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This paper addresses the design problem of the discrete-time stable unknown input estimator (UIE) based on parameter optimization using the artificial bee colony (ABC) algorithm. First, a stability-guaranteed design method for UIEs is presented, and a sufficient condition for the applicability of the design is provided. Next, to design UIEs with good disturbance rejection properties, a new objective function is developed that incorporates both waveform-based and norm-based performance criteria to allow direct evaluation of the adverse effects of disturbances on system performance. Finally, the proposed design method is compared with the previous one using an objective function based on the estimated disturbance to confirm the improvement of the disturbance rejection properties at the plant output. Furthermore, as another approach to the design of stable UIEs, the original UIE design method is combined with a constrained ABC algorithm, and the approach is compared with the proposed one in terms of disturbance rejection properties. • A design of the discrete-time stable unknown input estimator is addressed. • A new objective function is developed that incorporates both waveform-based and norm-based performance criteria. • The artificial bee colony algorithm is used to efficiently optimize the design parameters in the unknown input estimator. • A comparison with the constrained optimization approach is made. [ABSTRACT FROM AUTHOR]

The core element in solving constrained multi-objective problems (CMOPs) with evolutionary algorithms is simultaneously balancing objective optimization and constraint satisfaction. Maintaining this balance becomes more challenging for existing algorithms when dealing with complex CMOPs, as various complex feasible regions often result in CMOPs with very different characteristics. To address this issue, we propose a more flexible two-stage evolutionary algorithm based on automatic regulation (ARCMO), which can effectively control evolutionary trends to adapt to complex CMOPs. Specifically, the first stage performs a fast global search and passes the population information to the second stage. The second stage consists of two dynamically complementary sub-processes: the exploration subprocess and the convergence subprocess. The ratio of these two subprocesses is dynamically adjusted based on information from the first stage, allowing ARCMO to adapt to CMOPs with different complexities. Experiments on several recently proposed benchmark suites and real-world application problems show that ARCMO is more adaptable than the contender algorithms when solving different complex CMOPs. [ABSTRACT FROM AUTHOR]

An optimization spiking neural P (OSN P) system is a discrete optimization model without the aid of evolutionary operators of evolutionary algorithms or swarm intelligence algorithms. However, since the processing object of OSN P systems is a spike, where information is encoded by the timing of spikes or the number of spikes in neurons, OSN P systems are limited for solving continuous optimization problems. To break this limitation, an extended numerical spiking neural (ENSN P) system is proposed based on numerical spiking neural P (NSN P) systems and multiple (ENSN P) systems, called optimization numerical spiking neural P systems (ONSN P systems or ONSNPS), are designed to solve continuous constrained optimization problems. More specifically, in ENSN P systems, the production functions are selected by probability to achieve updated parameters. In OSN P systems, a guider algorithm is introduced to finish individuals' crossover and selection. The extensively experimental results in five benchmarks, thirty-two optimization problems including five benchmark problems, seventeen manufacturing design optimization problems and ten benchmarks from CEC show that ONSN P systems in this paper outperform or are competitive to twenty-eight optimization algorithms. Finally, algorithm complexity and Holm-Bonferroni procedure based on statistical results is used to test the complexity changing when we use different dimensionality of the search space and the difference in terms of statistical performance. The testing results indicate that the time complexity of ONSN P systems grows linearly with problem dimensions and ONSN P systems are better performance than the most algorithms. [ABSTRACT FROM AUTHOR]

• SADE-MI for mixed-integer expensive constrained optimization problems is proposed. • Experimental results and engineering optimization results demonstrate the effectiveness of SADE-MI. • Two variants of SADE-MI shows the effectiveness of the proposed operations. • SADE-MI can obtain competitive solutions under a limited computational budget. • SADE-MI obtained better solutions than the known optimal solutions in 2 problems. Many Surrogate-Assisted Evolutionary Algorithms (SAEAs) have been developed for expensive constrained optimization problems (ECOPs) with continuous variables. However, there exist some ECOPs that contain mixed-integer variables in real world engineering applications. The mixed-integer variables make the feasible regions of ECOPs exhibit complex disjoint characteristics, which brings two challenges for the existing methods, i.e., the classical surrogate-assisted pre-screening may easily fall into a local optimum and the population diversity tends to reduce with the influence of integer variables. For tackling these problems, a surrogate-assisted differential evolution for solving ECOPs involving mixed-integer variables (SADE-MI) is proposed. Firstly, the mutation strategy DE/best/2 is used to balance the local and global characteristics of the candidate solutions. Secondly, an adaptive pre-screening operation where the information of the population is effectively employed to construct the distance constraints is designed to avoid excessive exploitation in local regions. Finally, by selecting diversely-located individuals and limiting the number of individuals with the same integer variables, a population diversity maintenance operation is introduced to strengthen global exploration. Experimental studies on some benchmark problems and engineering optimization cases demonstrate that SADE-MI outperforms other classical algorithms for solving ECOPs with mixed-integer variables. [ABSTRACT FROM AUTHOR]

Particle swarm optimization (PSO) is a popular stochastic algorithm for solving nonlinear optimization problems. It has been used in various industrial applications because of its few parameters and ease of implementation. Various optimal problems must be frequently formed as nonlinear constrained optimization (NCO) problems because of global resource limitations. These problem-specific nonlinear constraints can result in many infeasible regions in the search space. Current PSO-based approaches are inherently designed for unconstrained optimization problems and cannot directly handle the constraint issue; therefore, they add the constraint handling technique (CHT) to account for NCO problems. This study proposes a double-track schema inside PSO called double-track PSO (DTPSO) to address the NCO problem. When an infeasible region blocks a particle, the DTPSO creates a copy of the particle. The original and copied particles utilize different search strategies to move to feasible and infeasible regions. The results indicate that the proposed DTPSO outperforms the seven referenced PSO-based methods in all 33 NCO problems and five recent strong methods in 19 mechanical design problems belonging to the IEEE CEC 2020 competition on real-world single-objective constrained optimization problems. Furthermore, the experiment results demonstrate the quality of the solution and the effective computation of the proposed DTPSO. [ABSTRACT FROM AUTHOR]

