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It is known that many-objective optimization problems (MaOPs) often face the difficulty of maintaining good diversity and convergence in the search process due to the high-dimensional objective space. To address this issue, this article proposes a novel multiobjective framework for many-objective optimization (Mo4Ma), which transforms the many-objective space into multiobjective space. First, the many objectives are transformed into two indicative objectives of convergence and diversity. Second, a clustering-based sequential selection strategy is put forward in the transformed multiobjective space to guide the evolutionary search process. Specifically, the selection is circularly performed on the clustered subpopulations to maintain population diversity. In each round of selection, solutions with good performance in the transformed multiobjective space will be chosen to improve the overall convergence. The Mo4Ma is a generic framework that any type of evolutionary computation algorithm can incorporate compatibly. In this article, the differential evolution (DE) is adopted as the optimizer in the Mo4Ma framework, thus resulting in an Mo4Ma-DE algorithm. Experimental results show that the Mo4Ma-DE algorithm can obtain well-converged and widely distributed Pareto solutions along with the many-objective Pareto sets of the original MaOPs. Compared with seven state-of-the-art MaOP algorithms, the proposed Mo4Ma-DE algorithm shows strong competitiveness and general better performance. [ABSTRACT FROM AUTHOR]

This article presents a rough-to-fine evolutionary multiobjective optimization algorithm based on the decomposition for solving problems in which the solutions are initially far from the Pareto-optimal set. Subsequently, a tree is constructed by a modified $k$ -means algorithm on $N$ uniform weight vectors, and each node of the tree contains a weight vector. Each node is associated with a subproblem with the help of its weight vector. Consequently, a subproblem tree can be established. It is easy to find that the descendant subproblems are refinements of their ancestor subproblems. The proposed algorithm approaches the Pareto front (PF) by solving a few subproblems in the first few levels to obtain a rough PF and gradually refining the PF by involving the subproblems level-by-level. This strategy is highly favorable for solving problems in which the solutions are initially far from the Pareto set. Moreover, the proposed algorithm has lower time complexity. Theoretical analysis shows the complexity of dealing with a new candidate solution is $\mathcal {O}(M \log N)$ , where $M$ is the number of objectives. Empirical studies demonstrate the efficacy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A mixed-integer programming (MIP) problem contains both constraints and integer restrictions. Integer restrictions divide the feasible region defined by constraints into multiple discontinuous feasible parts. In particular, the number of discontinuous feasible parts will drastically increase with the increase of the number of integer decision variables and/or the size of the candidate set of each integer decision variable. Due to the fact that the optimal solution is located in one of the discontinuous feasible parts, it is a challenging task to solve a MIP problem. This article presents a cutting and repulsion-based evolutionary framework (called CaR) to solve MIP problems. CaR includes two main strategies: 1) the cutting strategy and 2) the repulsion strategy. In the cutting strategy, an additional constraint is constructed based on the objective function value of the best individual found so far, the aim of which is to continuously cut unpromising discontinuous feasible parts. As a result, the probability of the population entering a wrong discontinuous feasible part can be decreased. In addition, in the repulsion strategy, once it has been detected that the population has converged to a discontinuous feasible part, the population will be reinitialized. Moreover, a repulsion function is designed to repulse the previously explored discontinuous feasible parts. Overall, the cutting strategy can significantly reduce the number of discontinuous feasible parts and the repulsion strategy can probe the remaining discontinuous feasible parts. Sixteen test problems developed in this article and two real-world cases are used to verify the effectiveness of CaR. The results demonstrate that CaR performs well in solving MIP problems. [ABSTRACT FROM AUTHOR]

This article surveys the interdisciplinary research of neuroscience, network science, and dynamic systems, with emphasis on the emergence of brain-inspired intelligence. To replicate brain intelligence, a practical way is to reconstruct cortical networks with dynamic activities that nourish the brain functions, instead of using only artificial computing networks. The survey provides a complex network and spatiotemporal dynamics (abbr. network dynamics) perspective for understanding the brain and cortical networks and, furthermore, develops integrated approaches of neuroscience and network dynamics toward building brain-inspired intelligence with learning and resilience functions. Presented are fundamental concepts and principles of complex networks, neuroscience, and hybrid dynamic systems, as well as relevant studies about the brain and intelligence. Other promising research directions, such as brain science, data science, quantum information science, and machine behavior are also briefly discussed toward future applications. [ABSTRACT FROM AUTHOR]

Constrained multiobjective optimization problems (CMOPs) involve both conflicting objective functions and various constraints. Due to the presence of constraints, CMOPs’ Pareto-optimal solutions are very likely lying on constraint boundaries. The experience from the constrained single-objective optimization has shown that to quickly obtain such an optimal solution, the search should surround the boundary of the feasible region from both the feasible and infeasible sides. In this article, we extend this idea to cope with CMOPs and, accordingly, we propose a novel constrained multiobjective evolutionary algorithm with bidirectional coevolution, called BiCo. BiCo maintains two populations, that is: 1) the main population and 2) the archive population. To update the main population, the constraint-domination principle is equipped with an NSGA-II variant to move the population into the feasible region and then to guide the population toward the Pareto front (PF) from the feasible side of the search space. While for updating the archive population, a nondominated sorting procedure and an angle-based selection scheme are conducted in sequence to drive the population toward the PF within the infeasible region while maintaining good diversity. As a result, BiCo can get close to the PF from two complementary directions. In addition, to coordinate the interaction between the main and archive populations, in BiCo, a restricted mating selection mechanism is developed to choose appropriate mating parents. Comprehensive experiments have been conducted on three sets of CMOP benchmark functions and six real-world CMOPs. The experimental results suggest that BiCo can obtain quite competitive performance in comparison to eight state-of-the-art-constrained multiobjective evolutionary optimizers. [ABSTRACT FROM AUTHOR]

Evolutionary multitask learning has achieved great success due to its ability to handle multiple tasks simultaneously. However, it is rarely used in the hyperheuristic domain, which aims at generating a heuristic for a class of problems rather than solving one specific problem. The existing multitask hyperheuristic studies only focus on heuristic selection, which is not applicable to heuristic generation. To fill the gap, we propose a novel multitask generative hyperheuristic approach based on genetic programming (GP) in this article. Specifically, we introduce the idea in evolutionary multitask learning to GP hyperheuristics with a suitable evolutionary framework and individual selection pressure. In addition, an origin-based offspring reservation strategy is developed to maintain the quality of individuals for each task. To verify the effectiveness of the proposed approach, comprehensive empirical studies have been conducted on the homogeneous and heterogeneous multitask dynamic flexible job shop scheduling. The results show that the proposed algorithm can significantly improve the quality of scheduling heuristics for each task in all the examined scenarios. In addition, the evolved scheduling heuristics verify the mutual help among the tasks in a multitask scenario. [ABSTRACT FROM AUTHOR]

Both objective optimization and constraint satisfaction are crucial for solving constrained multiobjective optimization problems, but the existing evolutionary algorithms encounter difficulties in striking a good balance between them when tackling complex feasible regions. To address this issue, this article proposes a two-stage evolutionary algorithm, which adjusts the fitness evaluation strategies during the evolutionary process to adaptively balance objective optimization and constraint satisfaction. The proposed algorithm can switch between the two stages according to the status of the current population, enabling the population to cross the infeasible region and reach the feasible regions in one stage, and to spread along the feasible boundaries in the other stage. Experimental studies on four benchmark suites and three real-world applications demonstrate the superiority of the proposed algorithm over the state-of-the-art algorithms, especially on problems with complex feasible regions. [ABSTRACT FROM AUTHOR]

