. Moreover, it shows that the existing diversity mechanism does not work well in combinatorial spaces, where the domain of each objective has a different size. The results indicate that a novel selection operator circumvents this issue. A set of Quality Measures is used to describe the desirable features of Pareto Front approximation: convergence, uniformity, and spread. The experiments are followed by a set of visualizations. Along with a set of Quality Measures, they give an insight into the characteristics of the method. The paper is concluded by a thorough theoretical analysis and possible directions for future work.

In this paper, we develop a novel multiple attribute decision making (MADM) method using the improved intuitionistic fuzzy weighted geometric (IIFWG) operator of intuitionistic fuzzy values (IFVs) proposed in this paper. First, we develop the IIFWG operator of IFVs to conquer the weak points of the existing operators of IFVs, where they have the drawbacks that their aggregated values are indeterminate in some situations. Based on the proposed IIFWG operator of IFVs, we present a MADM method to overcome the weak points of the existing MADM methods, which have the shortcomings that they obtain unreasonable ranking orders (ROs) of alternatives or they cannot discriminate the ROs of alternatives in some circumstances.

The maintenance of many subpopulations is an important technique employed in evolutionary methods. However, the use of a multi-population approach has its drawbacks. Among all, it requires spending high amounts of available resources. Therefore, the methods that dynamically manage the number of subpopulations gain an increasing interest due to their capability of adjusting the subpopulation number to their current state. They are shown to be capable of reaching excellent results. In this paper, we identify the Long-Way-To-Stuck effect and show it on the base of the practical, NP-complete problem. Such a phenomenon occurs when a randomly initialized population of an evolutionary method must be processed through many iterations before it is incapable of improving the best-found solution. If so, then a large amount of computational resources must be spent on subpopulation initialization, which may turn multi-population methods ineffective. Therefore, in this paper, we propose the Linkage Learning-Driven Subpopulation Initialization (LLDSI) that limits the costs of subpopulation initialization and significantly improves the effectiveness methods dynamically managing the subpopulation number.

A multi-objective evolutionary algorithm based on decomposition (MOEA/D) is a classic decomposition-based multi-objective optimization algorithm. In the standard MOEA/D algorithm, the update process of individuals is a forward search process without using the information of previous individuals. However, there is a lot of useful information in the previous iteration. Information Feedback Models (IFM) is a new strategy which can incorporate the information from previous iteration into the updating process. Therefore, this paper proposes a MOEA/D algorithm based on information feedback model, called MOEA/D-IFM. According to the different information feedback models, this paper proposes six variants of MOEA/D, and these algorithms can be divided into two categories according to the way of selecting individuals whether it is random or fixed. At the same time, a new selection strategy has been introduced to further improve the performance of MOEA/D-IFM. The experiments were carried out in four aspects. MOEA/D-IFM were compared with other state-of-the-art multi-objective evolutionary algorithms using CEC 2018 problems in two aspects. The best one of the six improved algorithms was chosen to test on large-scale many-objective problems. In addition, we also use MOEA/D-IFM to solve multi-objective backpack problems.

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. Population-based evolutionary algorithms have great potential to handle multiobjective optimisation problems. However, the performance of these algorithms depends largely on problem characteristics. There is a need to improve these algorithms for wide applicability. References, often specified by the decision maker’s preference in different forms, are very effective to boost the performance of algorithms. This paper proposes a novel framework for effective use of references to strengthen algorithms. This framework considers references as search targets which can be adjusted based on the information collected during the search. The proposed framework is combined with new strategies, such as reference adaptation and adaptive local mating, to solve different types of problems. The proposed algorithm is compared with state-of-the-arts on a wide range of problems with diverse characteristics. The comparison and extensive sensitivity analysis demonstrate that the proposed algorithm is competitive and robust across different types of problems studied in this paper.

Location is of vital importance in recommender systems . This paper proposes a novel multi-objective framework for location-based and preference-aware recommendation. Under this framework, location-based recommendation is modeled as a multiobjective optimization problem and two contradictory objective functions are taken into consideration. One objective function aims to depict the performance of recommendation algorithm to recommend similar items. Another objective function reflects the ability of recommendation algorithm to recommend diverse items. It is a challenge to optimize these two contradictory objective functions simultaneously. In this paper, a novel multi-objective evolutionary algorithm is proposed to solve this modeled multiobjective optimization problem. The proposed algorithm can return a series of high-quality recommendation candidate solutions in one run and every solution is a trade-off between these two objective functions. The proposed algorithm is applied on two real recommendation scenarios: movie recommendation and music recommendation. Experimental results show that the proposed algorithm can produce recommendation solutions which are much better than those produced by existing algorithms in location-based recommendation and the proposed algorithm also has great performance in alleviating data sparsity and cold-start problems.

In this paper, a novel method is proposed to solve the Regression-based Binary Recommendation problem (RBR). The RBR is a univariate minimization problem, which has been solved recently using the Trichotomy approach with a logarithmic time complexity. The Trichotomy can obtain the global optimal minimum of univariate quasi-convex function. In this paper, it has been asserted that the objective function of the RBR problem is not necessarily quasi-convex; therefore, the Trichotomy method cannot always find its optimal solution that can be ultimately achieved by using the full search. Nonetheless, the difficulty of the full search method is that for each possible value of the variable of the problem, the objective function of the problem must be computed which involves the user-item tables to be reviewed entirely for each possible value of the variable. Since these tables are usually large, the runtime of the full search method is very high. In this paper, to unravel this difficulty, we made use of a recursive method to compute the objective function. Our proposed algorithm requires only one review of the user-item tables. Hence, the runtime of our proposed method is far less than the two other methods.

