Dynamic Multimodal Optimization Problems (DMMOPs) demand algorithms capable of swiftly locating and tracking multiple optimal solutions over time. The primary challenge lies in controlling the population diversity to facilitate effective exploration, all within the limitation of computational resources between consecutive environmental changes. In this article, we study the utilization of density information derived from both current and historical populations to enhance exploration. First, for each active sub-population, we construct a density landscape based on the distribution of concurrently active sub-populations and establish dominance relationships between candidate solutions in the sub-population based on density and fitness values, directing this sub-population toward exploring low-density promising areas. Then, for each converged sub-population, we construct a density landscape based on the distribution of sub-populations that have historically become extinct, guiding the restart of this sub-population in low-density unexploited areas. Finally, we develop a comprehensive framework of Density-Assisted Evolutionary Algorithm (DAEA), which encompasses density-assisted search and restart, also combined with initialization. Moreover, we employ prediction and memory strategies to enhance the performance of DAEA in dynamic environments. Notably, the algorithm relies on an external monitor to detect environmental changes and trigger the dynamic response strategy. DAEA is tested on the CEC’2022 dynamic multimodal optimization benchmark suite and is compared against several state-of-the-art dynamic multimodal optimization algorithms. The experimental results demonstrate the competitiveness of DAEA in handling DMMOPs. Additionally, experimental results from the berth allocation problem further confirm the applicability of DAEA to real-world dynamic multimodal optimization tasks.

This paper develops a new Tourist Route Planning (TRP) model by incorporating the entrance fees and the experience values of scenic spots, the travelling costs between scenic spots, and the budget of the tourist. Resultantly, the new TRP aims at finding an optimal route by maximizing the travelling experience value of the tourist with the constraint that the total cost of the route including the travelling costs and the spot entrance fees does not exceed the given budget. To effectively solve this new TRP, this paper adapts the five classical ant colony optimization algorithms (ACO), namely ant system (AS), elite AS (EAS), rank-based AS (RAS), max-min AS (MMAS), and ant colony system (ACS). To this end, this paper first introduces a new heuristic information measure by integrating the experience values and the entrance fees of the scenic spots, and the traveling costs between scenic spots. Further, a new local search strategy encompassing 2-opt and one spot insertion operator is designed to further improve the quality of the route under the budget constraint. Abundant experiments have been carried out on various TRP instances of three scales, namely small-scale, medium-scale, and large-scale, involving different numbers of scenic spots and different settings of budgets. The experimental results demonstrate that all the adapted five ACO algorithms are very effective for addressing the new TRP. Among them, RAS performs the best on small-scale TRP instances, and ACS obtains the best results on medium-scale TRP instances, while MMAS is the most effective one in addressing large-scale TRP instances.

Leading exemplars play significant roles in updating particles to seek optimal solutions for Particle Swarm Optimization (PSO). Along this road, this paper devises an Individual-level Dominant Exemplar Selection (IDES) framework for PSO, giving rise to a new PSO variant named IDESPSO. Specifically, instead of using their own personally best positions and the globally best position of the entire swarm to update particles, IDES first randomly chooses two different exemplars for each particle from all personally best positions. Then, it compares the two selected exemplars with the personally best position of this particle. Based on the comparison results, different updating strategies are utilized to update different particles. This method notably enriches the variety among the chosen leading exemplars, thereby substantially bolstering the updating diversity of particles. Under IDES, this paper further develops seven selection strategies to help IDESPSO pick up promising exemplars for particles to evolve. Specifically, the seven selection schemes are the roulette wheel selection, the tournament selection, and five hybridizations of two basic models. A series of experiments have been undertaken on the universally used CEC2014 problem suite to compare IDESPSO with the seven selection schemes and two classic PSOs. The empirical results show that IDESPSO paired with anyone of the seven selection methods, markedly outperforms the two classical PSO variants, highlighting its significant performance.