The clique partitioning problem (CPP) of an edge-weighted complete graph is to partition the vertex set $V$ into $k$ disjoint subsets such that the sum of the edge weights within all cliques induced by the subsets is as large as possible. The problem has a number of practical applications in areas, such as data mining, engineering, and bioinformatics, and is, however, computationally challenging. To solve this NP-hard problem, we propose the first evolutionary algorithm that combines a dedicated merge–divide crossover operator to generate offspring solutions and an effective simulated annealing-based local optimization procedure to find high-quality local optima. The extensive experiments on three sets of 94 benchmark instances (including two sets of 63 classical benchmark instances and one new set of 31 large benchmark) show a remarkable performance of the proposed approach compared to the state-of-the-art methods. We analyze the key algorithmic ingredients to shed light on their impacts on the performance of the algorithm. The algorithm and its available source code can benefit people working on practical problems related to CPP. [ABSTRACT FROM AUTHOR]

In the past several years, it has become apparent that the effectiveness of Pareto-dominance-based multiobjective evolutionary algorithms deteriorates progressively as the number of objectives in the problem, given by $M$ , grows. This is mainly due to the poor discriminability of Pareto optimality in many-objective spaces (typically $M\geq 4$). As a consequence, research efforts have been driven in the general direction of developing solution ranking methods that do not rely on Pareto dominance (e.g., decomposition-based techniques), which can provide sufficient selection pressure. However, it is still a nontrivial issue for many existing non-Pareto-dominance-based evolutionary algorithms to deal with unknown irregular Pareto front shapes. In this article, a new many-objective evolutionary algorithm based on the generalization of Pareto optimality (GPO) is proposed, which is simple, yet effective, in addressing many-objective optimization problems. The proposed algorithm used an “($M-1$) + 1” framework of GPO dominance, ($M-1$)-GPD for short, to rank solutions in the environmental selection step, in order to promote convergence and diversity simultaneously. To be specific, we apply $M$ symmetrical cases of ($M-1$)-GPD, where each enhances the selection pressure of $M-1$ objectives by expanding the dominance area of solutions, while remaining unchanged for the one objective left out of that process. Experiments demonstrate that the proposed algorithm is very competitive with the state-of-the-art methods to which it is compared, on a variety of scalable benchmark problems. Moreover, experiments on three real-world problems have verified that the proposed algorithm can outperform the others on each of these problems. [ABSTRACT FROM AUTHOR]

It is very difficult to locate multiple global optimal solutions (GOSs) of multimodal optimization problems (MMOPs). To deal with this issue, a penalty-based multimodal optimization differential evolution (DE), called PMODE, is developed in this article. In PMODE, a penalty strategy with a dynamic penalty radius is constructed to solve MMOPs. An elite selection mechanism is designed to identify and select elite solutions. The neighboring areas of these elite solutions are penalized. PMODE uses a popular DE variant—JADE as its search engine. The proposed PMODE is compared with several other state-of-the-art multimodal optimization algorithms on 20 MMOPs used in the IEEE CEC2013 special session. The experimental results show that PMODE performs better than other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Feature selection (FS) is an important data preprocessing technique in data mining and machine learning, which aims to select a small subset of information features to increase the performance and reduce the dimensionality. Particle swarm optimization (PSO) has been successfully applied to FS due to being efficient and easy to implement. However, most of the existing PSO-based FS methods face the problems of trapping into local optima and computationally expensive high-dimensional data. Multifactorial optimization (MFO), as an effective evolutionary multitasking paradigm, has been widely used for solving complex problems through implicit knowledge transfer between related tasks. Inspired by MFO, this study proposes a novel PSO-based FS method to solve high-dimensional classification via information sharing between two related tasks generated from a dataset. To be specific, two related tasks about the target concept are established by evaluating the importance of features. A new crossover operator, called assortative mating, is applied to share information between these two related tasks. In addition, two mechanisms, which are variable-range strategy and subset updating mechanism, are also developed to reduce the search space and maintain the diversity of the population, respectively. The results show that the proposed FS method can achieve higher classification accuracy with a smaller feature subset in a reasonable time than the state-of-the-art FS methods on the examined high-dimensional classification problems. [ABSTRACT FROM AUTHOR]

Multimodal optimization problems (MMOPs) require algorithms to locate multiple optima simultaneously. When using evolutionary algorithms (EAs) to deal with MMOPs, an intuitive idea is to divide the population into several small “niches,” where different niches focus on locating different optima. These population partition strategies are called “niching” techniques, which have been frequently used for MMOPs. The algorithms for simultaneously locating multiple optima of MMOPs are called multimodal algorithms. However, many multimodal algorithms still face the difficulty of population partition since most of the niching techniques involve the sensitive niching parameters. Considering this issue, in this article, we propose a parameter-free niching method based on adaptive estimation distribution (AED) and develop a distributed differential evolution (DDE) algorithm, which is called AED-DDE, for solving MMOPs. In AED-DDE, each individual finds its own appropriate niche size to form a niche and acts as an independent unit to find a global optimum. Therefore, we can avoid the difficulty of population partition and the sensitivity of niching parameters. Different niches are co-evolved by using the master–slave multiniche distributed model. The multiniche co-evolution mechanism can improve the population diversity for fully exploring the search space and finding more global optima. Moreover, the AED-DDE algorithm is further enhanced by a probabilistic local search (PLS) to refine the solution accuracy. Compared with other multimodal algorithms, even the winner of CEC2015 multimodal competition, the comparison results fully demonstrate the superiority of AED-DDE. [ABSTRACT FROM AUTHOR]

Evolutionary multitasking (EMT) is a newly emerging research topic in the community of evolutionary computation, which aims to improve the convergence characteristic across multiple distinct optimization tasks simultaneously by triggering knowledge transfer among them. Unfortunately, most of the existing EMT algorithms are only capable of boosting the optimization performance for homogeneous problems which explicitly share the same (or similar) fitness landscapes. Seldom efforts have been devoted to generalize the EMT for solving heterogeneous problems. A few preliminary studies employ domain adaptation techniques to enhance the transferability between two distinct tasks. However, almost all of these methods encounter a severe issue which is the so-called degradation of intertask mapping. Keeping this in mind, a novel rank loss function for acquiring a superior intertask mapping is proposed in this article. In particular, with an evolutionary-path-based representation model for optimization instance, an analytical solution of affine transformation for bridging the gap between two distinct problems is mathematically derived from the proposed rank loss function. It is worth mentioning that the proposed mapping-based transferability enhancement technique can be seamlessly embedded into an EMT paradigm. Finally, the efficacy of our proposed method against several state-of-the-art EMTs is verified experimentally on a number of synthetic multitasking and many-tasking benchmark problems, as well as a practical case study. [ABSTRACT FROM AUTHOR]