Optimality of the premise, IF part is critical to a zero-order evolving intelligent system (EIS) because this part determines the validity of the learning results and overall system performance. Nonetheless, a systematic analysis of optimality has not been done yet in the state-of-the-art works. In this paper, we use the recently introduced self-organising neuro-fuzzy inference system (SONFIS) as an example of typical zero-order EISs and analyse the local optimality of its solutions. The optimality problem is firstly formulated in a mathematical form, and detailed optimality analysis is conducted. The conclusion is that SONFIS does not generate a locally optimal solution in its original form. Then, an optimisation method is proposed for SONFIS, which helps the system to attain local optimality in a few iterations using historical data. Numerical examples presented in this paper demonstrate the validity of the optimality analysis and the effectiveness of the proposed optimisation method. In addition, it is further verified numerically that the proposed concept and general principles can be applied to other types of zero-order EISs with similar operating mechanisms.

The existing literature on sustainable development problems mainly focuses on multicriteria decision analyses, and ignores the impact of uncertain information on optimal labor allocation decisions. It is necessary for sustainable development to implement suitable policies under uncertainty that integrate several competing aspects including economic, environmental, energy and social criteria. Based on type-2 fuzzy theory, this paper develops a distributionally robust optimization method for sustainable development problems. In our new model, the uncertain per capita gross domestic product (GDP), per capita electricity consumption and per capita greenhouse gas (GHG) emissions are characterized by parametric interval-valued (PIV) possibility distributions and their associated uncertainty distribution sets. Under two assumptions on the underlining decision-making environment, the robust counterpart of the original distributionally robust fuzzy sustainable development model is formally established. To solve the proposed robust sustainable development model, this paper discusses the computational issue concerning the infinitely many integral objective functions and credibilistic constraints, and turns the robust counterpart model into its computationally tractable equivalent deterministic submodels. Taking advantage of the structural characteristics of the equivalent submodels, a domain decomposition method is designed to find the robust optimal solution that can protect against distribution uncertainty. Finally, this paper applies the proposed optimization method for the key economic sectors of the United Arab Emirates (UAE) to provide quantitative justification in planning future labor and resource allocation.

In this paper, we present a multi-objective vehicle routing problem with flexible time windows (MOVRPFlexTW). In this problem, a fleet of vehicles can service a set of customers earlier and later than the required time with a given tolerance. This flexibility enables a logistics company to save distribution costs at the expense of customer satisfaction. This paper uses a direct interpretation of the vehicle routing problem with flexible time windows (VRPFlexTW) as a multi-objective problem, where the total distribution costs (including travel costs and fixed vehicle costs) are minimized and the overall customer satisfaction is maximized. We propose a solution strategy based on ant colony optimization and three mutation operators, which incorporates the concept of Pareto optimality for multi-objective optimization. The performance of the proposed approach was evaluated using the well-known benchmark Solomon’s problems. Our experimental results show that the suggested approach is effective, because it provides solutions that are comparative to the best known results in the literatures. Finally, we not only highlight the advantages of MOVRPFlexTW when compared with the single objective VRPFlexTW, but also illustrate its applicability and validation by analyzing a real case.

For a road networked system with stochastic travel demand, a two-stage model is proposed for period-dependent area traffic signal control. In this paper, a period-dependent mathematical program with equilibrium constraints (PMPEC) is presented to minimize total travel delay over successive time periods. For stochastic travel demand over multiple time periods, a period-dependent user equilibrium traffic assignment can be formulated as a variational inequality. Due to non-linearity of equilibrium constraints, a two-stage model is presented in this paper. In order to understand feasibility of the proposed model, numerical experiments using a real-data road network are conducted. The results indicate that the proposed model attains a promising system performance and exhibit computational advantage over existing alternatives.

Metaheuristic algorithms usually aim to solve nonconvex optimization problems in black-box and high-dimensional scenarios. Characterizing and understanding the properties of nonconvex problems is therefore important for effectively analyzing metaheuristic algorithms and their development, improvement and selection for problem solving. This paper establishes a novel analysis framework called nonconvex ratio analysis, which can characterize nonconvex continuous functions by measuring the degree of nonconvexity of a problem. This analysis uses two quantitative measures: the nonconvex ratio for global characterization and the local nonconvex ratio for detailed characterization. Midpoint convexity and Monte Carlo integral are important methods for constructing the measures. Furthermore, as a practical feature, we suggest a rapid characterization measure that uses the local nonconvex ratio and can characterize certain black-box high-dimensional functions using a much smaller sample. Throughout this paper, the effectiveness of the proposed measures is confirmed by numerical experiments using the COCO function set.

This paper presents a novel Differential Evolution algorithm for protein folding optimization that is applied to a three-dimensional AB off-lattice model. The proposed algorithm includes two new mechanisms. A local search is used to improve convergence speed and to reduce the runtime complexity of the energy calculation. For this purpose, a local movement is introduced within the local search. The designed evolutionary algorithm has fast convergence speed and, therefore, when it is trapped into the local optimum or a relatively good solution is located, it is hard to locate a better similar solution. The similar solution is different from the good solution in only a few components. A component reinitialization method is designed to mitigate this problem. Both the new mechanisms and the proposed algorithm were analyzed on well-known amino acid sequences that are used frequently in the literature. Experimental results show that the employed new mechanisms improve the efficiency of our algorithm and that the proposed algorithm is superior to other state-of-the-art algorithms. It obtained a hit ratio of 100% for sequences up to 18 monomers, within a budget of $10^{11}$ solution evaluations. New best-known solutions were obtained for most of the sequences. The existence of the symmetric best-known solutions is also demonstrated in the paper., Comment: 22 pages, 8 figures, 10 tables, journal