• The ECOPs with different time-consuming of objective and constraints are studied. • All constraints are effectively stratified based on their computational costs. • Constraints stratification information is gradually merged into search. • Three specific mechanisms are designed to balance exploration and exploitation. • Two real-world cases with two kinds of constraints are effectively investigated. The objective and constraints of expensive constrained optimization problems (ECOPs) are often evaluated using simulations with different computational costs. However, the existing algorithms always assume that both the objective and constraints can be simultaneously obtained after one expensive simulation, i.e., the most time-consuming one among the evaluations, based on parallel computing. This will affect the optimization efficiency since it is not necessary to call all the simulations of objective and constraints for each solution. Therefore, a general framework of surrogate-assisted evolutionary algorithms (GF-SAEAs) is proposed to adaptively arrange search strategies based on actual simulation cost differences. Specifically, all constraints are classified into several constraint levels by effectively quantifying the computational cost differences of objective and constraints, and a level-by-level feasible region-driven local search strategy is designed to locate potential sub-feasible regions for each constraint level. Then three different search mechanisms are employed to explore and exploit these located regions. Additionally, an adaptive population regeneration strategy is utilized to restart the algorithm and prevent premature convergence. In summary, GF-SAEAs can maintain a good balance between feasibility and convergence. Experimental studies on benchmark problems and two real-world cases show that GF-SAEAs performs better than other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

The existence of constrained multi-objective optimization problems (CMOPs) in real-world applications motivate researchers to focus more on developing constrained multi-objective evolutionary algorithms (CMOEAs). Due to the presence of constraints, an efficient constraint handling technique (CHT) is required in CMOEA to balance the constraint satisfaction and optimization of objective functions. Recently, different fitness based, ranking based, multi-population and multi-staged evolutionary approaches are proposed to handle CMOPs. However, most of the approaches still struggle while handling CMOPs with discontinuous feasible regions or whose feasible regions consist infeasible barriers. To overcome these issues, we propose a novel Dual-Population and Multi-Stage based Constrained Multi-objective Evolutionary Algorithm which is termed as CMOEA-DPMS. In CMOEA-DPMS, two populations are used to explore the search space and feasible regions. Along with two populations, an archive is also employed to store feasible, well converged and distributed solutions. To employ appropriate mating selection and environmental selection strategies according to the evolution of the populations, evolutionary process is divided into several stages. A strategy decider mechanism is proposed to determine the appropriate mating and environmental selections depending on the status of the population. In addition, a novel CHT named decomposition based constraint non-dominating sorting (DCDSort) is proposed by combining decomposition based selection with traditional constraint non-dominating sorting to maintain feasibility, convergence and diversity. The proposed algorithm is evaluated on five recent and popular test suites along with 36 real-world constrained multi-objective optimization problems against eight state-of-the-art algorithms. The empirical results suggests that CMOEA-DPMS is significantly superior or comparable to the considered algorithms and can tackle all kinds of CMOPs. [ABSTRACT FROM AUTHOR]

The significant issue to solve constrained multiobjective optimization problems (CMOPs) is to keep the balance between objectives and constraints, but the existing evolutionary algorithms are in the face of challenges for solving CMOPs with complex feasible regions. Based on this purpose, a constrained multiobjective evolutionary algorithm with the two-archive weak cooperation (CMOEA-TWC) is proposed in this article. In CMOEA-TWC, two archives are evolved, which are denoted as driving archive and normal archive, respectively. Besides, the weak cooperation of two archives is designed for sharing valuable information between archives. Specifically, the driving archive only considers objectives, while the normal archive considers both objectives and constraints. In addition, the minimum shift-based density estimation-based (SDE) distance is adopted to enhance the diversity of solutions in the driving archive, and a strict constrained dominance principle is designed to improve the feasibility of solutions in the normal archive. The proposed algorithm is tested on 47 CMOPs of 4 benchmark suites with the comparison of 4 state-of-the-art algorithms. The experimental results demonstrate that the average ranks in terms of inverted generational distance (IGD) outperform those of existing state-of-the-art competitors. [ABSTRACT FROM AUTHOR]

Most metaheuristic optimizers rely heavily on precisely setting their control parameters and search operators to perform well. Considering the complexity of real-world problems, it is always preferable to adjust control parameter values automatically rather than clamping them to a fixed value. In recent years, Spherical Search (SS) has emerged as a population-based stochastic optimization method that exploits the concepts of random projection matrices in linear algebra. As a result of the success of SS in solving non-convex, real-parameter optimization problems of various complexity, we have significantly extended SS in this paper by introducing a set of new algorithms, collectively known as Self Adaptive Spherical Search (SASS). Our proposal aims to enhance the performance of SS by using different projection matrix schemes in conjunction with improved search-direction calculations and an adaptive modification of parameter values. In our proposed adaptation scheme, parameters are modified to relevant values by applying a self-adaptive process that does not rely upon prior knowledge of the correlation between the parameter values and characteristics of the problem space. Consequently, we may apply the algorithms to bound and nonlinearly constrained optimization problems. For the benchmark suites derived from the most recent IEEE Congress on Evolutionary Computation (CEC) competitions, simulation results indicate that the SASS family of algorithms performs better than or is comparable to state-of-the-art algorithms from the other paradigms concerning robustness and convergence. [ABSTRACT FROM AUTHOR]

• The SCJL12-21 seeks a good representation by identifying unimportant data points. • The convergence of SCJL12-21 is verified theoretically and experimentally. • The effectiveness of the proposed SCJL12-21 is demonstrated on five datasets. Some of the data collected from practical applications are usually heavily corrupted. In subspace clustering, the common method is to use the specific regularization strategy to correct these corrupted data by virtue of the prior knowledge, which could result in a suboptimal clustering solution. To alleviate the problem, we develop a novel formulation named subspace clustering via joint ℓ 1 , 2 and ℓ 2 , 1 (L12-21) norms (SCJL12-21). Specifically, we identify and exclude the heavily corrupted data points (unimportant data points) from participating in the linear representation of other points by imposing the ℓ 1 , 2 norm on the representation matrix, and improve the robustness to outliers by enforcing the ℓ 2 , 1 constraint on the error matrix. The joint ℓ 1 , 2 and ℓ 2 , 1 minimization leads to a good representation matrix which enhances the clustering performance. Related ℓ 1 , 2 and ℓ 2 , 1 norm constrained optimization problem is solved by utilizing the augmented Lagrange multiplier method. The effectiveness of the proposed method is demonstrated through experiments on the constructed datasets as well as the two practical problems of motion segmentation and face clustering. [ABSTRACT FROM AUTHOR]

