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This study focuses on the quasisynchronization problem for reaction–diffusion neural networks (RDNNs) in the presence of deception attacks. Under deception attacks, a time–space sampled-data (TSSD) control mechanism is proposed for RDNNs. Compared with traditional control strategies, the proposed control mechanism can not only save network bandwidth but also improve the cybersecurity of communications. Inspired by Halanay’s inequality, a new inequality is proposed, which can be effectively applied to the quasisynchronization problem for dynamical systems. Then, by using this inequality and the Lyapunov functional approach, quasisynchronization criteria are set for RDNNs. The desired control gain is gained from solving a group of linear matrix inequalities. Moreover, in the absence of deception attacks, the exponential synchronization problem is studied for RDNNs. In the end, simulation results are given to demonstrate the usefulness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Nonlinear equation systems (NESs) are ubiquitous, and solving them is an important yet challenging task in numerical computation. Most of the NESs usually contain multiple roots. To locate multiple roots, the use of evolutionary algorithms attracts more attention recently. For the purpose of finding different roots within a limited computational budget in a single run simultaneously, in this article, a hybrid niching-based differential evolution with two archives, referred to as HNDE/2A, is proposed. It can be featured as: 1) two niching techniques, i.e., crowding and speciation, are combined to balance the diversity and convergence; 2) a root archive is used to save the found roots during the run. Additionally, if a root is saved into the root archive, it will be reinitialized immediately to further promote the population diversity; and 3) an inferior offspring archive is presented to utilize the useful information of the inferior offspring. To evaluate the performance of our proposal, 30 problems are chosen as the test suite. Moreover, HNDE/2A is also used to solve two real-world problems. Compared with other algorithms, HNDE/2A yields better results in terms of the root ratio and the success rate with a less computational budget. [ABSTRACT FROM AUTHOR]

Optimization modeling of real-world application problems usually involves noise from various sources. Noisy optimization imposes challenges to optimization methods since the objective values can be different for multiple evaluations. In this article, we propose a novel online population size learning (OPL) technique of evolution strategies for handling noisy optimization problems. By re-evaluating a fraction of the candidates, we measure the strength of noise level of the re-evaluated candidate solutions and adapt the population size according to the noise level. The proposed OPL combines the advantages of both explicit averaging by re-evaluations and the implicit averaging by large population size and overcomes their limitations. We incorporate it with the covariance matrix adaptation evolution strategy (CMA-ES) and obtain OPL-CMA-ES. Compared with the existing noise handling technique, the proposed OPL is much simpler in both concepts and computation. We conduct comprehensive experiments to evaluate the algorithm’s performance on standard problems with Gaussian noise. We further evaluate the performance of OPL-CMA-ES on the black-box optimization benchmarks (BBOBs) noisy testbed, which is a standard platform for comparing black-box optimization algorithms, compared with the state-of-the-art noise-handling algorithms. The experimental results show that OPL-CMA-ES achieves remarkable performance and outperforms the compared variants. [ABSTRACT FROM AUTHOR]

The energy-efficient flexible job shop scheduling problem (FJSP) has attracted much attention in deterministic cases; however, uncertainty is seldom incorporated into energy-efficient FJSP and the neglecting of uncertainty will greatly diminish the application value of scheduling results. These make it necessary to handle uncertainty in the problem. In this study, energy-efficient fuzzy FJSP (EFFJSP) is considered and a bi-population evolutionary algorithm with feedback (FBEA) is proposed to minimize fuzzy makespan and fuzzy total energy consumption and maximize minimum agreement index. The computation of fuzzy energy consumption is given and four heuristics are proposed to produce the initial population. An effective method is presented to evaluate the quality of two populations and a feedback mechanism based on population quality is adopted to dynamically adjust the size of each population. A novel process of reproduction, crossover and mutation is developed based on feedback. An enhanced local search is also used to produce high-quality solutions. Extensive experiments are conducted to test the performance of FBEA. FBEA can provide promising results for EFFJSP. [ABSTRACT FROM AUTHOR]