Particle swarm optimizations (PSOs) are drawing extensive attention from both research and engineering fields due to their simplicity and powerful global search ability. However, there are two issues needing to be improved: one is that the classical PSO converges slowly; the other is that classical PSO tends to result in premature convergence, especially for multi-modal problems. This paper attempts to address these two issues. Firstly, to improve the convergent efficiency, this paper proposes an asymptotic predicting model of the globally-optimal solution, which is used to predict the global optimum based on extracting the features reflecting the evolutionary trend. The predicted global optimum is then taken as the third exemplar, in a way similar to the individual historical best solution and the swarm historical best solution in guiding the evolutionary process of other particles. To reduce the probability that the population is trapped into a local optimum due to the premature phenomenon, this paper proposes an adaptive mutation strategy, which is used to help the trapped particles to escape away from the local optimum by using the extended non-uniform mutation operator. Finally, we combine the two entities to develop a globally-optimal prediction-based adaptive mutation particle swarm optimization (GPAM-PSO). In numerical experimental parts, we compare the proposed GPAM-PSO with 11 existing PSO variants by using 22 benchmark problems of 30-dimensions and 100-dimensions, respectively. Numerical experiments demonstrate that the proposed GPAM-PSO could improve the accuracy and efficiency remarkably, which means that the combination of the globally-optimal prediction-based search and the adaptive mutation strategy could accelerate the convergence and reduce premature phenomenon effectively. Generally speaking, GPAM-PSO performs most efficiently and robustly. Moreover, the performance on an engineering problem demonstrates the practical application of the proposed GPAM-PSO algorithm.

Differential evolution (DE) has been recognized as one of the most effective algorithms for solving numerical optimization problems. In this paper, we propose a tri-population differential evolution (TPDE) to further enhance the search capability of DE. More specifically, the parent population is partitioned into three sub-populations with different emphasises at each iteration based on a newly proposed zonal-constraint stepped division (ZSD) mechanism, which determines the size of each sub-population according to not only individual’s fitness value but also the evolutionary process. To make the best of information provided by elite individuals and play their leading role on other individuals, three elite-guided mutation strategies are presented for each sub-population. Moreover, three sets of adaptive control parameters including the scale factor F and crossover rate CR are configured for three mutations according to Gaussian distribution model, Cauchy distribution model and a triangular wave function respectively. The design of mutation strategies and control parameters for each sub-population is based on the principle of balancing the global exploration and local exploitation capabilities. To evaluate the performance of TPDE, comparative experiments are conducted based on 59 benchmark functions from CEC2014 and CEC2017 test suites. The results indicate that the proposed TPDE is significantly better than, or at least comparable to the recent nine state-of-the-art DE variants.

Hybridization in context to Evolutionary Computation (EC) strives to combine operators, components, and the best merits of different EC paradigms, to form a new evolutionary algorithm that enjoys a statistically superior performance, compared to its ancestors, over a wide range of application-specific optimization problems. In this paper, we propose a simple yet powerful amalgam composed of a modified Cultural Algorithm (CA) that is supported with an Enhanced Levy Flight Search (ELFS) to guide the search and further promote the harmony between the explorative and exploitative capacities of the conventional techniques. The novel amalgam, denoted by q-aCA + m IS, utilizes a balanced search scheme where it employs an adapted Influence Function (IF) with a novel quality function that establishes a harmony between the Knowledge Sources (KSs) in the Belief Space (BS), and between the BS and other components in the hybrid to produce the most suitable knowledge needed for a certain search mode. The CA framework is reinforced with an updated Selection Function (SF) that employs a successful selection strategy that uses the extended situational knowledge for the future selection of individuals. The proposed algorithm is tested using more than 50 benchmark functions that are taken from the IEEE CEC’06, and the IEEE CEC’19 competitions on constrained real-parameter optimization. Moreover, three well-known engineering design problems are used to test the validity of the algorithm for the solution of complex real-life problems. The comparative study indicates that the q-aCA + mIS algorithm was able to obtain a statistically superior performance and scalability behavior over most of the considered functions in comparison with other state-of-the-art algorithms.

The recent proliferation of population-based meta-heuristics designed for solving optimization problems and their successes confirm that more promising techniques inspired by physical phenomena or biological systems are desired. Therefore, in this paper, a novel hybridization approach is proposed to improve the performance of optimization algorithms. The approach replaces a small number of worst solutions obtained by a meta-heuristic with predicted candidates without altering its search operators. Specifically, a target fitness value of the predicted candidate is determined based on the fitness of the population and a search strategy. Then, a calibration problem is solved to infer its decision variables. In this study, the proposed hybridization technique is applied to ten state-of-the-art population-based algorithms. The meta-heuristics and hybrids are evaluated on 82 functions, four engineering problems, and a new challenging problem of estimating a constant in Markov’s inequality using minimal polynomials of different degrees. The experimental results reveal the superiority of the hybrids over their counterparts and confirm the suitability of the proposed approach for improving the efficiency of meta-heuristics.

This paper is devoted to the construction and analysis of a novel hybrid optimization model of the l 0 minimization and the l 1 minimization with a given support estimate. With the help of the Moreau envelop of the l 1 norm, we provide reasonable explanation for the claim that the capped- l 1 penalty is one of the continuous relaxation to the l 0 -norm penalty and thus develop the scale iteratively reweighed l 1 -minimization (SIRL1) aiming to achieve fast reconstruction and a reduced requirement on the number of measurements compared to the l 1 minimization approach. To illustrate the theoretical results, some numerical experiments are presented to demonstrate the effectiveness and flexibility of the proposed SIRL1 algorithm.