The integrated coal mine energy system (ICMES) is a kind of system with multiple scenarios, variables and parameters, which belongs to dynamic constrained multi-objective optimization problem (DCMOP). One of the challenges in solving ICMES lies in searching for feasible solutions when the frequency of changes is quick. To solve the above mentioned issues, this paper proposes a federated GAN network-based evolutionary constrained optimization for ICMES (FGECO). Firstly, multiple GAN networks are utilized in the framework of federated learning (FL) to estimate the distribution of feasible regions that satisfy each constraint. Following that, they are fused to realize the intersection of all feasible regions, and generate one feasible region that can meet all constrained requirements. Subsequently, an initial population with guidance of evolution is generated based on the proposed shared GAN network model. Finally, FGECO is compared with four popular dynamic constrained multi-objective evolutionary algorithms (DCMOEAs) on ICMES. Experimental results indicate its superiority. [ABSTRACT FROM AUTHOR]

Optimizing the convergence and diversity of solutions simultaneously under constraints is a challenge in solving constrained multiobjective optimization problems. In existing multiobjective optimization algorithms, general diversity maintenance mechanisms have difficulty determining all optimal solutions in discrete feasible regions. This paper proposes a staged constrained multiobjective optimization algorithm with a diversity enhancement method (SDEM), which can explore potential discrete feasible regions by retaining well-distributed offspring. Specifically, after solutions have converged to optimal feasible regions by niching-based constraint dominance in the early stage, the SDEM improves the diversity of solutions through a proposed diversity enhancement dominance principle in the mid-term. Finally, the optimize objective functions and constraints of all solutions are optimized under constraint dominance to balance convergence, diversity, and feasibility during the three stages. Experiments on four well-known test suites and six real-world case studies demonstrate that the SDEM is competitive with or comparable to seven state-of-the-art constrained multiobjective evolutionary algorithms. [ABSTRACT FROM AUTHOR]

The structural network control principle for identifying personalized drug targets (SNCPDTs) is a kind of constrained multiobjective optimization (CMO) problem with NP-hard features, which makes traditional mathematical methods difficult to adopt. Therefore, this study designs a knowledge-embedded multitasking constrained multiobjective evolutionary algorithm (KMCEA) to solve the SNCPDTs by mining relevant knowledge. Specifically, the relationships between two optimization objectives (minimizing the number of driver nodes and maximizing prior-known drug-target information) and constraints (guaranteeing network control) are analyzed from the perspective of CMO. We find that two objectives are difficult to optimize; thus two single-objective auxiliary tasks are created to optimize two objectives respectively, so as to maintain diversity along the Pareto front. Furthermore, we find that two optimization objectives have a complex reverse relation and a simple positive relation with constraints, respectively; thus, a population initialization method and a local auxiliary task are designed for two single-objective auxiliary tasks, respectively, so as to improve the performance of the algorithm on two objective functions. Finally, KMCEA is used to solve two kinds of models with three kinds of datasets. Compared with various methods, KMCEA can not only effectively discover clinical combinatorial drugs but also better solve the SNCPDTs regarding convergence and diversity. [ABSTRACT FROM AUTHOR]

Multi-task optimization problems in the real world often contain constraints. When dealing with these problems, it is necessary to consider multiple tasks and their respective constraints simultaneously. However, most of existing research on multi-task optimization neglects the influence of constraints, which leads to slow convergence speed and susceptibility to local optima. To address the aforementioned issues, this paper proposes a reinforcement learning assisted constrained multi-task evolutionary algorithm. First, to meet the different requirements of different tasks and constraints, an adaptive operator selection strategy based on reinforcement learning is proposed. Second, to enhance population diversity, a multi-population method with different constraint handling techniques is introduced. This method assigns two independent populations to each task. The main population aims to find feasible solutions, while the auxiliary population focuses on exploring the entire search space. Finally, considering the individual differences between tasks, a dimension-based knowledge transfer is employed to facilitate positive information exchange. Compared with other state-of-the-art constrained evolutionary algorithms, the experimental results on constrained multi-task benchmark suite demonstrate the superiority of the proposed algorithm. The source code can be obtained from https://github.com/yufeiyng/RL-CMTEA. • A reinforcement learning-based evolutionary algorithm designed for constrained multi-task optimization. • A multi-population method is employed to facilitate populations traversal through infeasible regions. • An adaptive operator selection strategy based on Q-Learning with upper confidence bound. • An dimension-based knowledge transfer is employed for constrained multi-task optimization. • Comprehensive experiments confirming the effectiveness and superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

• Two linguistic information granulation models are proposed. • A tournament selection operator-guided PSO solution approach is developed. • An estimation method for expert and attribute weight is designed. • A new energy vehicles evaluation problem is analyzed using the proposals. • The effectiveness and efficiency of the solution approach are discussed. This study investigates linguistic information-based granular computing for supporting multi-attribute group decision-making where relative importance of experts/attributes, and outcomes of pairwise comparisons over alternatives are recorded in the form of distributed linguistic preference relations. First, we propose two linguistic information granulation models based on the measures of consistency and consensus to realize the operability of two types of linguistic information, respectively. The granulation of the weight linguistic information is closely linked with that of the alternative preference linguistic information in a way that two sets of control factors are introduced. Second, an estimation method for expert/attribute weights is developed based on the optimal control factors and solutions to the aforesaid linguistic information granulation models. The proposed linguistic information granulation models are in fact constrained non-linear optimization problems which may be neither effectively nor efficiently solved by general optimization methods. Third, we therefore propose a novel solution approach named tournament selection operator-guided particle swarm optimization (TSOG-PSO). Compared with the standard PSO and its variants, the TSOG-PSO enjoys more feasibility and lower complexity. A new energy vehicle evaluation problem is analyzed using the proposals to demonstrate their applicability. Some discussions and comparative studies are conducted to illustrate the effectiveness of the proposals. [ABSTRACT FROM AUTHOR]

