LCS & GBML Central

Surrogate models have shown to be effective in assisting metaheuristic algorithms for solving computationally expensive complex optimization problems. The effectiveness of existing surrogate-assisted metaheuristic algorithms, however, has only been verified on low-dimensional optimization problems. In this paper, a surrogate-assisted cooperative swarm optimization algorithm is proposed, in which a surrogate-assisted particle swarm optimization (PSO) algorithm and a surrogate-assisted social learning-based PSO (SL-PSO) algorithm cooperatively search for the global optimum. The cooperation between the PSO and the SL-PSO consists of two aspects. First, they share promising solutions evaluated by the real fitness function. Second, the SL-PSO focuses on exploration while the PSO concentrates on local search. Empirical studies on six 50-D and six 100-D benchmark problems demonstrate that the proposed algorithm is able to find high-quality solutions for high-dimensional problems on a limited computational budget.

The balance between convergence and diversity is the cornerstone of evolutionary multiobjective optimization (EMO). The recently proposed stable matching-based selection provides a new perspective to handle this balance under the framework of decomposition multiobjective optimization. In particular, the one-one stable matching between subproblems and solutions, which achieves an equilibrium between their mutual preferences, is claimed to strike a balance between convergence and diversity. However, the original stable marriage model has a high risk of matching a solution with an unfavorable subproblem, which finally leads to an imbalanced selection result. In this paper, we introduce the concept of incomplete preference lists into the stable matching model to remedy the loss of population diversity. In particular, each solution is only allowed to maintain a partial preference list consisting of its favorite subproblems. We implement two versions of stable matching-based selection mechanisms with incomplete preference lists: one achieves a two-level one-one matching and the other obtains a many-one matching. Furthermore, an adaptive mechanism is developed to automatically set the length of the incomplete preference list for each solution according to its local competitiveness. The effectiveness and competitiveness of our proposed methods are validated and compared with several state-of-the-art EMO algorithms on 62 benchmark problems.

This paper analyzes the stochastic runtime of the cross-entropy (CE) algorithm for the well-studied standard problems OneMax and LeadingOnes. We prove that the total number of solutions the algorithm needs to evaluate before reaching the optimal solution (i.e., its runtime) is bounded by a polynomial ${Q(n)}$ in the problem size ${n}$ with a probability growing exponentially to 1 with ${n}$ if the parameters of the algorithm are adapted to ${n}$ in a reasonable way. Our polynomial bound ${Q(n)}$ for OneMax outperforms the well-known runtime bound of the 1-ANT algorithm, a particular ant colony optimization algorithm. Our adaptation of the parameters of the CE algorithm balances the number of iterations needed and the size of the samples drawn in each iteration, resulting in an increased efficiency. For the LeadingOnes problem, we improve the runtime of the algorithm by bounding the sampling probabilities away from 0 and 1. The resulting runtime outperforms the known stochastic runtime for a univariate marginal distribution algorithm, and is very close to the known expected runtime of variants of max-min ant systems. Bounding the sampling probabilities allows the CE algorithm to explore the search space even for test functions with a very rugged landscape as the LeadingOnes function.

Metaheuristics have yielded very promising results for the frequency assignment problem (FAP). However, the results obtainable using currently published methods are far from ideal in complex, large-scale instances. This paper applies and extends some of the most recent advances in evolutionary algorithms to two common variants of the FAP, and shows how, in traditional techniques, two common issues affect their performance: 1) premature convergence and 2) the way in which neutral networks are handled. A recent replacement-based diversity management strategy is successfully applied to alleviate the premature convergence drawback. Additionally, by properly defining a distance metric, the performance in the presence of neutrality can also be greatly improved. The replacement strategy combines the principle of transforming a single-objective problem into a multiobjective one by considering diversity as an additional objective, with the idea of adapting the balance induced between exploration and exploitation to the requirements of the different optimization stages. Tests with 44 publicly available instances yield very competitive results. New best-known frequency plans were generated for 11 instances, whereas in the remaining ones the best-known solutions were replicated. Comparisons with a large number of strategies designed to delay convergence of the population clearly show the advantages of our novel proposals.

Multimodal optimization (MMO) aiming to locate multiple optimal (or near-optimal) solutions in a single simulation run has practical relevance to problem solving across many fields. Population-based meta-heuristics have been shown particularly effective in solving MMO problems, if equipped with specifically-designed diversity-preserving mechanisms, commonly known as niching methods. This paper provides an updated survey on niching methods. This paper first revisits the fundamental concepts about niching and its most representative schemes, then reviews the most recent development of niching methods, including novel and hybrid methods, performance measures, and benchmarks for their assessment. Furthermore, this paper surveys previous attempts at leveraging the capabilities of niching to facilitate various optimization tasks (e.g., multiobjective and dynamic optimization) and machine learning tasks (e.g., clustering, feature selection, and learning ensembles). A list of successful applications of niching methods to real-world problems is presented to demonstrate the capabilities of niching methods in providing solutions that are difficult for other optimization methods to offer. The significant practical value of niching methods is clearly exemplified through these applications. Finally, this paper poses challenges and research questions on niching that are yet to be appropriately addressed. Providing answers to these questions is crucial before we can bring more fruitful benefits of niching to real-world problem solving.

We present a model of changing the intensity of interaction based on the individual behavior to study the iterated prisoner’s dilemma game in social networks. In this model, each individual has an assessed score of reputation which is obtained by considering the evaluation level of interactive partners for its present behavior. We focus on the effect of evaluation level on the changing intensity of interaction between individuals. For an individual with good behavior, the higher the evaluation level of its partners for its good behavior, the better its reputation, and the higher the probability of surrounding partners interaction with it. On the contrary, for an individual with bad behavior, the lower the evaluation level of its partners for its bad behavior, the worse its reputation, and the less the probability of surrounding neighbors interaction with it. Simulation results show that this effective mechanism can drastically facilitate the emergence and maintenance of cooperation in the population under a treacherous chip. Interestingly, for a small or moderate treacherous chip, the cooperation level monotonously ascends as the evaluation level increases; however, for a higher treacherous chip, existing an optimal evaluation level, which can result in the best promotion of cooperation. Furthermore, we find better agreement between simulation results and theoretical predictions obtained from an extended pair-approximation method, although there are some tiny deviations. We also show some typical snapshots of the system and investigate the reason for appearance and persistence of cooperation. The results further show the importance of evaluation level of individual behavior in coevolutionary relationships.

Cooperative co-evolution (CC) is an explicit means of problem decomposition in multipopulation evolutionary algorithms for solving large-scale optimization problems. For CC, subpopulations representing subcomponents of a large-scale optimization problem co-evolve, and are likely to have different contributions to the improvement of the best overall solution to the problem. Hence, it makes sense that more computational resources should be allocated to the subpopulations with greater contributions. In this paper, we study how to allocate computational resources in this context and subsequently propose a new CC framework named CCFR to efficiently allocate computational resources among the subpopulations according to their dynamic contributions to the improvement of the objective value of the best overall solution. Our experimental results suggest that CCFR can make efficient use of computational resources and is a highly competitive CCFR for solving large-scale optimization problems.