Teaching-learning-based optimization (TLBO) is a population-based metaheuristic algorithm which simulates the teaching and learning mechanisms in a classroom. The TLBO algorithm has emerged as one of the most efficient and attractive optimization techniques. Even though the TLBO algorithm has an acceptable exploration capability and fast convergence speed, there may be a possibility to converge into a local optimum during solving complex optimization problems and there is a need to keep a balance between exploration and exploitation capabilities. Hence, a Balanced Teaching-Learning-Based Optimization (BTLBO) algorithm is proposed in this paper. The proposed BTLBO algorithm is a modification of the TLBO algorithm and it consists of four phases: (1) Teacher Phase in which a weighted mean is used instead of a mean value for keeping the diversity, (2) Learner Phase, which is same as the learner phase of basic TLBO algorithm, (3) Tutoring Phase, which is a powerful local search for exploiting the regions around the best ever found solution, and (4) Restarting Phase, which improves exploration capability by replacing inactive learners with new randomly initialized learners. An acceptable balance between the exploration and exploitation capabilities is achieved by the proposed BTLBO algorithm. To evaluate the performance of BTLBO algorithm, several experimental studies are conducted on standard benchmark suits and the results are compared with several TLBO variants and state-of-the-art population-based optimization algorithms. The results are in excellent agreement and confirm the efficiency of BTLBO algorithm with accelerated exploitation and exploration capabilities with an appropriate balance between such criteria for solving complex optimization problems.

The capacities and the Choquet integral are powerful tools to represent decision problems with dependencies and aggregate correlated decision criteria. Random generation of suitable capacities is a vital and challenging task in this decision model because of an exponential number of the involved parameters as well as the associated monotonicity restrictions. In this paper we present various approaches to representing decision makers’ preferences on aggregation through linear constraints , random generation of capacities from the selected polytope , testing the uniformity of the resulting distribution, and constructing the dominance relations between the alternatives, which are subsequently used to get the most credible ranking of the alternatives.

Due to the widespread interest in dynamic multiobjective optimization in real-world applications, more and more approaches exploiting machine learning are deployed to tackle this type of problems. Unfortunately, recent works do not make full use of the data obtained during the optimization process, which could be benefit for model training thereby mining the dynamic characteristics of the underlying problem. To address this issue, this paper proposes a dynamic multiobjective evolutionary algorithm driven by inverse reinforcement learning to solve the dynamic multiobjective optimization problems. IRL is widely used to recover the unknown reward function, making it possible to perform at an expert level. The notable features of the proposed algorithm mainly consist of data-driven evolutionary technique, which uses inverse reinforcement learning as a surrogate-assisted model for model training. This design makes full use of the surrogate management strategy based on inverse reinforcement learning to optimize the reward function within a reinforcement learning framework. At the same time, the algorithm can generate a promising policy based on limited training data during the optimization process to achieve better algorithm evolution and guide the search. The experimental results on the benchmark problems validate that the proposed algorithm is effective in dealing with dynamic multiobjective optimization.

Penalty function is well-known for constrained evolutionary optimization. An open question in the penalty function is how to tune the penalty coefficient. This paper proposes an adaptive fuzzy penalty method to address this issue, where the coefficient is adjusted at both the individual level and the population level. At the individual level, each individual chooses a penalty coefficient from a predefined domain according to some fuzzy rules. At the population level, the domain of the crisp output is adjusted adaptively by using population information. To enhance the population diversity, an effective mutation scheme is developed. Due to its numerous merits, differential evolution is used to design a search algorithm. By the above processes, a constrained optimization evolutionary algorithm called AFPDE is proposed. Since the objective function value and the degree of constraint violation are normalized, AFPDE is less problem-dependent than the seminal work of the fuzzy penalty method. AFPDE introduces a lower penalty value in the early stage of AFPDE while a higher one in the later stage. Thus, it can escape local optima in the infeasible region. Experiments on three well-known benchmark test sets and two mechanical design problems validate that AFPDE is competitive.

Multicriteria group decision-making (MCGDM), with the strong uncertainty and randomness, has always been a hotspot in the world. The chief purpose of the paper is to address the problem with Atanassov’s interval-valued intuitionistic fuzzy sets (AIVIFSs), Z-numbers, and trapezium clouds. First, some related concepts and former operators of AIVIFSs, Z-numbers, and trapezium clouds are reviewed, meanwhile, AIVIFSs and Z-numbers are synthesized to come up with a novel linguistic expression. Then, Z-trapezium-trapezium cloud (ZTTC) is proposed to quantify the linguistic evaluation information to avoid excessive computation caused by traditional methods. Later, a new approach of calculating the objective weight vector is presented based on entropy weight method (EWM). To take the huge advantages of technique for order preference by similarity to ideal solution (TOPSIS) method in ranking, 2-norm in mathematical theory is applied to derive a way of calculating the distance between different ZTTCs. Finally, an example about the grade assessment of coronavirus Disease 2019 (COVID-19) is given. For further confirming the validity and feasibility, sensitivity analysis and comparison with other methods are conducted.

In this paper, we consider two parametric dominance-based rough set approaches (DRSA) proposed in the literature: variable precision DRSA (VP-DRSA) and variable consistency DRSA (VC-DRSA). They were introduced to cope with classification data encountered in practice for which the original definition of lower approximations is too restrictive. Both these extensions allow an augmentation of lower approximations, which is controlled parametrically in different ways. We give statistical interpretations for VP-DRSA and VC-DRSA from the perspective of empirical risk minimization typical for machine learning . Given families of classifiers and loss functions, we consider classification problems which relate directly VP-DRSA and VC-DRSA to ordinal classification. Then, we characterize the parametrically augmented lower approximations of both approaches as optimal solutions of associated empirical risk minimization problems. As a consequence, a connection between parametric DRSA and statistical learning is established. Moreover, new characterizations of the augmented lower approximations allow us to exhibit differences and similarities between VP-DRSA and VC-DRSA.

In this paper, the time-varying output formation-containment (TV-OFC) problem of homogeneous and heterogeneous descriptor fractional-order multi-agent systems (DFO-MASs) is investigated. The results obtained in previous works for nonsingular integer-order multi-agent systems can be regarded as particular cases of our results. This control aims at making leaders keep time-varying shape to move and followers move inside the convex hull spanned by leaders simultaneously. First, both the output feedback control strategy and observer-based control algorithm are designed to address the TV-OFC problem of heterogeneous DFO-MASs, where the virtual leader provides the reference trajectory for leaders to achieve the formation tracking. Then, sufficient conditions with less computation complexity are presented and the methods to determine gain matrices of the schemes are proposed for homogeneous and heterogeneous DFO-MASs, so as to achieve the TV-OFC. Finally, numerical examples are given to demonstrate the effectiveness of theoretical conclusions.