Constrained multiobjective optimization problems commonly arise in real-world applications. In the presence of constraints and multiple conflicting objectives, finding a set of feasible solutions which can best tradeoff different objectives is quite challenging. In this study, an ε -constrained multiobjective differential evolution using linear population size expansion is proposed to solve such a kind of problems. First, the ε -constraint-handling method, which originally solves constrained optimization problems with only one objective, is further improved to handle constraints in a multiobjective optimization way. Second, to achieve a better approximation to the feasible Pareto front, a linear population size expansion strategy is developed. Once enough feasible solutions have been found, the population size will be linearly increased to find more promising solutions. As a result, a simple yet efficient constrained multiobjective differential evolution is proposed. Experiments are conducted to evaluate the performance of the proposed algorithm on 35 benchmark test functions with different numbers of constraints and objectives. Obtained results are compared with seven state-of-the-art algorithms. Empirical results and comparisons demonstrate that our proposed algorithm achieves better or at least comparable performance to the competitors, and is capable of obtaining a set of representative feasible solutions for the selected real-world constrained multiobjective optimization problems, especially for highly constrained problems. [ABSTRACT FROM AUTHOR]

• Landscape analysis is extended to constrained multiobjective optimization. • New landscape features are derived to facilitate problem characterization. • Test suites of constrained multiobjective optimization problems are thoroughly analyzed. • Artificial test problems fail to fully represent real-world problem characteristics. • The main source of complexity in artificial test problems is violation multimodality. Despite the increasing interest in constrained multiobjective optimization in recent years, constrained multiobjective optimization problems (CMOPs) are still insufficiently understood and characterized. For this reason, the selection of appropriate CMOPs for benchmarking is difficult and lacks a formal background. We address this issue by extending landscape analysis to constrained multiobjective optimization. By employing four exploratory landscape analysis techniques, we propose 29 landscape features (of which 19 are novel) to characterize CMOPs. These landscape features are then used to compare eight frequently used artificial test suites against a recently proposed suite consisting of real-world problems based on physical models. The experimental results reveal that the artificial test problems fail to adequately represent some realistic characteristics, such as strong negative correlation between the objectives and the overall constraint violation. Moreover, our findings show that all the studied artificial test suites have advantages and limitations, and that no "perfect" suite exists. Additionally, the effectiveness of the proposed features at predicting algorithm performance is demonstrated for two multiobjective optimization algorithms. Benchmark designers can use the obtained results to select or generate appropriate CMOP instances based on the characteristics they want to explore. [ABSTRACT FROM AUTHOR]

In numerous applications across all science and engineering areas, there are optimization problems where both the objective function and the constraints have no closed-form expression or are too complex to be managed analytically, so that they can only be evaluated through experiments. To address such issues, we design a global optimization technique for problems with black-box objective and constraints. Assuming Lipschitz continuity of the cost and constraint functions, a Set Membership framework is adopted to build a surrogate model of the optimization program, that is used for exploitation and exploration routines. The resulting algorithm, named Set Membership Global Optimization with black-box constraints (SMGO- Δ), features one tunable risk parameter, which the user can intuitively adjust to trade-off safety, exploitation, and exploration. The theoretical properties of the algorithm are derived, and the optimization performance is compared with representative techniques from the literature in several benchmarks. An extension to uncertain cost/constraint function outcomes is presented, too, as well as computational aspects. Lastly, the approach is tested and compared with constrained Bayesian optimization in a case study pertaining to model predictive control tuning for a servomechanism with disturbances and plant uncertainties, addressing practically-motivated task-level constraints. [ABSTRACT FROM AUTHOR]

The challenge in solving constrained multi-objective optimization problems (CMOPs) is how to balance minimizing objectives and satisfying constraints, especially when the infeasible region is very large. To address this issue, this work proposes a fuzzy constraint handling technique, which uses the fuzzy set theory to accurately characterize the difference between solutions on objective function values and constraint violation degrees. On this basis, a new concept, called "fuzzy advantage", is introduced to comprehensively quantify the degree to which one solution is better than others, allowing the infeasible solutions with promising fitness to survive. The proposed method is integrated with a decomposition-based multi-objective evolutionary algorithm to verify its effectiveness. Compared with nine state-of-the-art MOEAs on a number of test problems and a real-world optimization problem, the proposed algorithm shows high competitiveness in solving a variety of CMOPs. [ABSTRACT FROM AUTHOR]

Distributed optimization algorithms have the advantages of privacy protection and parallel computing. However, the distributed nature of these algorithms makes the system vulnerable to external attacks. This paper presents two penalty function based resilient algorithms for constrained distributed optimization under static and dynamic attacks. The objective function of the optimization problem is extended to nonsmooth ones and the convergence of the proposed algorithms in this case are proved under some mild conditions. Simulation experiments are performed and compared with some existing resilient primal-dual optimization algorithms using median-based mean estimator. For static attack, the proposed algorithm has better performance and faster convergence rate in the simulation experiments. For dynamic attack, the proposed algorithm has better performance and robustness in the simulation experiments, which illustrate that the proposed algorithms are more effective. [ABSTRACT FROM AUTHOR]

For data analysis, learning treatment rules in stratified medicine require the optimization of multiple responses. A common approach is to use a multi-objective function to find the optimal setting of the controllable factors. For patients, the optimal setting is a treatment regimen that yields the optimal value of potential responses. However, subclasses of patients are often stratified by their covariates. Thus, this paper proposes a new model called constrained optimization for stratified treatment rules (COSTAR) with multiple responses. This model incorporates covariates to build separate models for optimal responses and stratifies the patients with the balancing score from covariates. The optimal solution enables us to choose the optimal treatment for each subclass of patients. Theoretical results guarantee the identifiability of the solutions with conditional optimal values of multiple responses from survival probabilities. Examples of experiments with factorial designs and survival data validate the efficacy of the proposed method. The results suggest that this method improves the significance of the parameters and the adjusted R 2 in fitting on the primary response, while the unsupervised clustering method (i.e., k -means) does not. This method, with the fitting model, is more interpretable than the conventional method and provides optimal treatment rules for stratified patients. [ABSTRACT FROM AUTHOR]