Surrogate-assisted evolutionary algorithms (SAEAs) are well suited for computationally expensive optimization. However, most existing SAEAs only focus on low- or medium-dimensional expensive optimization. Thus, a novel SAEA for high-dimensional expensive optimization, denoted as surrogate-assisted multipopulation particle swarm optimizer (SA-MPSO), is proposed and fully investigated in this work. The proposed algorithm employs a parameter-free clustering technique, denoted as affinity propagation clustering, to generate several subswarms. A surrogate-assisted learning strategy-based particle swarm optimizer is proposed for guiding the search of each subswarm. Furthermore, a model management strategy is adapted to choose the promising particles for real fitness evaluations. Finally, a subswarm diversity maintenance scheme and a surrogate-based trust region local search technique are introduced to enhance both exploration and exploitation. The experimental results on commonly used benchmark test problems with dimensions varying from 30 to 100 and airfoil design problem have shown that SA-MPSO outperforms some state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Convergence, diversity and feasibility are three important issues when solving constrained multiobjective optimization problems (CMOPs). To deal with the balance among convergence, diversity and feasibility well, this article proposes a cooperative multiobjective evolutionary algorithm with propulsive population (CMOEA-PP) for solving CMOPs. CMOEA-PP has two populations, including propulsive population and normal population, and these two populations work cooperatively. Specifically, propulsive population focuses on convergence. Normal population gives priority to feasibility and is obligated to maintain diversity. To cross through the infeasible region and reach the Pareto front (PF), propulsive population does not consider constraints in the early stage and only considers constraints in the later stage. To further accelerate the speed of convergence, propulsive population only searches for corner solutions and center solutions, while normal population searches for the whole PF. As a result, propulsive population can cross through the infeasible region because of the lack of attention to feasibility. In addition, propulsive population also can guide and accelerate the convergence of the evolutionary process. Comprehensive experiment results on several sets of benchmark problems demonstrate that CMOEA-PP is better than existing state-of-the-art competitors. [ABSTRACT FROM AUTHOR]

Evolutionary games and population dynamics are finding increasing applications in design learning and control protocols for a variety of resource allocation problems. The implicit requirement for full communication has been the main limitation of the evolutionary game dynamic approach in engineering tasks with various information constraints. This article intends to build population games and dynamics with both static and dynamical graphical communication structures. To this end, we formulate a population game model with graphical strategy interactions and derive its corresponding population dynamics. In particular, we first introduce the concept of generalized Nash equilibria for population games with graphical strategy interactions, and establish the equivalence between the set of generalized Nash equilibria and the set of rest points of its distributed population dynamics. Furthermore, the conditions for convergence to generalized Nash equilibrium and particularly to Nash equilibrium are obtained for the distributed population dynamics with both static and dynamical graphical structures. These results provide a new approach to design distributed Nash equilibrium seeking algorithms for population games with both static and dynamical communication networks, and hence, expand the applicability of the population game dynamics in the design of learning and control protocols under distributed circumstances. [ABSTRACT FROM AUTHOR]

Solving constrained multiobjective optimization problems brings great challenges to an evolutionary algorithm, since it simultaneously requires the optimization among several conflicting objective functions and the satisfaction of various constraints. Hence, how to adjust the tradeoff between objective functions and constraints is crucial. In this article, we propose a dynamic selection preference-assisted constrained multiobjective differential evolutionary (DE) algorithm. In our approach, the selection preference of each individual is suitably switching from the objective functions to constraints as the evolutionary process. To be specific, the information of objective function, without considering any constraints, is extracted based on Pareto dominance to maintain the convergence and diversity by exploring the feasible and infeasible regions; while the information of constraint is used based on constrained dominance principle to promote the feasibility. Then, the tradeoff in these two kinds of information is adjusted dynamically, by emphasizing the utilization of objective functions at the early stage and focusing on constraints at the latter stage. Furthermore, to generate the promising offspring, two DE operators with distinct characteristics are selected as components of the search algorithm. Experiments on four test suites including 56 benchmark problems indicate that the proposed method exhibits superior or at least competitive performance, in comparison with other well-established methods. [ABSTRACT FROM AUTHOR]

The published stability criteria for impulsive neural networks are scale-free on time line, which is only appropriate for discrete or continuous ones. The issue of global exponential stability for impulsive delayed neural networks on time scales is analyzed by employing the convex combination method in this article. Several algebraic and linear matrix inequality conditions are proved by constructing impulse-dependent Lyapunov functionals and using timescale inequality techniques. Unlike the published works, impulsive control strategies can be designed by utilizing our theoretical results to stabilize delayed neural networks on time scales if they are unstable before introducing impulses. Sufficient criteria for global exponential stability in this article are derived based on the timescale theory, and they are applicable to discrete-time impulsive neural networks, their continuous-time analogues, and neural networks whose states are discrete at one time and continuous at another time. Four numerical examples are offered to demonstrate the effectiveness and superiority of our new theoretical results in the end. [ABSTRACT FROM AUTHOR]