Clustering, as an important part of data mining, is inherently a challenging problem. This article proposes a differential evolution algorithm with adaptive niching and ${k}$ -means operation (denoted as DE_ANS_AKO) for partitional data clustering. Within the proposed algorithm, an adaptive niching scheme, which can dynamically adjust the size of each niche in the population, is devised and integrated to prevent premature convergence of evolutionary search, thus appropriately searching the space to identify the optimal or near-optimal solution. Furthermore, to improve the search efficiency, an adaptive ${k}$ -means operation has been designed and employed at the niche level of population. The performance of the proposed algorithm has been evaluated on synthetic as well as real datasets and compared with related methods. The experimental results reveal that the proposed algorithm is able to reliably and efficiently deliver high quality clustering solutions and generally outperforms related methods implemented for comparisons. [ABSTRACT FROM AUTHOR]

Multipopulation methods are highly effective in solving dynamic optimization problems. Three factors affect this significantly: 1) the exclusion mechanisms to avoid the convergence to the same peak by multiple subpopulations; 2) the resource allocation mechanism that assigns the computational resources to the subpopulations; and 3) the control mechanisms to adaptively adjust the number of subpopulations by considering the number of optima and available computational resources. In the existing exclusion mechanisms, when the distance (i.e., the distance between their best found positions) between two subpopulations becomes less than a predefined threshold, the inferior one will be removed/reinitialized. However, this leads to incapability of algorithms in covering peaks/optima that are closer than the threshold. Moreover, despite the importance of resource allocation due to the limited available computational resources between environmental changes, it has not been well studied in the literature. Finally, the number of subpopulations should be adapted to the number of optima. However, in most existing adaptive multipopulation methods, there is no predefined upper bound for generating subpopulations. Consequently, in problems with large numbers of peaks, they can generate too many subpopulations sharing limited computational resources. In this article, a multipopulation framework is proposed to address the aforementioned issues by using three adaptive approaches: 1) subpopulation generation; 2) double-layer exclusion; and 3) computational resource allocation. The experimental results demonstrate the superiority of the proposed framework over several peer approaches in solving various benchmark problems. [ABSTRACT FROM AUTHOR]

The artificial colony (ABC) algorithm shows a relatively powerful exploration search capability but is constrained by the curse of dimensionality, especially on nonseparable functions, where its convergence speed slows dramatically. In this article, based on an analysis of the difference between updating mechanisms that include both all-variable and one-variable updating mechanisms, we find that when equipped with the former strategy, the algorithm rapidly converges to an optimal region, while with the latter strategy, it searches the solution space thoroughly. To utilize multivariable and one-variable updating mechanisms on nonseparable and separable functions, respectively, we embed an improved linkage identification strategy into the ABC by detecting the linkage between variables more effectively. Then, we propose three common strategies for ABC to improve its performance. First, a new approach that considers the historic experiences of the population is proposed to balance exploration and exploitation. Second, a new strategy for initializing scout bees is used to reduce the number of function evaluations. Finally, the individual with the worst performance is updated with a defined probability on multiple dimensions instead of one dimension, causing it to follow the population steps on nonseparable functions. This article is the first to propose all these concepts, which could be adopted for other ABC variants. The effectiveness of our algorithm is validated through basic, CEC2010, CEC2013, and CEC2014 functions and real-world problems. [ABSTRACT FROM AUTHOR]

Most reference vector-based decomposition algorithms for solving multiobjective optimization problems may not be well suited for solving problems with irregular Pareto fronts (PFs) because the distribution of predefined reference vectors may not match well with the distribution of the Pareto-optimal solutions. Thus, the adaptation of the reference vectors is an intuitive way for decomposition-based algorithms to deal with irregular PFs. However, most existing methods frequently change the reference vectors based on the activeness of the reference vectors within specific generations, slowing down the convergence of the search process. To address this issue, we propose a new method to learn the distribution of the reference vectors using the growing neural gas (GNG) network to achieve automatic yet stable adaptation. To this end, an improved GNG is designed for learning the topology of the PFs with the solutions generated during a period of the search process as the training data. We use the individuals in the current population as well as those in previous generations to train the GNG to strike a balance between exploration and exploitation. Comparative studies conducted on popular benchmark problems and a real-world hybrid vehicle controller design problem with complex and irregular PFs show that the proposed method is very competitive. [ABSTRACT FROM AUTHOR]

Maintaining a balance between convergence and diversity is particularly crucial in evolutionary multiobjective optimization. Recently, a novel dominance relation called “strengthened dominance relation” (SDR) is proposed, which outperforms the existing dominance relations in balancing convergence and diversity. In this article, two points that influence the performance of SDR are studied and a new dominance relation, which is mainly based on SDR, is proposed (CSDR). An adaptation strategy is presented to dynamically adjust the dominance relation according to the current generation number. The CSDR is embedded into NSGA-II to substitute the Pareto dominance, labeled as NSGA-II/CSDR. The performance of our proposed method is validated by comparing it with five state-of-the-art algorithms on commonly used benchmark problems. NSGA-II/CSDR outperforms other algorithms in the most test instances considering both convergence and diversity. [ABSTRACT FROM AUTHOR]

This article proposes a simple yet effective multiobjective evolutionary algorithm (EA) for dealing with problems with irregular Pareto front. The proposed algorithm does not need to deal with the issues of predefining weight vectors and calculating indicators in the search process. It is mainly based on the thought of adaptively selecting multiple promising search directions according to crowdedness information in local objective spaces. Concretely, the proposed algorithm attempts to dynamically delete an individual of poor quality until enough individuals survive into the next generation. In this environmental selection process, the proposed algorithm considers two or three individuals in the most crowded area, which is determined by the local information in objective space, according to a probability selection mechanism, and deletes the worst of them from the current population. Thus, these surviving individuals are representative of promising search directions. The performance of the proposed algorithm is verified and compared with seven state-of-the-art algorithms [including four general multi/many-objective EAs and three algorithms specially designed for dealing with problems with irregular Pareto-optimal front (PF)] on a variety of complicated problems with different numbers of objectives ranging from 2 to 15. Empirical results demonstrate that the proposed algorithm has a strong competitiveness power in terms of both the performance and the algorithm compactness, and it can well deal with different types of problems with irregular PF and problems with different numbers of objectives. [ABSTRACT FROM AUTHOR]

Performance of multi/many-objective evolutionary algorithms (MOEAs) based on decomposition is highly impacted by the Pareto front (PF) shapes of multi/many-objective optimization problems (MOPs), as their adopted weight vectors may not properly fit the PF shapes. To avoid this mismatch, some MOEAs treat solutions as weight vectors to guide the evolutionary search, which can adapt to the target MOP’s PF automatically. However, their performance is still affected by the similarity metric used to select weight vectors. To address this issue, this article proposes a fuzzy decomposition-based MOEA. First, a fuzzy prediction is designed to estimate the population’s shape, which helps to exactly reflect the similarities of solutions. Then, ${N}$ least similar solutions are extracted as weight vectors to obtain ${N}$ constrained fuzzy subproblems (${N}$ is the population size), and accordingly, a shared weight vector is calculated for all subproblems to provide a stable search direction. Finally, the corner solution for each of ${m}$ least similar subproblems (${m}$ is the objective number) is preserved to maintain diversity, while one solution having the best aggregated value on the shared weight vector is selected for each of the remaining subproblems to speed up convergence. When compared to several competitive MOEAs in solving a variety of test MOPs, the proposed algorithm shows some advantages at fitting their different PF shapes. [ABSTRACT FROM AUTHOR]