• A novel completely stealthy attack model is proposed. • The remote estimation error is analyzed which is more complicated. • The optimal policy is derived by solving the transformed optimization problem. This paper investigates the problem of designing the optimal completely stealthy attacks in cyber-physical systems. Different from the strictly stealthy attacks in the existing results which still have the possibilities to trigger the alarm and be invalid, a completely stealthy attack model is proposed such that the attack signals are able to bypass the detector successfully without being detected. Under the framework of the attacks, the remote estimation error is analyzed by deriving the recursion of the error covariance matrix, based on which the problem of attack design is transformed into a constrained optimization problem. By employing the Lagrange multiplier method, the optimal attack policy is derived which maximizes the remote estimation error and guarantees the complete stealthiness to the detector concurrently. Finally, simulation examples are provided to illustrate the effectiveness of this work. [ABSTRACT FROM AUTHOR]

For the short-term crude oil scheduling problem, it is difficult to guarantee the feasibility of a schedule due to complicated constraints. Meanwhile, uncertainty is a very important concern in refineries, such as unexpected breakdown of charging tanks. Therefore, it is a great challenge to make a schedule feasible. Most existing works on multi-objective optimization of short-term crude oil scheduling are developed for refineries processing low-fusion-point oil (L-oil) only and little is done for the case with dual pipelines for processing both L-oil and high-fusion-point oil (H-oil). With five objectives and many constraints, it is challenging for a metaheuristic algorithm to find a feasible schedule. To solve this problem, in this work, constraint violation is used to describe the degree of constraint violation. Thus, an adaptive enhanced selection pressure algorithm based on NSGA-II-CDP (NSGA-II-APE) is proposed to efficiently solve the problem for processing both L-oil and H-oil. This algorithm can effectively enhance the selection pressure in the later iterations. Industrial case problems are used to test the proposed method and compare its performance with 11 state-of-the-art constrained multi-objective evolution algorithms (CMOEAs). Results show its superiority over the existing ones in terms of convergence, solution diversity, and time efficiency. [ABSTRACT FROM AUTHOR]

Space Surveillance Network (SSN) task scheduling plays a crucial role in maintaining the catalog of Resident Space Objects (RSO). However, various emergencies, such as RSO maneuvering, collisions, or rocket launch, may disrupt the original scheduled scheme. Therefore, it is essential to rapidly regenerating emergency schemes while minimizing disturbance to the initial scheduling scheme. This paper introduces an Emergency Task Scheduling model, referred to as MM-ETS, which aims to Maximize observation profits and Minimize disturbance. This model incorporates constraints related to observability, tasks, and resources, which are derived from practical applications. Additionally, a Hierarchical Distributed Dynamic Emergency Scheduling algorithm, encompassing Task assignment, Conflict resolution, Resource negotiation, and Center collaboration (HD-TCRC-DES), is proposed. The presented algorithm is activated by emergencies and a Rolling Horizon Strategy (RHS) is employed to break down long-term, large-scale problems into short-term, small-scale problems, thus improving feasibility and emergency response capabilities. At each layer of the proposed algorithm, heuristic rules are utilized to solve the new scheme, which helps allocate the computational load to resource nodes, and quickly adjust the initial scheduling scheme. Experimental scenarios involving 15 ground observation resources and 1000 emergency tasks are constructed, and the simulation results demonstrate that the proposed method can enhance Comprehensive Benefits Indicators (CBI) by approximately 24.65%, 24.7%, 24.91%, and 30.5% compared to the baselines. Consequently, it is suitable for SSN emergency task scheduling. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problems (CMOPs) require a delicate balance between satisfying constraints and optimizing objectives. Existing constrained multi-objective evolutionary algorithms (CMOEAs) often struggle to balance convergence, diversity, and feasibility, especially when dealing with CMOPs that have complex feasible regions. This paper proposes a multi-task-based self-organizing mapping evolutionary algorithm (MTSOM) to tackle this challenge, which includes a main and auxiliary task. Two populations independently optimize two tasks without considering constraints in the early stage. Subsequently, in the middle stage, both tasks explore the distribution structure of the population in parallel by employing a novel constraint-to-constraint self-organizing mapping (SOM) approach. In the late stage, the main task fully considers feasibility, while the auxiliary task focuses solely on the highest priority constraints. This approach enables rapid convergence toward feasible regions. To evaluate MTSOM's effectiveness, we conducted a series of experiments on five benchmark suites. Results indicate that MTSOM is competitive when compared to other state-of-the-art CMOEAs. Additionally, our proposed constraint-to-constraint SOM is superior in handling complex CMOPs. [ABSTRACT FROM AUTHOR]

In the constrained multi-objective optimization problems, the pursuit of feasibility could improve convergence but will lead to the loss of diversity. For optimization algorithm, balancing the weight between convergence and diversity dynamically is a challenge, especially in problems with low proportion of feasible regions. In this paper, a constrained multi-objective optimization algorithm is proposed based on a hybrid driven strategy to enhance both the feasibility and diversity performance of the approximate Pareto solutions. The proposed algorithm contains two archives, that one is driven by feasibility information and the other is driven by diversity information. A self-adaptive archive selection mechanism and a conditional tournament selection strategy are proposed to provide mating parent solutions according to the evolutionary stage. Moreover, in the update of the feasibility archive, an evolutionary direction prediction mechanism is proposed and adopted to improve the evolutionary efficiency. Compared to four other multi-objective algorithms on three benchmark suits of different types, the performance of the proposed algorithm is better than the peer algorithms, especially in large-infeasible-regions multi-objective optimization problems. [ABSTRACT FROM AUTHOR]

• The weight recursive least squares are employed to update SCN in real time. • SCN-based cascade GPC (SCN-CGPC) for the MST is derived. • Simplification of the KKT conditions saves iterative process. • Industrial application illustrates its practicality and effectiveness. The main steam temperature (MST) in power plants suffers from nonlinearity and large time delay, which cause large overshoot and long settling time under widely used cascade proportion integration differentiation (PID) controller. In order to cope with the negative effects, we propose a stochastic configuration network (SCN) based cascade generalized predictive control (GPC) scheme to improve the performance of the MST. A three-layer SCN is employed to model the MST process. The SCN is constructed by two phases, i.e., initial phase and real-time phase. The initial phase determines the structure and primary parameters of the learner model using the stochastic configuration algorithm. The real-time phase employs weighted recursive least squares (WRLS) for building the real-time MST process model for GPC design. Taking into account some constraints of the MST process, Karush–Kuhn–Tucker (KKT) conditions are applied for solving the constrained receding-horizon optimization problem. The derived explicit solutions of GPC avoid the implicit form which usually has to be solved iteratively. Comparative simulations demonstrate the superiority of the proposed SCN based cascade GPC (SCN-CGPC). Finally, the proposed SCN-CGPC is implemented via a standalone external MST control system in a power plant. The effectiveness and practicability are validated with the real-world application. [ABSTRACT FROM AUTHOR]