A mixed-integer programming (MIP) problem contains not only constraints but also integer restrictions. Integer restrictions divide the feasible region defined by constraints into multiple discontinuous feasible parts with different sizes. Several popular methods (e.g., rounding and truncation) have been proposed to deal with integer restrictions. Although it is easy for these methods to generate an integer, they tend to converge to an integer which is located in a feasible part with a big size. If the optimal solution is not in this feasible part, they are very likely to converge to a local optimal solution due to the loss of diversity of the population. To overcome this shortcoming, a biobjective optimization-based two-phase method is proposed in this article. In the first phase, a measure function is designed to compute the degree that a solution violates integer restrictions. By employing this measure function as the second objective function and removing integer restrictions, a MIP problem is transformed into a constrained biobjective optimization problem (CBOP). It can be proven that the Pareto optimal solution of the transformed CBOP which satisfies integer restrictions is the optimal solution of the original MIP problem. To solve the transformed CBOP, a new comparison rule is designed. After the first phase, the population can approach the Pareto optimal solution which satisfies integer restrictions. Then, the second phase is implemented to enhance the convergence precision and obtain the optimal solution. In addition, we design 12 test problems to verify the effectiveness of the proposed method. The results demonstrate that the proposed method shows better performance against five state-of-the-art evolutionary algorithms for MIP. [ABSTRACT FROM AUTHOR]

Quantum-inspired differential evolution (QDE) is an evolutionary algorithm, which can effectively solve complex optimization problems. However, sometimes, it easily leads to premature convergence and low search ability and falls to local optima. To overcome these problems, based on the MSIQDE (improved QDE with multistrategies) algorithm, an enhanced MSIQDE algorithm based on mixing multiple strategies, namely, EMMSIQDE is proposed in this article. In the EMMSIQDE, a new differential mutation strategy of a difference vector is proposed to enhance the search ability and descent ability. Then, a new multipopulation mutation evolution mechanism is designed to ensure the relative independence of each subpopulation and the population diversity. The feasible solution space transformation strategy is used to achieve the optimal solution by mapping the quantum chromosome from a unit space to solution space. Finally, some multidimensional unimodal and multimodal functions are selected to demonstrate the optimization performance of EMMSIQDE. The results demonstrate that the EMMSIQDE is significantly better than the DE, QDE, QGA, and MSIQDE, and has better optimization ability, scalability, efficiency, and stability. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms and swarm intelligence algorithms have been widely used for constrained optimization problems for decades and numerous techniques for constraint handling have been proposed. The ${\varepsilon }$ -constrained method is a very effective one. In the literature, the ${\varepsilon }$ value was usually controlled via an exponential function, which is not competent for solving certain types of constrained optimization problems, e.g., whose global optima are located near the boundary of the feasible and infeasible regions. To solve this problem, this article proposes a new adaptive ${\varepsilon }$ control method and incorporate it into a basic differential evolution (DE) algorithm: (DE/rand/1/exp). Based on the information of constraint violation in the current population, the adaptive method controls the value of ${\varepsilon }$ through a simple heuristic rule. Compared with the traditional exponential function-based control methods, the proposed adaptive method can prevent the algorithm from being trapped into local optima while retaining the obtained near-optimal candidate solutions in the infeasible region for generating promising searching paths. Besides, we set the crossover rate (CR) as a more reasonable value for DE/rand/1/exp, which can enhance the efficiency significantly. The well-known 2006 IEEE Congress on Evolutionary Computation (CEC 2006) competition on real-parameter single-objective constrained optimization benchmark is adopted to evaluate the effectiveness of the proposed adaptive ${\varepsilon }$ -constrained DE. Fifteen constrained engineering optimization problems are collected from the literature to test the proposed algorithm. Moreover, the adaptive ${\varepsilon }$ control method is extended to an adaptive algorithm to solve the benchmark problems from CEC 2017. The comparison results confirm the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In brain storm optimization (BSO), the convergent operation utilizes a clustering strategy to group the population into multiple clusters, and the divergent operation uses this cluster information to generate new individuals. However, this mechanism is inefficient to regulate the exploration and exploitation search. This article first analyzes the main factors that influence the performance of BSO and then proposes an orthogonal learning framework to improve its learning mechanism. In this framework, two orthogonal design (OD) engines (i.e., exploration OD engine and exploitation OD engine) are introduced to discover and utilize useful search experiences for performance improvements. In addition, a pool of auxiliary transmission vectors with different features is maintained and their biases are also balanced by the OD decision mechanism. Finally, the proposed algorithm is verified on a set of benchmarks and is adopted to resolve the quantitative association rule mining problem considering the support, confidence, comprehensibility, and netconf. The experimental results show that the proposed approach is very powerful in optimizing complex functions. It not only outperforms previous versions of the BSO algorithm but also outperforms several famous OD-based algorithms. [ABSTRACT FROM AUTHOR]