The multidimensional knapsack problem (MKP) is a well-known combinatorial optimization problem with many real-life applications. In this article, a memetic algorithm based on probability learning (MA/PL) is proposed to solve MKP. The main highlights of this article are two-fold: 1) problem-dependent heuristics for MKP and 2) a novel framework of MA/PL. For the problem-dependent heuristics, we first propose two kinds of logarithmic utility functions (LUFs) based on the special structure of MKP, in which the profit value and weight vector of each item are considered simultaneously. Then, LUFs are applied to effectively guide the repair operator for infeasible solutions and the local search operator. For the framework of MA/PL, we propose two problem-dependent probability distributions to extract the special knowledge of MKP, that is, the marginal probability distribution (MPD) of each item and the joint probability distribution (JPD) of two conjoint items. Next, learning rules for MPD and JPD, which borrow ideas from competitive learning and binary Markov chain, are proposed. Thereafter, we generate MA/PL’s offspring by integrating MPD and JPD, such that the univariate probability information of each item as well as the dependency of conjoint items can be sufficiently used. Results of experiments on 179 benchmark instances and a real-life case study demonstrate the effectiveness and practical values of the proposed MKP. [ABSTRACT FROM AUTHOR]

Multivariate time-series prediction is a challenging research topic in the field of time-series analysis and modeling, and is continually under research. The echo state network (ESN), a type of efficient recurrent neural network, has been widely used in time-series prediction, but when using ESN, two crucial problems have to be confronted: 1) how to select the optimal subset of input features and 2) how to set the suitable parameters of the model. To solve this problem, the modified biogeography-based optimization ESN (MBBO-ESN) system is proposed for system modeling and multivariate time-series prediction, which can simultaneously achieve feature subset selection and model parameter optimization. The proposed MBBO algorithm is an improved evolutionary algorithm based on biogeography-based optimization (BBO), which utilizes an $S$ -type population migration rate model, a covariance matrix migration strategy, and a Lévy distribution mutation strategy to enhance the rotation invariance and exploration ability. Furthermore, the MBBO algorithm cannot only optimize the key parameters of the ESN model but also uses a hybrid-metric feature selection method to remove the redundancies and distinguish the importance of the input features. Compared with the traditional methods, the proposed MBBO-ESN system can discover the relationship between the input features and the model parameters automatically and make the prediction more accurate. The experimental results on the benchmark and real-world datasets demonstrate that MBBO outperforms the other traditional evolutionary algorithms, and the MBBO-ESN system is more competitive in multivariate time-series prediction than other classic machine-learning models. [ABSTRACT FROM AUTHOR]

In contrast to the traditional single-tasking evolutionary algorithms, evolutionary multitasking (EMT) travels in the search space of multiple optimization tasks simultaneously. Through sharing knowledge across the tasks, EMT is able to enhance solving the optimization tasks. However, if knowledge transfer is not properly carried out, the performance of EMT might become unsatisfactory. To address this issue and improve the quality of knowledge transfer among the tasks, a novel multiobjective EMT algorithm based on subspace alignment and self-adaptive differential evolution (DE), namely, MOMFEA-SADE, is proposed in this article. Particularly, a mapping matrix obtained by subspace learning is used to transform the search space of the population and reduce the probability of negative knowledge transfer between tasks. In addition, DE characterized by a self-adaptive trial vector generation strategy is introduced to generate promising solutions based on previous experiences. The experimental results on multiobjective multi/many-tasking optimization test suites show that MOMFEA-SADE is superior or comparable to other state-of-the-art EMT algorithms. MOMFEA-SADE also won the Competition on Evolutionary Multitask Optimization (the multitask multiobjective optimization track) within IEEE 2019 Congress on Evolutionary Computation. [ABSTRACT FROM AUTHOR]

Population synthesis is the foundation of the agent-based social simulation. Current approaches mostly consider basic population and households, rather than other social organizations. This article starts with a theoretical analysis of the iterative proportional updating (IPU) algorithm, a representative method in this field, and then gives an extension to consider more social organization types. The IPU method, for the first time, proves to be unable to converge to an optimal population distribution that simultaneously satisfies the constraints from individual and household levels. It is further improved to a bilevel optimization, which can solve such a problem and include more than one type of social organization. Numerical simulations, as well as population synthesis using actual Chinese nationwide census data, support our theoretical conclusions and indicate that our proposed bilevel optimization can both synthesize more social organization types and get more accurate results. [ABSTRACT FROM AUTHOR]

In recent years, dynamic multiobjective optimization problems (DMOPs) have drawn increasing interest. Many dynamic multiobjective evolutionary algorithms (DMOEAs) have been put forward to solve DMOPs mainly by incorporating diversity introduction or prediction approaches with conventional multiobjective evolutionary algorithms. Maintaining a good balance of population diversity and convergence is critical to the performance of DMOEAs. To address the above issue, a DMOEA based on decision variable classification (DMOEA-DVC) is proposed in this article. DMOEA-DVC divides the decision variables into two and three different groups in static optimization and changes response stages, respectively. In static optimization, two different crossover operators are used for the two decision variable groups to accelerate the convergence while maintaining good diversity. In change response, DMOEA-DVC reinitializes the three decision variable groups by maintenance, prediction, and diversity introduction strategies, respectively. DMOEA-DVC is compared with the other six state-of-the-art DMOEAs on 33 benchmark DMOPs. The experimental results demonstrate that the overall performance of the DMOEA-DVC is superior or comparable to that of the compared algorithms. [ABSTRACT FROM AUTHOR]

Generally, decomposition-based evolutionary algorithms in many-objective optimization (MaOEA/Ds) have widely used reference vectors (RVs) to provide search directions and maintain diversity. However, their performance is highly affected by the matching degree on the shapes of the RVs and the Pareto front (PF). To address this problem, this article proposes a self-guided RV (SRV) strategy for MaOEA/Ds, aiming to extract RVs from the population using a modified ${k}$ -means clustering method. To give a promising clustering result, an angle-based density measurement strategy is used to initialize the centroids, which are then adjusted to obtain the final clusters, aiming to properly reflect the population’s distribution. Afterward, these centroids are extracted to obtain adaptive RVs for self-guiding the search process. To verify the effectiveness of this SRV strategy, it is embedded into three well-known MaOEA/Ds that originally use the fixed RVs. Moreover, a new strategy of embedding SRV into MaOEA/Ds is discussed when the RVs are adjusted at each generation. The simulation results validate the superiority of our SRV strategy, when tackling numerous many-objective optimization problems with regular and irregular PFs. [ABSTRACT FROM AUTHOR]