Many domination-based multi-objective evolutionary algorithms (MOEAs) are designed for constrained multi-objective optimization problems (CMOPs). However, they still face the challenge of balancing the feasibility, convergence and distribution. This paper tackles this issue by proposing a multi-objective differential evolution algorithm based on domination and a mechanism of constraint-handling switching (MODE-CHS). In constraint-handling switching, if there are no feasible solutions in the population, the population evolves by constraint-handling; otherwise, the population evolves without handling constraints. This mechanism enhances the rate of population convergence to the maximum while obtaining the feasible solutions. Furthermore, in MODE-CHS, the feasible solutions are saved to an external archive and evolve together with the population to explore the feasible region. Meanwhile, to enhance the distribution, the offspring of the external archive also participates in the individual-update procedure of the population. 27 bench-mark test problems and two real-world problems are used for the performance comparison of the proposed algorithm with other five state-of-the-art algorithms. In the experiment, the proposed algorithm, MODE-CHS, is shown to produce satisfactory solutions for most of the tested functions, where other five MOEAs perform relatively worse. The experiment results demonstrate MODE-CHS is very competitive for solving CMOPs. [ABSTRACT FROM AUTHOR]

• The proposed algorithm has a higher utilization of its secondary population. • Proposed algorithm enhance cooperation appropriately to have a better performance. • The proposed algorithm is competitive when compared to the Dual-popualtion CMOEAs. It is challenging to solve constrained multi-objective optimization problems (CMOPs). Different from the traditional multi-objective optimization problem, the feasibility, convergence, and diversity of the population must be considered in the optimization process of a CMOP. How these factors are balanced will affect the performance of the constrained multi-objective optimization algorithm. To solve this problem, we propose a dual-population multi-objective optimization evolutionary algorithm. The proposed algorithm can make good use of its secondary population and alternative between evolution and degeneration according to the state of the secondary population to provide better information for the main population. The test results of three benchmark constrained multi-objective optimization problem suites, and four real-world constrained multi-objective optimization problems show that the algorithm is better than existing dual-population multi-objective optimization, especially when there is a distance between the unconstrained PF and the constrained PF. [ABSTRACT FROM AUTHOR]

A key issue in evolutionary constrained optimization is how to achieve a balance between feasible and infeasible solutions. The quality of generated solutions in decomposition-based multi-objective evolutionary algorithms (MOEAs) depends strongly on the weights' setting. To fully utilize both the promising feasible and infeasible solutions, this paper proposes two-type weight adjustments based on MOEA/D for solving highly constrained many-objective optimization problems (CMaOPs). During the course of the search, the number of infeasible weights is dynamically reduced, to guide infeasible solutions with better convergence to cross the infeasible barrier, and also to lead infeasible solutions with better diversity to locate multiple feasible subregions. Feasible weights are evenly distributed and keep unchanged throughout the evolution process, which aims to guide the population to search Pareto optimal solutions. The effectiveness of the proposed algorithm is verified by comparing it against six state-of-the-art CMaOEAs on three sets of benchmark problems. Experimental results show that the proposed algorithm outperforms compared algorithms on majority problems, especially on highly constrained optimization problems. Besides, the effectiveness of the proposed algorithm has also been verified on an antenna array synthesis problem. [ABSTRACT FROM AUTHOR]

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-a CA + 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-a CA + m IS 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. [ABSTRACT FROM AUTHOR]

• The niche-based density estimation and angle-based selection strategy are devised. • Individuals with poor diversity are identified by niche-based density estimation. • Individuals with worse convergence are removed via angle-based selection. • NAEA can be easily extended to constrained many-objective optimization problems. It is well known that balancing population diversity and convergence plays a crucial role in evolutionary many-objective optimization. However, most existing multiobjective evolutionary algorithms encounter difficulties in solving many-objective optimization problems. Thus, this paper suggests niche-based and angle-based selection strategies for many-objective evolutionary optimization. In the proposed algorithm, two strategies are included: niche-based density estimation strategy and angle-based selection strategy. Both strategies are employed in the environmental selection to eliminate the worst individual from the population in an iterative way. To be specific, the former estimates the diversity of each individual and finds the most crowded area in the population. The latter removes individuals with weak convergence in the same niche. Experimental studies on several well-known benchmark problems show that the proposed algorithm is competitive compared with six state-of-the-art many-objective algorithms. Moreover, the proposed algorithm has also been verified to be scalable to deal with constrained many-objective optimization problems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

• An efficient constrained global optimization algorithm via the Gaussian process regression model is developed. • A clustering assisted multi-objective infill criterion is developed. • The accuracy of constraint model is considered. • The trade-off between objective and constraints is balanced. • The selection of sample points is adaptively. • The efficiency and robustness of the proposed approach are tested through 20 cases. Constrained optimization problems trouble engineers and researchers because of their high complexity and computational cost. When the objective function and constraints are both expensive black-box problems, there are many difficulties in solving them due to the unknown mathematical expressions and limited computational resources. To address these difficulties, we propose an efficient constrained global optimization algorithm. In the proposed algorithm, Gaussian process regression models are used to approximate the expensive objective function and constraints. Differential evolution (DE) is adopted to find the minimum value of the constrained lower confidence bounding (LCB). To further improve the accuracy of the Gaussian process regression models for the objective and constraints simultaneously, a clustering-assisted multiobjective infill criterion is proposed. The multiobjective infill criterion is utilized to balance the exploration between the objective and constraints. The clustering selection method is used to maintain the diversity of the sample points. The experimental results show that the proposed algorithm is better than or at least comparable to classic algorithms and other state-of-the-art algorithms [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we correct some errors in the extended first and second Gordan's theorems in a recent paper—Information Sciences 504 (2019) 276–292. [ABSTRACT FROM AUTHOR]