Interval reciprocal preference relations (IRPRs) have been extensively applied to real-life decision-making problems. This paper aims at introducing two new decision-making methods with IRPRs. To overcome drawbacks of several extant order relations of intervals, a new admissible order relation of intervals is proposed. An algorithm is then introduced to rank a series of intervals. We define a new consistency index and the satisfactory consistency of IRPRs. For improving the consistency level of IRPRs, a linear programming model is built. Subsequently, a new individual decision-making (IDM) method with an IRPR is introduced. For group decision making, a group consensus index is proposed. To improve the group consensus degree, an interactive convergent iterative algorithm is designed. Decision makers’ weights are determined by combining the logarithmic Manhattan distance between two IRPRs with the consistency indices of IRPRs. Accordingly, a novel consistent and consensus-based group decision-making (GDM) method with IRPRs is presented. Eventually, a decision support system is developed based on the proposed IDM method and GDM method. Illustrative examples and simulation experiments are provided to illustrate the superiority of the proposed IDM method and GDM method.

To solve constrained optimization problems (COPs), it is crucial to guide the infeasible solution to a feasible region. Gradient-based repair (GR) is a successful repair strategy, where the forward difference is often used to estimate the gradient. However, GR has major deficiencies. First, it is difficult to deal with individuals falling into the local optima. Second, large amounts of fitness evaluations are required to estimate the gradient. In this paper, we proposed a new repair strategy, random direction repair (RDR). RDR generates a set of random directions, and calculates the repair direction and the repair step size of infeasible individual to reduce its constraint violation. Since the introduction of randomness, RDR could deal with individuals falling into the local optima. Furthermore, RDR only requires a few number of fitness evaluation. To demonstrate the performance of RDR, RDR was embedded into two state-of-the-art evolutionary continuous constrained optimization algorithms, tested on the Congress on Evolutionary Computation 2017 constrained real-parameter optimization benchmark. Experimental results demonstrated that RDR combined with evolutionary algorithms are highly competitive.

Recently the max-product fuzzy relation inequalities were applied to describe the wireless communication station system. However, when an arbitrary line fault appears between the emission basic station and the signal testing point, the classical max-product system is no longer effective. Considering an arbitrary line fault in the wireless communication station system, we introduce and investigate the so-called arbitrary-term-absent (ATA) max-product fuzzy relation inequalities in this paper. In order to reduce the damage caused by the electromagnetic radiation from the basic stations, a minimal solution is usually desired. However, the structure of solution set to the ATA max-product fuzzy relation inequalities shows that the minimal solutions are not unique in most cases. Hence, we further introduce the lexicographic order and define the relevant concept of lexicographic minimal solution. A lexicographic minimal solution is indeed an optimal scheduling, minimizing the electromagnetic radiations in a lexicographic order. An efficient algorithm with polynomial complexity is developed for obtaining the unique lexicographic minimal solution of the ATA max-product system. At last, our proposed resolution algorithm is compared to the existing one and illustrated by a numerical example.

Convergence is always a major concern for many-objective optimization problems. Over the past few decades, various methods have been designed for measuring the convergence. However, according to our mathematical and empirical analyses, most of these methods are more focused on the convergence, and may neglect the exploration of boundary solutions, resulting in the incomplete Pareto fronts and the poor extent of spread achieved among the obtained non-dominated solutions. Regarding this issue, this paper proposes a Many-Objective Evolutionary Algorithm with Adaptive Reference Vector (MaOEA-ARV). In MaOEA-ARV, an adaptive reference vector strategy is designed to dynamically adjust the reference vectors according to the current distribution of candidate solutions for ensuring the spread and convergence simultaneously. Additionally, a hierarchical clustering strategy is employed to adaptively partition candidate solutions into multiple clusters for the diversity of candidate solutions. Experimental results on DTLZ, BT, ZDT and WFG test suites with up to 12 objectives demonstrate the effectiveness of MaOEA-ARV.

Networked evolutionary game theory is an important tool to study the emergence and maintenance of cooperation in natural, social, and economical systems. In this paper, we investigate the dynamics and convergence of a generalized networked evolutionary game, i.e., delayed hyper-networked evolutionary game (HNEG), which considers the multi-players in fundamental network game and time delay in strategies simultaneously. Based on the tool of semi-tensor product (STP) of matrices, the definition of delayed potential HNEG and representation of potential function are given. Moreover, we conclude the steps to analyze the dynamics and convergence of delayed potential HNEGs. Considering the efficiency in updating process, we define a new strategy updating rule based on the myopic best response adjustment rule (MBRAR), which is called delayed group-based sequential MBRAR. Furthermore, we prove that delayed potential HNEG converges to one of the pure Nash equilibrium trajectories under this rule. Finally, public good game is provided to illustrate the realistic application of our results.

Rumor propagation on complex networks is rapidly affecting people’s life. As we all know, the regulatory control of rumors by regulators has a specific impact on the spread of rumors. Limited regulatory resources may saturate the regulatory level. Therefore, in this paper, we have introduced a saturation treatment function to model this phenomenon and further establish an SIS rumor propagation model with consideration of some comprehensive influence on rumor diffusion. First of all, we prove the boundedness of solutions, and the basic reproduction number R 0 is obtained by the method of the next generation matrix . Secondly, by constructing Lyapunov function and applying the linearization method of differential equations, the stability conditions of the equilibrium points are derived. Further, we determine the condition for the backward bifurcation of the rumor propagation model. Moreover, in order to control the spread of rumors, we propose targeted immunization control, acquaintance immunization control and optimal control strategies based on complex networks. Finally, the sensitivity analysis of the basic reproduction number is carried out, and the correctness of the theoretical results is verified by numerical simulations. Our results may provide us with useful insights into the dynamics of online rumor propagation. For example, the basic reproduction number R 0 gives the threshold of rumor propagation, which provides control conditions for suppressing the spread of rumors. Stability analysis indicates the likelihood of local or global outbreaks for rumors. In addition, the comparison of the effect for control strategies gives a variety of options for the control method.