Numerous multiobjective evolutionary algorithms (EAs) have been designed for constrained optimization over the past two decades. The idea behind these algorithms is to transform constrained optimization problems (COPs) into multiobjective optimization problems without any constraint, and then solve them. In this article, we propose a new multiobjective method for constrained optimization, which works by converting a COP into a problem with helper and equivalent objectives. An equivalent objective means that its optimal solution set is the same as that of the constrained problem but a helper objective does not. Then, this multiobjective optimization problem is decomposed into a group of subproblems using the weighted sum approach. Weights are dynamically adjusted so that each subproblem eventually tends to a problem with an equivalent objective. We theoretically analyze the computational time of the helper and equivalent objective method on a hard problem called “wide gap.” In a wide gap problem, an algorithm needs exponential time to cross between two fitness levels (a wide gap). We prove that using helper and equivalent objectives can shorten the time of crossing the wide gap. We conduct a case study for validating our method. An algorithm with helper and equivalent objectives is implemented. The experimental results show that its overall performance is ranked first when compared with other eight state-of-the-art EAs on IEEE CEC2017 benchmarks in constrained optimization. [ABSTRACT FROM AUTHOR]

Multimodal optimization problems have multiple satisfactory solutions to identify. Most of the existing works conduct the search based on the information of the current population, which can be inefficient. This article proposes a probabilistic niching evolutionary computation framework that guides the future search based on more sufficient historical information, in order to locate diverse and high-quality solutions. A binary space partition tree is built to structurally organize the space visiting information. Based on the tree, a probabilistic niching strategy is defined to reinforce exploration and exploitation by making full use of the structural historical information. The proposed framework is universal for incorporating various baseline niching algorithms. In this article, we integrate the proposed framework with two niching algorithms: 1) a distance-based differential evolution algorithm and 2) a topology-based particle swarm optimization algorithm. The two new algorithms are evaluated on 20 multimodal optimization test functions. The experimental results show that the proposed framework helps the algorithms obtain competitive performance. They outperform a number of state-of-the-art niching algorithms on most of the test functions. [ABSTRACT FROM AUTHOR]

In this article, we consider an emergent problem in the sensor fusion area in which unreliable sensors need to be identified in the absence of the ground truth. We devise a novel solution to the problem using the theory of replicator dynamics that require mild conditions compared to the available state-of-the-art approaches. The solution has a low computational complexity that is linear in terms of the number of involved sensors. We provide some sound theoretical results that catalog the convergence of our approach to a solution where we can clearly unveil the sensor type. Furthermore, we present some experimental results that demonstrate the convergence of our approach in concordance with our theoretical findings. [ABSTRACT FROM AUTHOR]

Many Pareto-based multiobjective evolutionary algorithms require ranking the solutions of the population in each iteration according to the dominance principle, which can become a costly operation particularly in the case of dealing with many-objective optimization problems. In this article, we present a new efficient algorithm for computing the nondominated sorting procedure, called merge nondominated sorting (MNDS), which has a best computational complexity of $O(N\log N)$ and a worst computational complexity of $O(MN^{2})$ , with $N$ being the population size and $M$ being the number of objectives. Our approach is based on the computation of the dominance set, that is, for each solution, the set of solutions that dominate it, by taking advantage of the characteristics of the merge sort algorithm. We compare MNDS against six well-known techniques that can be considered as the state-of-the-art. The results indicate that the MNDS algorithm outperforms the other techniques in terms of the number of comparisons as well as the total running time. [ABSTRACT FROM AUTHOR]

Agent-based simulation is a useful approach for the analysis of dynamic population evolution. In this field, the existing models mostly treat the migration behavior as a result of utility maximization, which partially ignores the endogenous mechanisms of human decision making. To simulate such a process, this article proposes a new cognitive architecture called the two-layered integrated decision cycle (TiDEC) which characterizes the individual’s decision-making process. Different from the previous ones, the new hybrid architecture incorporates deep neural networks for its perception and implicit knowledge learning. The proposed model is applied in China and U.S. population evolution. To the best of our knowledge, this is the first time that the cognitive computation is used in such a field. Computational experiments using the actual census data indicate that the cognitive model, compared with the traditional utility maximization methods, cannot only reconstruct the historical demographic features but also achieve better prediction of future evolutionary dynamics. [ABSTRACT FROM AUTHOR]

It is known that the Pareto-based approach is not well suited for optimization problems with a large number of objectives, even though it is a class of mainstream methods in multiobjective optimization. Typically, a Pareto-based algorithm comprises two parts: 1) a Pareto dominance-based criterion and 2) a diversity estimator. The former guides the selection toward the optimal front, while the latter promotes the diversity of the population. However, the Pareto dominance-based criterion becomes ineffective in solving optimization problems with many objectives (e.g., more than 3) and, thus, the diversity estimator will determine the performance of the algorithm. Unfortunately, the diversity estimator usually has a strong bias toward dominance resistance solutions (DRSs), thereby failing to push the population forward. DRSs are solutions that are far away from the Pareto-optimal front but cannot be easily dominated. In this article, we propose a new Pareto-based algorithm to resolve the above issue. First, to eliminate the DRSs, we design an interquartile range method to preprocess the solution set. Second, to balance convergence and diversity, we present a penalty mechanism of alternating operations between selection and penalty. The proposed algorithm is compared with five state-of-the-art algorithms on a number of well-known benchmarks with 3–15 objectives. The experimental results show that the proposed algorithm can perform well on most of the test functions and generally outperforms its competitors. [ABSTRACT FROM AUTHOR]

Sensor activity scheduling is critical for prolonging the lifetime of wireless sensor networks (WSNs). However, most existing methods assume sensors to have one fixed sensing range. Prevalence of sensors with adjustable sensing ranges posts two new challenges to the topic: 1) expanded search space, due to the rise in the number of possible activation modes and 2) more complex energy allocation, as the sensors differ in the energy consumption rate when using different sensing ranges. These two challenges make it hard to directly solve the lifetime maximization problem of WSNs with range-adjustable sensors (LM-RASs). This article proposes a neighborhood-based estimation of distribution algorithm (NEDA) to address it in a recursive manner. In NEDA, each individual represents a coverage scheme in which the sensors are selectively activated to monitor all the targets. A linear programming (LP) model is built to assign activation time to the schemes in the population so that their sum, the network lifetime, can be maximized conditioned on the current population. Using the activation time derived from LP as individual fitness, the NEDA is driven to seek coverage schemes promising for prolonging the network lifetime. The network lifetime is thus optimized by repeating the steps of the coverage scheme evolution and LP model solving. To encourage the search for diverse coverage schemes, a neighborhood sampling strategy is introduced. Besides, a heuristic repair strategy is designed to fine-tune the existing schemes for further improving the search efficiency. Experimental results on WSNs of different scales show that NEDA outperforms state-of-the-art approaches. It is also expected that NEDA can serve as a potential framework for solving other flexible LP problems that share the same structure with LM-RAS. [ABSTRACT FROM AUTHOR]

In recent years, numerous many-objective evolutionary algorithms (MaOEAs) have been developed to search for well-diversified and well-converged Pareto optimal solutions for high-dimensional many-objective optimization problems (MaOPs). However, existing MaOEAs have to tackle some daunting challenges, including the emergence of dominance resistance solutions, effective diversity preservation scheme, management of a large population size, extremely high computational complexity, sensitivity to the shape of Pareto front (PF), and overly relying on high-quality reference points. In this article, we present an evolution strategy (ES) for solving MaOPs, called MaOES, which can solve these challenges efficiently and effectively. Inspired by the Vector Equilibrium phenomenon in magnetic fields, isotropic magnetic particles would automatically repel from each other, keep the uniform distance from the nearest neighbors, and extend the entire magnetic fields as far as possible, all at the same time. In the proposed algorithm, an efficient self-adaptive Precision-Controllable Mutation operator is designed for individuals to explore and exploit the decision space. In addition, the Maximum Extension Distance strategy, which emulates the isotropic magnetic particle behavior in a magnetic field, is developed to guide individuals to keep uniform distance and extension to approximate the entire PF. As a result, the MaOES can obtain a well-converged and well-diversified PF with much less population size and far lower computational complexity. The larger the number of individuals, the sharper the contour the resulting approximate PF will be. Finally, the proposed algorithm is evaluated by the scalable MaOPs test suites on DTLZ and WFG. The experimental results have been demonstrated to provide a competitive and oftentimes better performance when compared against some chosen state-of-the-art MaOEAs. [ABSTRACT FROM AUTHOR]