• A novel Kriging-assisted two-phase optimization framework is proposed based on TLBO's unique structure. • A data management approach is proposed to collect and organize the dynamically updated expensive samples. • Two prescreening operators are proposed in Kriging-assisted Teaching and Learning Phases to select elite individuals. • KTLBO performs efficient on 18 benchmark cases and can successfully solve actual engineering applications. 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. [ABSTRACT FROM AUTHOR]

Network pruning has been a hot topic in recent years, and many popular pruning methods rely on network design expertise. However, the pruning process usually involves manual intervention and can be difficult for users who lack prior knowledge. Automatic pruning using evolutionary algorithms shows great promise, but it must address the challenge of performing time-consuming model evaluations and searching through a large solution space. Dataset distillation is a technique that compresses the original dataset to decrease the cost of fine-tuning models. In this paper, we explore the potential of using the distilled dataset to exhibit a similar role as the real dataset in network pruning, and proposed the evolutionary pruning framework using distilled dataset. Specifically, the network pruning pipeline is carried out on the distilled dataset to significantly reduce the model evaluation cost, and the number of filters in the convolutional layer is directly coded to narrow the search space. In addition, a tailored evolutionary algorithm is proposed that takes the form of constrained optimization to search the most suitable pruned network. The experiments conducted on VGG16, VGG19, ResNet56, and ResNet110 demonstrate that the proposed method reduces at least 41.56% of the flops and achieves competitive results with little compromising accuracy. • Distillation dataset is first applied to network pruning. • A constrained evolutionary algorithm with double-balanced multi-branch is proposed. • Deep convolutional neural network pruning is performed using the constrained evolutionary algorithm. [ABSTRACT FROM AUTHOR]

Balancing multiple objectives and various constraints is crucial for effectively solving constrained multi-objective optimization problems (CMOPs). Excessive focus on either convergence or feasibility may not result in favorable outcomes of the algorithm. To confront this challenge, this paper proposes a cooperative evolutionary algorithm named SaE-CMO, which aims to achieve a harmonious balance between convergence and feasibility by extracting valuable information from both feasible and infeasible regions. To achieve this, SaE-CMO employs a dual-population approach to enhance search progress, consisting of a main population, Population1, and an auxiliary population, Population2. These two populations complement each other to achieve optimal results. A newly proposed self-adaptive epsilon method is employed in both Population1 and Population2, using different comparison criteria to select next population from mating pools, respectively. Population2 can retain some solutions that are well-constrained but poorly converged, thereby preserving information about both the constrained and the unconstrained Pareto front. This property enables Population2 to assist Population1 in maintaining diversity in certain complex CMOPs. To verify the effectiveness of SaE-CMO, we conduct experiments on three benchmark test instances and four real-world CMOPs with some related state-of-the-art constrained multi-objective optimization algorithms, experimental results prove that the proposed algorithm outperforms the compared algorithms. [ABSTRACT FROM AUTHOR]

In the last few decades, genetic algorithms (GAs) demonstrated to be an effective approach for solving real-world optimization problems. However, it is known that, in presence of a huge solution space and many local optima, GAs cannot guarantee the achievement of global optimality. In this work, in order to make GAs more effective in finding the global optimal solution, we propose a hybrid GA which combines the classical genetic mechanisms with the gradient-descent (GD) technique for local searching and constraints management. The basic idea is to exploit the GD capability in finding local optima to refine search space exploration and to place individuals in areas that are more favorable for achieving convergence. This confers to GAs the capability of escaping from the discovered local optima, by progressively moving towards the global solution. Experimental results on a set of test problems from well-known benchmarks showed that our proposal is competitive with other more complex and notable approaches, in terms of solution precision as well as reduced number of individuals and generations. [ABSTRACT FROM AUTHOR]

Integrative multi-view subspace clustering aims to partition observed samples into underlying clusters through fusing representative subspace information from different views into a latent space. The clustering performance relies on the accuracy of sample affinity measurement. However, existing approaches leverage the subspace representation of each view and overlook the learning of appropriate sample affinities. This paper proposes to learn a consensus affinity directly by merging subspace representations of different views on a Grassmann manifold while maintaining their geometric structures across these views. The proposed method not only preserves the structure of the most informative individual view, but also discovers a latent common structure across all views. The associated constrained optimization problem is solved using the alternating direction method of multipliers. Extensive experiments on synthetic and real-world datasets show that the proposed method outperforms several state-of-the-art multi-view subspace clustering methods. The affinity matrix obtained by our method can extract highly representative and latent common information to enhance the clustering performance. [ABSTRACT FROM AUTHOR]

In this paper, the problem of designing the worst-case ϵ-stealthy false data injection attacks in cyber-physical systems is investigated. The attacker attempts to degrade the remote state estimation performance by modifying the transmitted sensor measurements. Different from the existing ϵ-stealthy actuator attacks where the effect of the attacks is characterized by the information theoretic analysis, the remote estimation error is calculated with the statistical characteristics of the innovations and the problem is transformed into a constrained optimization problem with multiple decision variables. By utilizing the properties of the K-L divergence and mutual information, the problem is solved with the Lagrange multiplier method and the worst-case attack strategy is derived, which maximizes the estimation error and guarantees the stealthiness. Finally, simulation examples are provided to demonstrate the results. [ABSTRACT FROM AUTHOR]

Benefiting from its efficiency and quick convergence, the feasibility rule (FR) is well-known for its ability to solve constrained optimization problems (COPs). However, it is highly criticized for its heavy preference for constraints. Thus, an individual-dependent feasibility rule (IDFR) was designed by alleviating the preference from two aspects. Some information of constraints, which might be nonsignificant, is depressed. By contrast, some promising information of objective function is leveraged. The extent of information is individual-dependent. To further enhance the diversity, a two-phase diversity strategy was developed. Due to their numerous merits, two differential evolution (DE) operators were selected as components of the search algorithm. By the above process, we proposed a constrained DE (i.e., IDFRDE). To the best of our knowledge, we made the first attempt to improve FR from the individual perspective. IDFR is more robust than FR while keeping the same computational time complexity. However, it would converge slower than FR on some easy COPs. Experiments on three widely used benchmarks show that: 1) IDFRDE outperforms or gets similar results comparing with other known algorithms; 2) IDFR is more effective than FR on complex COPs; 3) both, the search algorithm and the diversity strategy are important to IDFRDE. [ABSTRACT FROM AUTHOR]