Evolutionary algorithms have been proven to be effective in solving multi-objective optimization problems. However, their performance deteriorates progressively in handling many-objective optimization problems due to the sensitivity upon the curvature of Pareto front, as well as the implicit evaluation on similarity in high dimensionality. This paper proposes an on-line Pareto front curvature estimator for an adaptive selection, in which the achievement scalarizing function is used to identify the pivotal solution to extrapolate the geometric information. Then an adaptive scalarizing function based fitness assessment, which guarantees the Pareto optimality, is presented. The diversity of the Pareto optimal solutions is also ensured by introducing a novel similarity metric. Finally, an extensive experimental analysis is presented to corroborate the analytical result by evaluating problems with various types of Pareto fronts. The experimental results substantiate the efficacy of the results with competitive performance.

With the development and the progress of science and technology, the spread of rumors presents new characteristics. The spreaders publish false and malicious rumors on public social networks media, and individuals visit these networks and share them with their friends through the friendship network, which provides a convenient hotbed for the indiscriminate spread of rumors. In this paper, an improved rumor spreading model is established to explore the new characteristics of rumor spreading process on the basis of considering the delay of interactive system. By studying the dynamic behavior of the delay spreading model, we calculate the threshold of rumor spreading extinction, and prove the local and global asymptotic behavior of the boundary equilibrium point and endemic equilibrium point of the model. On this basis, we further consider the control strategies such as deleting rumor posts, popular science education, immunotherapy, etc., and propose an optimal control problem to minimize the spread scale and control cost of rumors. The optimal condition of the optimal control problem is calculated by mathematical analysis, and the correctness of the theoretical results is verified by numerical simulations. Finally, we compare the influence of time delays, optimal control and the media network on rumor spreading.

This paper is mainly devoted to the distributed second-order multi-agent optimization problem with unbalanced and directed networks, where the gradient of the private objective functions might be unbounded. To deal with this problem, a new distributed algorithm is proposed based on the local neighbor information and the private objective functions. By a coordination transformation, the closed-loop system is divided into two simple first-order subsystems. Under the assumption of the strong connectivity of networks, it is proved that all agents can collaboratively converge to some optimal solution of the team objective function. At last, we give two numerical examples to show the effectiveness of our proposed algorithm.

In the crowdsourcing task allocation scheme, there is an emerging and realistic co-opetition phenomenon. To availably solve the crowdsourcing task allocation problem with co-opetition, this paper designs a two-stage co-opetition model by constructing novel three-way decision (TWD), including a competition-optimization model and a negotiation-cooperation model. Unlike the other studies, the two-stage co-opetition model with TWD can not only protect the profits of the task candidates, but also optimize the overall benefits. Specifically speaking, in the competition-optimization model, we construct an optimization model based on the data envelopment analysis (DEA) method in advance, which maximizes the personal benefit. By integrating information system and the loss function matrix, we consider the linkage of evaluation information and risk information and then improve the original TWD to make an initial allocation. In the negotiation-cooperation model, considering that the relationship among the candidates may influence the task performance, the fuzzy measure is introduced to describe a broader partnership. Meanwhile, we also design two different schemes to coordinate and optimize the best task allocations based on the initial allocation. In order to choose the best scheme, the selection strategy between schemes is further investigated under the guidance of the utility and the loss. Finally, we give an example of a medical supply chain crowdsourcing problem to illustrate and verify our proposed approach.

This paper presents the development and verification of a new multi-stage genetic programming (MSGP) technique, called MSGP-LASSO, which was applied for univariate streamflow forecasting in the Sedre River, an intermittent river in Turkey. The MSGP-LASSO is a practical and cost-neutral improvement over classic genetic programming (GP) that increases modelling accuracy, while decreasing its complexity by coupling the MSGP and multiple regression LASSO methods. The new model uses average mutual information to identify the optimum lags, and root mean-square technique to minimize forecasting error. Based on Nash-Sutcliffe efficiency and bias-corrected Akaike information criterion, MSGP-LASSO is superior to GP, multigene GP, MSGP, and hybrid MSGP-least-square models. It is explicit and promising for real-life applications.

In this paper, we propose an optimization-based group decision making (GDM) method using interval-valued intuitionistic fuzzy preference relations (IVIFPRs). First, the concept of consistency of intuitionistic fuzzy preference relations (IFPRs) is provided. Moreover, the consistency index for IFPRs is presented. Subsequently, by splitting an IVIFPR into two IFPRs, an additive consistency is proposed for IVIFPRs. Afterward, a consensus index is presented for GDM. When the consistency and the consensus do not achieve the requirement, we propose several models to reach the requirement. Furthermore, individual IVIFPRs are integrated into a collective IVIFPR. After that, a procedure is offered to obtain the interval-valued intuitionistic fuzzy (IVIF) priority weights of the alternatives. Moreover, a new GDM method with IVIFPRs is offered. Finally, some application examples are offered. The proposed GDM method can conquer the shortcomings of the existing GDM methods. It offers us a useful way for GDM in the IVIF context.