In this article, a multiscale generative adversarial network (MS-GAN) is proposed for generating high-quality crowd density maps of arbitrary crowd density scenes. The task of crowd counting has many challenges, such as severe occlusions in extremely dense crowd scenes, perspective distortion, and high visual similarity between the pedestrians and background elements. To address these problems, the proposed MS-GAN combines a multiscale convolutional neural network (generator) and an adversarial network (discriminator) to generate a high-quality density map and accurately estimate the crowd count in complex crowd scenes. The multiscale generator utilizes the fusion features from multiple hierarchical layers to detect people with large-scale variation. The resulting density map produced by the multiscale generator is processed by a discriminator network trained to solve a binary classification task between a poor quality density map and real ground-truth ones. The additional adversarial loss can improve the quality of the density map, which is critical to accurately estimate the crowd counts. The experiments were conducted on multiple datasets with different crowd scenes and densities. The results showed that the proposed method provided better performance compared to current state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Objectives optimization and constraints satisfaction are two equally important goals to solve constrained many-objective optimization problems (CMaOPs). However, most existing studies for CMaOPs can be classified as feasibility-driven-constrained many-objective evolutionary algorithms (CMaOEAs), and they always give priority to satisfy constraints, while ignoring the maintenance of the population diversity for dealing with conflicting objectives. Consequently, the population may be pushed toward some locally feasible optimal or locally infeasible areas in the high-dimensional objective space. To alleviate this issue, this article presents a problem transformation technique, which transforms a CMaOP into a dynamic CMaOP (DCMaOP) for handling constraints and optimizing objectives simultaneously, to help the population cross the large and discrete infeasible regions. The well-known reference-point-based NSGA-III is tailored under the problem transformation model to solve CMaOPs, namely, DCNSGA-III. In this article, $\boldsymbol {\varepsilon }$ -feasible solutions play an important role in the proposed algorithm. To this end, in DCNSGA-III, a mating selection mechanism and an environmental selection operator are designed to generate and choose high-quality $\boldsymbol {\varepsilon }$ -feasible offspring solutions, respectively. The proposed algorithm is evaluated on a series of benchmark CMaOPs with three, five, eight, ten, and 15 objectives and compared against six state-of-the-art CMaOEAs. The experimental results indicate that the proposed algorithm is highly competitive for solving CMaOPs. [ABSTRACT FROM AUTHOR]

Due to the population-based and iterative-based characteristics of evolutionary computation (EC) algorithms, parallel techniques have been widely used to speed up the EC algorithms. However, the parallelism usually performs in the population level where multiple populations (or subpopulations) run in parallel or in the individual level where the individuals are distributed to multiple resources. That is, different populations or different individuals can be executed simultaneously to reduce running time. However, the research into generation-level parallelism for EC algorithms has seldom been reported. In this article, we propose a new paradigm of the parallel EC algorithm by making the first attempt to parallelize the algorithm in the generation level. This idea is inspired by the industrial pipeline technique. Specifically, a kind of EC algorithm called local version particle swarm optimization (PSO) is adopted to implement a pipeline-based parallel PSO (PPPSO, i.e., P3SO). Due to the generation-level parallelism in P3SO, when some particles still perform their evolutionary operations in the current generation, some other particles can simultaneously go to the next generation to carry out the new evolutionary operations, or even go to further next generation(s). The experimental results show that the problem-solving ability of P3SO is not affected while the evolutionary speed has been substantially accelerated in a significant fashion. Therefore, generation-level parallelism is possible in EC algorithms and may have significant potential applications in time-consumption optimization problems. [ABSTRACT FROM AUTHOR]

Multiagent reinforcement learning (MARL) has recently attracted considerable attention from both academics and practitioners. Core issues, e.g., the curse of dimensionality due to the exponential growth of agent interactions and nonstationary environments due to simultaneous learning, hinder the large-scale proliferation of MARL. These problems deteriorate with an increased number of agents. To address these challenges, we propose an adversarial collaborative learning method in a mixed cooperative–competitive environment, exploiting friend-or-foe Q-learning and mean-field theory. We first treat neighbors of agent $i$ as two coalitions ($i$ ’s friend and opponent coalition, respectively), and convert the Markov game into a two-player zero-sum game with an extended action set. By exploiting mean-field theory, this new game simplifies the interactions as those between a single agent and the mean effects of friends and opponents. A neural network is employed to learn the optimal mean effects of these two coalitions, which are trained via adversarial max and min steps. In the max step, with fixed policies of opponents, we optimize the friends’ mean action to maximize their rewards. In the min step, the mean action of opponents is trained to minimize the friends’ rewards when the policies of friends are frozen. These two steps are proved to converge to a Nash equilibrium. Then, another neural network is applied to learn the best response of each agent toward the mean effects. Finally, the adversarial max and min steps can jointly optimize the two networks. Experiments on two platforms demonstrate the learning effectiveness and strength of our approach, especially with many agents. [ABSTRACT FROM AUTHOR]

Dynamic multiobjective optimization problems (DMOPs) are characterized by optimization functions that change over time in varying environments. The DMOP is challenging because it requires the varying Pareto-optimal sets (POSs) to be tracked quickly and accurately during the optimization process. In recent years, transfer learning has been proven to be one of the effective means to solve dynamic multiobjective optimization. However, the negative transfer will lead the search of finding the POS to a wrong direction, which greatly reduces the efficiency of solving optimization problems. Minimizing the occurrence of negative transfer is thus critical for the use of transfer learning in solving DMOPs. In this article, we propose a new individual-based transfer learning method, called an individual transfer-based dynamic multiobjective evolutionary algorithm (IT-DMOEA), for solving DMOPs. Unlike existing approaches, it uses a presearch strategy to filter out some high-quality individuals with better diversity so that it can avoid negative transfer caused by individual aggregation. On this basis, an individual-based transfer learning technique is applied to accelerate the construction of an initial population. The merit of the IT-DMOEA method is that it combines different strategies in maintaining the advantages of transfer learning methods as well as avoiding the occurrence of negative transfer; thereby greatly improving the quality of solutions and convergence speed. The experimental results show that the proposed IT-DMOEA approach can considerably improve the quality of solutions and convergence speed compared to several state-of-the-art algorithms based on different benchmark problems. [ABSTRACT FROM AUTHOR]