This paper presents an online-learning ensemble framework for nonstationary time series prediction. Optimal granular fuzzy rule-based models with different objective functions and constraints are evolved from data streams. Evolving optimal granular systems (eOGS) consider multiobjective optimization, the specificity of information, model compactness, and variability and coverage of the data within the process of modeling data streams. Forecasts of individual base eOGS models are combined using averaging aggregation functions: ordered weighted averaging (OWA), weighted arithmetic mean, median, and linear non-inclusive centered OWA. Some aggregation functions use specific weights for the relevance of the base models and exclude extreme values and outliers. The weights of other aggregation functions are adapted over time based on a quadratic programming problem and the data within a sliding window. This paper investigates whether an online-learning ensemble can outperform individual eOGS models, and which aggregation function provides the most accurate forecasts. Real multivariate weather time series, particularly time series of daily mean temperature, air humidity, and wind speed from different weather stations, such as Paris–Orly, Frankfurt–Main, Reykjavik, and Oslo–Blindern, are used for evaluation. The results show that ensemble schemes outperform individual models. The proposed linear non-inclusive centered OWA function provided the most accurate numerical predictions. [ABSTRACT FROM AUTHOR]

This paper presents an extended Karush-Kuhn-Tucker condition to characterize efficient solutions to constrained interval optimization problems. We develop the theory from the geometrical fact that at an optimal solution the cone of feasible directions and the set of descent directions have an empty intersection. With the help of this fact, we derive a set of first-order optimality conditions for unconstrained interval optimization problems. In the sequel, we extend Gordan's theorems of the alternative for the existence of a solution to a system of interval linear inequalities. Using Gordan's theorem, we derive Fritz John and Karush-Kuhn-Tucker necessary optimality conditions for constrained interval optimization problems. It is observed that these optimality conditions appear with inclusion relations instead of equations. The derived Karush-Kuhn-Tucker condition is applied to the binary classification problem with interval-valued data using support vector machines. [ABSTRACT FROM AUTHOR]

In constrained optimization problems (COPs), a crucial issue is that most constraint-handling evolutionary algorithms (EAs) approach the optimum either mainly from feasible regions or mainly from infeasible regions. This may result in bias in search of feasible and infeasible solutions. To address this issue, we propose a feasible-ratio control technique which controls the ratio of feasible solutions in the population. By using the control technique, an EA can maintain the search balance from feasible and infeasible regions. Based on this technique, we propose a constraint-handling EA, named FRC-CEA. It consists of two-stage optimization. In the first stage, an enhanced dynamic multi-objective evolutionary algorithm (DCMOEA) with the feasible-ratio control technique is adopted to handle constraints. In the second stage, a commonly used differential evolution (DE) is used to speed up the convergence. The performance of the proposed method is evaluated and compared with six state-of-the-art constraint-handling algorithms on two sets of benchmark test suites. Experimental results suggest that the proposed method outperforms or is highly competitive against the compared algorithms on most test problems. [ABSTRACT FROM AUTHOR]

Gold cyanide leaching is a critical step in the extraction of gold from ore. The desire for a higher leaching rate often leads to increased cyanide concentrations, which pose safety risks and raise the cost of waste treatment. To address this problem, this study introduces a novel safe reinforcement learning algorithm that satisfies joint chance constraints with a high probability for multi-constraint gold cyanide leaching processes. In particular, the proposed algorithm employs chance control barrier functions to maintain the state within the desired safe set with high probability and transforms the joint chance constraint into a cumulative cost form using a constraint relaxation method. This relaxation method guarantees the satisfaction of safety requirements within a specified time horizon. A surrogate objective function optimized by stochastic gradient ascent is derived to ensure monotonic improvement of the policy in the trust region. The augmented Lagrangian-based constrained policy optimization is utilized, converting the constrained optimization problem into an unconstrained saddle-point optimization problem and avoiding the periodic performance oscillations common in the general Lagrangian method. Case studies demonstrate that the proposed algorithm outperforms baseline algorithms in terms of policy improvement, and constraint satisfaction and operates safely in multi-constraint scenarios. [ABSTRACT FROM AUTHOR]

It is of necessity to select appropriate optimization algorithms from an algorithm library due to the universality of constrained multi-objective optimization problems and the suitability of intelligent optimization algorithms, which requires a rich optimization algorithm library. This paper proposes a migration-based method of enriching the algorithm library for constrained multi-objective optimization problems. After calculating the similarity between problems based on their landscape features, the proposed method calculates the migration probabilities of intelligent optimization algorithms solving similar problems based on the performance of each algorithm and the similarity between problems. According to the redundancy and compatibility of components, the algorithms with large migration probabilities enrich the algorithm library for solving the current problem. Based on the enhanced algorithm library, a Softmax regression model is trained to generate an optimal intelligent algorithm to solve the current problem. The proposed method is applied to solve a series of constrained multi-objective optimization benchmark problems and the operation optimization problems of an integrated coal mine energy system, and the experimental results verify its effectiveness and feasibility. • A method based on landscape features is proposed to determine similar problems. • A method is given to select migrated algorithms based on similarity and performance. • A method based on redundancy and compatibility is presented to enrich an IOAL. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problems (CMOPs) are challenging due to the complexity of feasible regions caused by constraints, especially when facing small feasible ranges, multiple feasible regions, and complex distribution of feasible regions. Existing algorithms struggle to balance population convergence, diversity, and feasibility. This paper proposes a constrained multi-objective evolutionary algorithm framework based on global and local feasible solutions search to address this issue. The proposed framework is divided into three stages, and an adaptive method is proposed to decide when to switch the search state. In the first two stages, the evolution of the population is relatively free and not subject to constraint restrictions. Feasible solutions in the population are saved in the FeasiblePool for environmental selection during these two stages. The FeasiblePool does not affect the evolving population during these stages. In the first stage, the framework uses global search operator to fully explore the decision space and determine the rough range of feasible solutions in the decision space. In the second stage, the framework uses local search operator to enhance the diversity of FeasiblePool within this determined range. In the last stage, the framework reuses these excellent feasible solutions information to guide population evolution while considering constraints. The proposed framework has been compared with four state-of-the-art constrained multi-objective algorithms on four benchmark suites and three real-world applications. The complete experimental results show that the proposed framework has high competitiveness for solving CMOPs. [ABSTRACT FROM AUTHOR]