Mini-batch sub-sampling (MBSS) in neural network training is unavoidable due to growing data demands, memory-limited computational resources such as graphical processing units, and the dynamics of on-line learning. This study distinguishes between static MBSS and dynamic MBSS. In static MBSS, mini-batches are intermittently fixed during training, resulting in smooth but biased loss functions. During dynamic MBSS, mini-batches are resampled at every loss evaluation, resulting in sampling induced discontinuities by trading sampling bias for sampling variance. This renders classical minimization strategies ineffective in dynamic MBSS losses, as these may locate spurious sampling induced minima, while critical points may not exist. This paper re-evaluates the information used to define optima in stochastic loss functions of neural networks by defining the solution to a stochastic optimization problem as the stochastic non-negative associated gradient projection point (SNN-GPP). We demonstrate that SNN-GPPs offer a more robust description of full-batch optima than minimizers and critical points. An empirical investigation compares local minima to SNN-GPPs for the potential training of a simple neural network training problem with different activation functions. Since SNN-GPPs better approximate the location of true optima, we conclude that line searches locating SNN-GPPs can contribute significantly to automating neural network training.

Constrained multi-objective optimization problems (CMOPs) are difficult to handle because objectives and constraints need to be considered simultaneously, especially when the constraints are extremely complex. Some recent algorithms work well when dealing with CMOPs with a simple feasible region; however, the effectiveness of most algorithms degrades considerably for CMOPs with complex feasible regions. To address this issue, this paper proposes a multi-stage evolutionary algorithm, where constraints are added one after the other and handled in different stages of evolution. Specifically, in the early stages, the algorithm only considers a small number of constraints, which can make the population efficiently converge to the potential feasible region with good diversity. As the algorithm moves to the later stages, more constraints are considered to search the optimal solutions based on the solutions obtained in the previous stages. Furthermore, a strategy for sorting the constraint-handling priority according to the impact on the unconstrained Pareto front is proposed, which can accelerate the convergence of the algorithm. Experimental results on five benchmark suites and three real-world applications showed that the proposed algorithm outperforms several state-of-the-art constraint multi-objective evolutionary algorithms when dealing with CMOPs, especially for problems with complex constraints.

This work extends the randomized shortest paths (RSP) model by investigating the net flow RSP and adding capacity constraints on edge flows. The standard RSP is a model of movement, or spread, through a network interpolating between a random-walk and a shortest-path behavior (Kivimaki et al., 2014; Saerens et al., 2009; Yen et al., 2008). The framework assumes a unit flow injected into a source node and collected from a target node with flows minimizing the expected transportation cost, together with a relative entropy regularization term . In this context, the present work first develops the net flow RSP model considering that edge flows in opposite directions neutralize each other (as in electric networks), and proposes an algorithm for computing the expected routing costs between all pairs of nodes. This quantity is called the net flow RSP dissimilarity measure between nodes. Experimental comparisons on node clustering tasks indicate that the net flow RSP dissimilarity is competitive with other state-of-the-art dissimilarities. In the second part of the paper, it is shown how to introduce capacity constraints on edge flows, and a procedure is developed to solve this constrained problem by exploiting Lagrangian duality. These two extensions should improve significantly the scope of applications of the RSP framework.

In this paper, we study the vehicle routing problem (VRP) with multiple firms in depot with focus on the carbon cap-and-trade policy. By establishing the upper-level carbon trading revenue model from the government’s perspective and the lower-level model from the firm’s perspective, we describe the VRP based on the Stackelberg game framework. In addition, a traffic density objective is put forward. As a consequence, the lower-level model is a double objective optimization model including transportation cost and traffic density. Due to the influence of uncontrollable factors, the batches of distributed vehicles are uncertain and characterized as random fuzzy variables with uncertain credibility distribution. To address this situation, we propose a new distributionally robust equilibrium optimization (DREO) method, in which it describes the existence range of the real credibility distribution by constructing the uncertainty distribution set. For a given specific uncertainty distribution set, we derive its equivalent formulation for the proposed method. Moreover, given the single-period, we reduce the derived model to a single-layer multi-criteria optimization model by using the parameter-driven approach, so as to avoid solving the complicated original model. Besides, we analyze dynamic process of the multi-period Stackelberg game model. Finally, we apply a lexicographic optimization algorithm to solve the proposed model under the single-period, thereby verifying its effectiveness and also obtaining some promising results.

In this paper, a novel algorithm KTLBO is presented to achieve computationally expensive constrained optimization. In KTLBO, Kriging is adopted to develop dynamically updated surrogate models for costly objective and inequality constraints. A data managing method aiming at solving expensive constrained problems is developed to archive, classify and update expensive samples, where a penalty function is set to adaptively select elite individuals. Moreover, based on the Teaching-Learning-based Optimization (TLBO), a Kriging-assisted two-phase optimization framework is presented to alternately conduct local and global searches. In Kriging-assisted Teaching and Learning Phases, two different prescreening operators considering the probability of feasibility are respectively proposed to select the high-quality samples around the present best solution and the samples exhibiting better space-filling performance, as an attempt to balance exploitation of surrogates and exploration of unknown area. In brief, KTLBO retains the meta-heuristic search mechanism of TLBO while adopting Kriging to accelerate its search, thereby acting as a novel idea for surrogate-assisted constrained optimization. Lastly, KTLBO is compared with 6 well-known methods on 27 benchmark cases, and then its significant advantages in expensive constrained optimization are verified. Furthermore, KTLBO is adopted to design the structure of a Blended-Wing-Body underwater glider, and the satisfactory solution is yielded.

In the last decade, the decomposition-based multiobjective optimization evolutionary algorithm (MOEA/D) has displayed promising performance when dealing with multiobjective optimization problems (MOPs). However, for some complex MOPs, the conventional MOEA/D often leads to the loss of population diversity in the iterative process, and the convergence performance of the population is weakened in the mean time. In this paper, a novel MOEA/D, based on improved multiple adaptive dynamic selection strategies and elite archive strategy (MOEA/D-IMA), is proposed to improve the population diversity and convergence. First, a novel differential evolution (DE) operator is constructed, which constitutes an operator pool with other DE operators. According to the search information of the current population, an adaptive dynamic selection strategy is proposed, which is used by MOEA/D-IMA to select a suitable DE operator to replace the simulated binary crossover (SBX) operator. Second, a parameter adaptive dynamic selection strategy is proposed to enhance the robustness of MOEA/D-IMA by using the information of population evolution state. Third, an elite archive strategy is introduced to improve the convergence and diversity of the population where mutual dominance of individuals and their aggregation distance is employed. Finally, the proposed MOEA/D-IMA is compared with several state-of-the-art algorithms on three suits of 18 test problems. Experimental results indicate that the proposed MOEA/D-IMA can significantly improve the optimization performance when coping with MOPs.