Suppression of excessively synchronous beta frequency (12–35 Hz) oscillatory activity in the basal ganglia is believed to correlate with the alleviation of hypokinetic motor symptoms of the Parkinson’s disease. Delayed feedback is an effective strategy to interrupt the synchronization and has been used in the design of closed-loop neuromodulation methods computationally. Although tremendous efforts in this are being made by optimizing delayed feedback algorithm and stimulation waveforms, there are still remaining problems in the selection of effective parameters in the delayed feedback control schemes. In most delayed feedback neuromodulation strategies, the stimulation signal is obtained from the local field potential (LFP) of the excitatory subthalamic nucleus (STN) neurons and then is administered back to STN itself only. The inhibitory external globus pallidus (GPe) nucleus in the excitatory–inhibitory STN–GPe reciprocal network has not been involved in the design of the delayed feedback control strategies. Thus, considering the role of GPe, this paper proposes three schemes involving GPe in the design of the delayed feedback strategies and compared their effectiveness to the traditional paradigm using STN only. Based on a neural mass model of STN–GPe network having capability of simulating the LFP directly, the proposed stimulation strategies are tested and compared. Our simulation results show that the four types of delayed feedback control schemes are all effective, even if with a simple linear delayed feedback algorithm. But the three new control strategies we propose here further improve the control performance by enlarging the oscillatory suppression space and reducing the energy expenditure, suggesting that they may be more effective in applications. This paper may guide a new approach to optimize the closed-loop deep brain stimulation treatment to alleviate the Parkinsonian state by retargeting the measurement and stimulation nucleus. [ABSTRACT FROM AUTHOR]

Many-objective optimization problems (MaOPs) pose a big challenge to the traditional Pareto-based multiobjective evolutionary algorithms (MOEAs). As the number of objectives increases, the number of mutually nondominated solutions explodes and MOEAs become invalid due to the loss of Pareto-based selection pressure. Indicator-based many-objective evolutionary algorithms (MaOEAs) have been proposed to address this issue by enhancing the environmental selection. Indicator-based MaOEAs are easy to implement and of good versatility, however, they are unlikely to maintain the population diversity and coverage very well. In this article, a new indicator-based MaOEA with boundary protection, namely, MaOEA-IBP, is presented to relieve this weakness. In MaOEA-IBP, a worst elimination mechanism based on the ${I}_{{\epsilon }^{+}}$ indicator and boundary protection strategy is devised to enhance the balance of population convergence, diversity, and coverage. Specifically, a pair of solutions with the smallest ${I}_{{\epsilon }^{+}}$ value are first identified from the population. If one solution dominates the other, the dominated solution is eliminated. Otherwise, one solution is eliminated by the boundary protection strategy. MaOEA-IBP is compared with four indicator-based algorithms (i.e., ${I}_{{{ {SDE}}}^{+}}$ , SRA, MaOEAIGD, and ARMOEA) and other five state-of-the-art MaOEAs (i.e., KnEA, MaOEA-CSS, 1by1EA, RVEA, and EFR-RR) on various benchmark MaOPs. The experimental results demonstrate that MaOEA-IBP can achieve competitive performance with the compared algorithms. [ABSTRACT FROM AUTHOR]

In many practical applications, it is crucial to perform automatic data clustering without knowing the number of clusters in advance. The evolutionary computation paradigm is good at dealing with this task, but the existing algorithms encounter several deficiencies, such as the encoding redundancy and the cross-dimension learning error. In this article, we propose a novel elastic differential evolution algorithm to solve automatic data clustering. Unlike traditional methods, the proposed algorithm considers each clustering layout as a whole and adapts the cluster number and cluster centroids inherently through the variable-length encoding and the evolution operators. The encoding scheme contains no redundancy. To enable the individuals of different lengths to exchange information properly, we develop a subspace crossover and a two-phase mutation operator. The operators employ the basic method of differential evolution and, in addition, they consider the spatial information of cluster layouts to generate offspring solutions. Particularly, each dimension of the parameter vector interacts with its correlated dimensions, which not only adapts the cluster number but also avoids the cross-dimension learning error. The experimental results show that our algorithm outperforms the state-of-the-art algorithms that it is able to identify the correct number of clusters and obtain a good cluster validation value. [ABSTRACT FROM AUTHOR]

Many real-world optimization problems involve multiple objectives, constraints, and parameters that may change over time. These problems are often called dynamic multiobjective optimization problems (DMOPs). The difficulty in solving DMOPs is the need to track the changing Pareto-optimal front efficiently and accurately. It is known that transfer learning (TL)-based methods have the advantage of reusing experiences obtained from past computational processes to improve the quality of current solutions. However, existing TL-based methods are generally computationally intensive and thus time consuming. This article proposes a new memory-driven manifold TL-based evolutionary algorithm for dynamic multiobjective optimization (MMTL-DMOEA). The method combines the mechanism of memory to preserve the best individuals from the past with the feature of manifold TL to predict the optimal individuals at the new instance during the evolution. The elites of these individuals obtained from both past experience and future prediction will then constitute as the initial population in the optimization process. This strategy significantly improves the quality of solutions at the initial stage and reduces the computational cost required in existing methods. Different benchmark problems are used to validate the proposed algorithm and the simulation results are compared with state-of-the-art dynamic multiobjective optimization algorithms (DMOAs). The results show that our approach is capable of improving the computational speed by two orders of magnitude while achieving a better quality of solutions than existing methods. [ABSTRACT FROM AUTHOR]

Due to the curse of dimensionality of search space, it is extremely difficult for evolutionary algorithms to approximate the optimal solutions of large-scale multiobjective optimization problems (LMOPs) by using a limited budget of evaluations. If the Pareto-optimal subspace is approximated during the evolutionary process, the search space can be reduced and the difficulty encountered by evolutionary algorithms can be highly alleviated. Following the above idea, this article proposes an evolutionary algorithm to solve sparse LMOPs by learning the Pareto-optimal subspace. The proposed algorithm uses two unsupervised neural networks, a restricted Boltzmann machine, and a denoising autoencoder to learn a sparse distribution and a compact representation of the decision variables, where the combination of the learnt sparse distribution and compact representation is regarded as an approximation of the Pareto-optimal subspace. The genetic operators are conducted in the learnt subspace, and the resultant offspring solutions then can be mapped back to the original search space by the two neural networks. According to the experimental results on eight benchmark problems and eight real-world problems, the proposed algorithm can effectively solve sparse LMOPs with 10000 decision variables by only 100000 evaluations. [ABSTRACT FROM AUTHOR]

Multiobjective multitasking optimization (MTO), which is an emerging research topic in the field of evolutionary computation, was recently proposed. MTO aims to solve related multiobjective optimization problems at the same time via evolutionary algorithms. The key to MTO is the knowledge transfer based on sharing solutions across tasks. Notably, positive knowledge transfer has been shown to facilitate superior performance characteristics. However, how to find more valuable transferred solutions for the positive transfer has been scarcely explored. Keeping this in mind, we propose a new algorithm to solve MTO problems. In this article, if a transferred solution is nondominated in its target task, the transfer is positive transfer. Furthermore, neighbors of this positive-transfer solution will be selected as the transferred solutions in the next generation, since they are more likely to achieve the positive transfer. Numerical studies have been conducted on benchmark problems of MTO to verify the effectiveness of the proposed approach. Experimental results indicate that our proposed framework achieves competitive results compared with the state-of-the-art MTO frameworks. [ABSTRACT FROM AUTHOR]