Cooperative coevolution (CC) is a paradigm equipped with the divide-and-conquer strategy for solving large-scale optimization problems (LSOPs). Currently, the computational resource allocation schemes of most CC could be divided into two categories, namely, equal allocation to all subproblems and preference allocation to the subproblems with a large contribution. However, the difficult subproblems are not carefully considered by the existing computational resource allocation schemes. For these subproblems, the investment of computational resources cannot quickly improve the fitness value, which leads to their small early contribution and being neglected. In this article, we comprehensively analyze the imbalanced nature of the subproblems from their difficulty and contribution in LSOPs. First, we propose a method to quantify the optimization difficulty of the problems during the evolution process, which considers both the difficulty of the fitness landscape and the behaviors of the optimization algorithm. Then, we propose a novel both difficulty and contribution-based CC framework, called DCCC, which encourages the allocation of the computational resources to more contributing and more difficult subproblems. DCCC is tested on the CEC’2010 and CEC’2013 large-scale optimization benchmarks, and is compared with several typical CC frameworks and state-of-the-art large-scale optimization algorithms. The experimental results demonstrate that DCCC is very competitive.

As a special class of multiobjective optimization problems (MOPs), multiparty multiobjective optimization prob-lems (MPMOPs) widely exist in real-world applications. In MPMOPs, there are multiple decision makers (DMs) concerning multiple different conflicting objectives. The goal of solving MPMOPs is to catch the best solutions satisfying all DMs as far as possible. To our best knowledge, there is little attention on solving MPMOPs, and only two optimization algorithms, i.e., OptMPNDS and OptMPNDS2, are proposed. These two algorithms are both based on non-dominated sorting genetic algorithm II (NSGA-II). However, there is no algorithm pro-posed from the decomposition perspective to solve MPMOPs. Multiobjective evolutionary algorithm based on decomposition (MOEA/D) is a popular multiobjective evolutionary optimization algorithm for MOPs. In this paper, we embed the party-by-party strategy into MOEA/D and propose the novel optimization algorithm MOEA/D-MP to solve MPMOPs. The experimental results on the benchmarks have demonstrated the effectiveness of MOEA/D-MP.

Multimodal optimization problems (MMOPs) are common problems with multiple optimal solutions. In this article, a novel method of population division, called nearest-better-neighbor clustering (NBNC), is proposed, which can reduce the risk of more than one species locating the same peak. The key idea of NBNC is to construct the raw species by linking each individual to the better individual within the neighborhood, and the final species of the population is formulated by merging the dominated raw species. Furthermore, a novel algorithm is proposed called NBNC-PSO-ES, which combines the advantages of better exploration in particle swarm optimization (PSO) and stronger exploitation in the covariance matrix adaption evolution strategy (CMA-ES). For the purpose of demonstrating the performance of NBNC-PSO-ES, several state-of-the-art algorithms are adopted for comparisons and tested using typical benchmark problems. The experimental results show that NBNC-PSO-ES performs better than other algorithms.

Nearest-Better Clustering (NBC) is an emergent niching technique in Swarm and Evolutionary Computation for optimization, which does not need to fix the number or radius of clusters in advance. The key idea of NBC is to first link each individual to its nearest better neighbor to form a spanning tree of all individuals in the population, and then partition all individuals into clusters by deleting the longer edges in the spanning tree. In this paper, a survey on the Nearest-Better Clustering algorithms and applications in multimodal and dynamic optimization is provided. First, the basic NBC algorithm is introduced. Second, the improvements of the basic NBC are detailed. Third, multimodal and dynamic optimization algorithms powered by NBC are enlisted and discussed.

Multimodal optimization problems (MMOPs) are common in real-world applications and involve identifying multiple optimal solutions for decision makers to choose from. The core requirement for dealing with such problems is to balance the ability of exploration in the global space and exploitation in the multiple optimal areas. In this paper, based on the differential evolution (DE), we propose a novel algorithm focusing on the formulation, balance, and keypoint of species for MMOPs, called FBK-DE. First, nearest-better clustering (NBC) is used to divide the population into multiple species with minimum size limitations. Second, to avoid placing too many individuals into one species, a species balance strategy is proposed to adjust the size of each species. Third, two keypoint-based mutation operators named DE/keypoint/1 and DE/keypoint/2 are proposed to evolve each species together with traditional mutation operators. The experimental results of FBK-DE on 20 benchmark functions are compared with 15 state-of-the-art multimodal optimization algorithms. The comparisons show that the proposed FBK-DE performs competitively with these algorithms.