The best consistency index (BCI) and the worst consistency index (WCI) were introduced into interval additive preference relations (IAPRs) to guarantee that any APR within an IAPR would have a satisfactory best or worst consistency. However, the methods for controlling the BCI and WCI consistencies were not clear, and consensus reaching problems based on the BCI and WCI, which are a key issue in group decision making using IAPRs, have not yet been addressed. Therefore, to address this particular omission, this paper suggests various optimization approaches for the modeling of both consistency and consensus. First, an APR that corresponds to the worst consistency is determined using the IAPR boundary elements, after which an optimization model is introduced to improve the BCI and WCI that minimizes the amount of change. It was found that if all individual IAPRs had acceptable WCIs, the group IAPR also had an acceptable WCI for the group decision making. An optimal consensus model is also proposed to deal with the consistency and consensus. These models were found to be able to effectively manage the worst consistency in the decision process. Some numerical examples and comparison analyses are given to validate the efficiency of the developed decision models.

The decomposition-based multi-objective evolutionary algorithm (MOEA/D) shows strong performance in solving complex multi-objective problems (MOPs), wherein evolutionary operators have great influence on the search ability. Appropriate operators can greatly improve the performance of MOEA/D. However, one omnipotent operator usually cannot handle all different MOPs very well. According to the characteristics of the problems, the operators that adapt to the problems are also different. This paper proposes an adaptive operator selection strategy called Leader Recommend Operator Selection (LROS). We construct an operator pool consisting of Simulated Binary Crossover (SBX) and three operators of Differential Evolution (DE). Meanwhile, we divide the entire evolutionary process into several stages, and each stage is divided into Part 1 and Part 2. In Part 1 of each stage, we use a subset of individuals to test the performance of each operator in the operator pool and choose the best performance. In Part 2, we adopt the best performing operator selected in Part 1 to generate offspring, meanwhile we verify the actual quality of these offspring to decide in the next stage whether to continue using this operator to generate offspring or to choose a more suitable operator. Experimental results demonstrate the effectiveness of LROS.

As a special model of three-way decision, three-way approximations in the fuzzy probability space can be interpreted, represented, and implemented as dividing the universe into three pair-wise disjoint regions, i.e., the positive, negative and boundary regions, which are transformed from the fuzzy membership grades with respect to the fuzzy concept. To consider the temporality and uncertainty of data simultaneously, this paper focuses on the integration of dynamics and fuzziness in the context of three-way approximations. We analyze and investigate three types of fuzzy conditional probability functions based on the fuzzy T-norm operators. Besides, we introduce the matrix-based fuzzy probability decision-theoretic models to dynamic three-way approximations based on the principle of least cost. Subsequently, to solve the time-consuming computational problem, we design the incremental algorithms by the updating strategies of matrices when the attributes evolve over time. Finally, a series of comparative experiments is reported to demonstrate and verify the performance of proposed models.

Hard C-means (HCM) is one of the most widely used partitive clustering methods and was extended to rough C-means (RCM) by referencing to the perspective of rough set theory to deal with the certain, possible, and uncertain belonging of object to clusters. Furthermore, rough set C-means (RSCM) and rough membership C-means (RMCM) have been proposed as clustering models on an approximation space considering the granularity of the universe (object space) based on binary relations. Although these rough set-based C-means methods are practical, they are not formulated based on objective functions, but are built on heuristic schemes. Objective function-based methods can be a basis for discussion of the validity of clustering and further theoretical developments. In this paper, we propose a novel RMCM framework, which is called RMCM version 2 (RMCM2), based on an objective function. The objective function is designed to derive the same updating rule for cluster centers as in RMCM. We demonstrate the characteristics of RMCM2 by visualizing cluster boundaries on a grid point dataset. Furthermore, we verify the clustering performance of RMCM2 through numerical experiments by using real-world datasets.

Recently, many advanced multimodal multi-objective evolutionary algorithms (MMOEAs) have been presented to solve multimodal multi-objective optimization problems (MMOPs). However, most of these approaches struggle not only to find the entire Pareto sets and Pareto front, but also ignoring the problem of Multi-Criteria Decision Making (MCDM) to be handled at a later stage. As a matter of fact, it is a very eclectic and challenging burden for decision makers to choose some trade-off optimal solutions from an enormous collection of non-dominated Pareto-optimal individuals. In this paper, we propose a knee based evolutionary algorithm, named MMO-EvoKnee, which incorporates MCDM strategy into solving MMOPs. The proposed algorithm is designed to search for a complete set of global knee solutions instead of an entire Pareto front and Pareto sets. Firstly, the EvoKnee Selection is adopted to find target global knee solutions and boundary individuals. Secondly, the Knee Multimodal Solutions Selection focuses on decision space exploitation to obtain well-converged multiple Pareto-optimal knee solutions. Thirdly, the Maximum Spanning Subset Selection is designed to accurately identify a complete number of knee solutions from overcrowded Pareto regions. Fourthly, the Boundary Multimodal Solutions Selection can find and maintain well-diversified and well-converged boundary solutions. As a result, MMO-EvoKnee can consistently find all knee solutions of interest quickly, and it relieves the burden for decision makers. Finally, the performance of the proposed algorithm is evaluated on thirteen benchmark MMOPs. The experiment results clearly show that the proposed MMO-EvoKnee provides a competitive edge over the chosen state-of-the-art MMOEAs.