Recently, evolutionary multitasking (EMT) has been proposed in the field of evolutionary computation as a new search paradigm, for solving multiple optimization tasks simultaneously. By sharing useful traits found along the evolutionary search process across different optimization tasks, the optimization performance on each task could be enhanced. The autoencoding-based EMT is a recently proposed EMT algorithm. In contrast to most existing EMT algorithms, which conduct knowledge transfer across tasks implicitly via crossover, it intends to perform knowledge transfer explicitly among tasks in the form of task solutions, which enables the employment of task-specific search mechanisms for different optimization tasks in EMT. However, the autoencoding-based explicit EMT can only work on continuous optimization problems. It will fail on combinatorial optimization problems, which widely exist in real-world applications, such as scheduling problem, routing problem, and assignment problem. To the best of our knowledge, there is no existing effort working on explicit EMT for combinatorial optimization problems. Taking this cue, in this article, we thus embark on a study toward explicit EMT for combinatorial optimization. In particular, by using vehicle routing as an illustrative combinatorial optimization problem, the proposed explicit EMT algorithm (EEMTA) mainly contains a weighted l1-norm-regularized learning process for capturing the transfer mapping, and a solution-based knowledge transfer process across vehicle routing problems (VRPs). To evaluate the efficacy of the proposed EEMTA, comprehensive empirical studies have been conducted with the commonly used vehicle routing benchmarks in multitasking environment, against both the state-of-the-art EMT algorithm and the traditional single-task evolutionary solvers. Finally, a real-world combinatorial optimization application, that is, the package delivery problem (PDP), is also presented to further confirm the efficacy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A multifactorial evolutionary algorithm (MFEA) is a recently proposed algorithm for evolutionary multitasking, which optimizes multiple optimization tasks simultaneously. With the design of knowledge transfer among different tasks, MFEA has demonstrated the capability to outperform its single-task counterpart in terms of both convergence speed and solution quality. In MFEA, the knowledge transfer across tasks is realized via the crossover between solutions that possess different skill factors. This crossover is thus essential to the performance of MFEA. However, we note that the present MFEA and most of its existing variants only employ a single crossover for knowledge transfer, and fix it throughout the evolutionary search process. As different crossover operators have a unique bias in generating offspring, the appropriate configuration of crossover for knowledge transfer in MFEA is necessary toward robust search performance, for solving different problems. Nevertheless, to the best of our knowledge, there is no effort being conducted on the adaptive configuration of crossovers in MFEA for knowledge transfer, and this article thus presents an attempt to fill this gap. In particular, here, we first investigate how different types of crossover affect the knowledge transfer in MFEA on both single-objective (SO) and multiobjective (MO) continuous optimization problems. Furthermore, toward robust and efficient multitask optimization performance, we propose a new MFEA with adaptive knowledge transfer (MFEA-AKT), in which the crossover operator employed for knowledge transfer is self-adapted based on the information collected along the evolutionary search process. To verify the effectiveness of the proposed method, comprehensive empirical studies on both SO and MO multitask benchmarks have been conducted. The experimental results show that the proposed MFEA-AKT is able to identify the appropriate knowledge transfer crossover for different optimization problems and even at different optimization stages along the search, which thus leads to superior or competitive performances when compared to the MFEAs with fixed knowledge transfer crossover operators. [ABSTRACT FROM AUTHOR]

The decomposition-based algorithms [e.g., multiobjective evolutionary algorithm based on decomposition (MOEA/D)] transform a multiobjective optimization problem (MOP) into a number of single-objective optimization subproblems and solve them in a collaborative manner. It is a natural framework for using single-objective local search (LS) to solve combinatorial MOPs. However, commonly used decomposition methods, such as weighted sum (WS), Tchebycheff (TCH), and penalty-based boundary intersection (PBI) may not be good at maintaining the population diversity while providing diverse initial solutions for different LS procedures in a collaborative way. Based on our previous work on the constrained decomposition with grids (CDG), this article proposes a dynamic CDG (DCDG) framework used to design a multiobjective memetic algorithm (DCDG-MOMA). DCDG uses grids for maintaining diversity, supporting the collaborative LS. In addition, DCDG dynamically increases the number of grids for obtaining more nondominated solutions as well as the better collaborative search among them. DCDG-MOMA has been compared with several classical and state-of-the-art algorithms on multiobjective traveling salesman problem (MOTSP), multiobjective quadratic assignment problem (MOQAP), and multiobjective capacitated arc routing problem (MOCARP). [ABSTRACT FROM AUTHOR]

The complexity of an optimization problem is determined by its decision and objective spaces. Over the past few decades, a large number of works have focused on the performance improvement of metaheuristic algorithms via the objective space, whereas studies related to the decision space have attracted little attentions. Moreover, metaheuristic algorithms may not obtain satisfactory results within an entire feasible region, even if sufficient computational resources are available. Therefore, reducing the search space (i.e., finding a trust region) may be an effective method to ensure that the convergence is sufficiently close to the global optimal region. However, inappropriate subspace size may also weaken the performance of algorithms except for ones with a sufficiently small search space. To alleviate aforementioned problems, a variable search space (VSS) strategy based on a sequential trust region determination approach is proposed in this paper. In the VSS, the entire optimization process is divided into two stages: the first stage is to use an optimization approach for sequentially finding the trust domain of each variable and then determine the best-matched subspace; the second stage is to employ the optimization method for searching an optimal/near-optimal solution within the found trust region. The effectiveness of the VSS is evaluated using two widely used test suites, that is, IEEE CEC2014 and BBOB2012. Experimental results indicate that improving the algorithm performance is an important method for tackling problems, but locating a trust region is also beneficial for metaheuristic algorithms to improve the solution precision, especially for complex optimization problems. [ABSTRACT FROM AUTHOR]

Large-scale optimization has become a significant and challenging research topic in the evolutionary computation (EC) community. Although many improved EC algorithms have been proposed for large-scale optimization, the slow convergence in the huge search space and the trap into local optima among massive suboptima are still the challenges. Targeted to these two issues, this article proposes an adaptive granularity learning distributed particle swarm optimization (AGLDPSO) with the help of machine-learning techniques, including clustering analysis based on locality-sensitive hashing (LSH) and adaptive granularity control based on logistic regression (LR). In AGLDPSO, a master–slave multisubpopulation distributed model is adopted, where the entire population is divided into multiple subpopulations, and these subpopulations are co-evolved. Compared with other large-scale optimization algorithms with single population evolution or centralized mechanism, the multisubpopulation distributed co-evolution mechanism will fully exchange the evolutionary information among different subpopulations to further enhance the population diversity. Furthermore, we propose an adaptive granularity learning strategy (AGLS) based on LSH and LR. The AGLS is helpful to determine an appropriate subpopulation size to control the learning granularity of the distributed subpopulations in different evolutionary states to balance the exploration ability for escaping from massive suboptima and the exploitation ability for converging in the huge search space. The experimental results show that AGLDPSO performs better than or at least comparable with some other state-of-the-art large-scale optimization algorithms, even the winner of the competition on large-scale optimization, on all the 35 benchmark functions from both IEEE Congress on Evolutionary Computation (IEEE CEC2010) and IEEE CEC2013 large-scale optimization test suites. [ABSTRACT FROM AUTHOR]