Large-scale optimization problems and constrained optimization problems have attracted considerable attention in the swarm and evolutionary intelligence communities and exemplify two common features of real problems, i.e., a large scale and constraint limitations. However, only a little work on solving large-scale continuous constrained optimization problems exists. Moreover, the types of benchmarks proposed for large-scale continuous constrained optimization algorithms are not comprehensive at present. In this article, first, a constraint-objective cooperative coevolution (COCC) framework is proposed for large-scale continuous constrained optimization problems, which is based on the dual nature of the objective and constraint functions: modular and imbalanced components. The COCC framework allocates the computing resources to different components according to the impact of objective values and constraint violations. Second, a benchmark for large-scale continuous constrained optimization is presented, which takes into account the modular nature, as well as both imbalanced and overlapping characteristics of components. Finally, three different evolutionary algorithms are embedded into the COCC framework for experiments, and the experimental results show that COCC performs competitively.

Some real-world optimization problems involve multiple decision makers holding different positions, each of whom has multiple conflicting objectives. These problems are defined as multiparty multiobjective optimization problems (MPMOPs). Although evolutionary multiobjective optimization has been widely studied for many years, little attention has been paid to multiparty multiobjective optimization in the field of evolutionary computation. In this paper, a class of MPMOPs, that is, MPMOPs having common Pareto optimal solutions, is addressed. A benchmark for MPMOPs, obtained by modifying an existing dynamic multiobjective optimization benchmark, is provided, and a multiparty multiobjective evolutionary algorithm to find the common Pareto optimal set is proposed. The results of experiments conducted using the benchmark show that the proposed multiparty multiobjective evolutionary algorithm is effective.

Deep neural networks (DNNs) are used in various domains, such as image classification, natural language processing and face recognition, etc. However, the presence of malicious examples, generated by specific methods, could result in DNNs misclassification. Such maliciously modified examples are called adversarial examples. So far, most work about adversarial examples mainly focuses on the multi-class classification tasks, and only a little work has been done in the field of multi-label classification.In this study, we have proposed a novel algorithm that generates effective multi-label adversarial examples by solving a linear programming problem (MLA-LP). We minimize the l∞norm of distortion while constraining the changes in the label loss of the example after being perturbed. Then, we transform this constrained optimization problem into a linear programming problem for reducing the time cost. In comparison to the existing multi-label classification model attack algorithms, the attack performance of the proposed MLA-LP is found to be competitive, and the adversarial examples generated by MLA-LP have significantly smaller distortions.

In evolutionary multi-objective optimization, the results generated by an evolutionary algorithm usually contain an approximation, as good as possible, of the entire Pareto-optimal front. However, sometimes the number of Pareto-optimal solutions may be so large that the decision maker (DM) is incapable of manipulating or understanding them. Methods for considering only the Pareto-optimal solutions that the DM prefers indeed constitute a hot research topic in the evolutionary computation field. In this paper, we introduce a new dominance relation called $\hat g$-dominance, which is an improved version of the g-dominance relation and can be easily implemented in traditional multi-objective evolutionary algorithms. In this work, the proposed $\hat g$-dominance is implemented in NSGA-II. Our experimental results show the effectiveness of $\hat g$-NSGA-II with respect to the original g-NSGA-II.

Both Particle Swarm Optimization (PSO) and Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) exhibit good performance when solving global optimization problems. However, PSO could be misled by historical information and falls into a local optimum. Further, CMA-ES cannot fully utilize global information. Therefore, in this paper, we first propose a time-window PSO (TW-PSO) as an improvement of PSO, which could enhance the exploration ability of the algorithm. Second, we design a hybrid algorithm of TW-PSO, PSO and CMA-ES, i.e., HTPC, which combines the advantages of TW-PSO, PSO, and CMA-ES. We test HTPC on single-objective optimization problems from the CEC-2019 100-Digit Challenge, and the experimental results show that the performance of HTPC is competitive.