LCS & GBML Central

In multi-/many-objective evolutionary algorithms (MOEAs), there are varieties of vector ranking schemes, including nondominated sorting, dominance counting, and so on. Usually, these vector ranking schemes in the classical MOEAs are of high computational complexity. Thus, in recent years, many researchers put emphasis on the further improvement of the computational complexity of the vector ranking schemes. In this paper, we propose the dominance degree matrix for a set of vectors and design a fast method to construct this new data structure, which requires ${O}$ (mNlog ${N}$ ) comparisons on average. The dominance degree matrix is constructed based on the properties of Pareto domination, and it can convert the dominance comparison into counting the number of special element pairs. Based on the dominance degree matrix, we develop a new and efficient implementation of nondominated sorting called dominance degree approach for nondominated sorting (DDA-NS), which has an average time complexity of ${O}$ (mN $^{2}$ ) but only requires ${O}$ (mNlog ${N}$ ) objective function value comparisons on average. Empirical results demonstrate that DDA-NS clearly outperforms six other representative approaches for nondominated sorting in most cases and DDA-NS performs well when dealing with large-size and many-objective populations. In addition, we also use the dominance degree matrix to form a new method for calculating the dominance strength for Strength Pareto Evolutionary Algorithm (SPEA)2, which greatly –
mproves the efficiency of the naive calculation method in SPEA2. Experiments on benchmark problems show that the Nondominated Sorting Genetic Algorithm (NSGA)-II and NSGA-III framework embedding DDA-NS and the SPEA2 framework embedding the new method of calculating the dominance strength indeed achieve the improvement of the runtime.

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Dynamic constrained optimization problems (DCOPs) are difficult to solve because both objective function and constraints can vary with time. Although DCOPs have drawn attention in recent years, little work has been performed to solve DCOPs with multiple dynamic feasible regions from the perspective of locating and tracking multiple feasible regions in parallel. Moreover, few benchmarks have been proposed to simulate the dynamics of multiple disconnected feasible regions. In this paper, first, the idea of tracking multiple feasible regions, originally proposed by Nguyen and Yao, is enhanced by specifically adopting multiple subpopulations. To this end, the dynamic species-based particle swam optimization (DSPSO), a representative multipopulation algorithm, is adopted. Second, an ensemble of locating and tracking feasible regions strategies is proposed to handle different types of dynamics in constraints. Third, two benchmarks are designed to simulate the DCOPs with dynamic constraints. The first benchmark, including two variants of G24 (called G24v and G24w), could control the size of feasible regions. The second benchmark, named moving feasible regions benchmark (MFRB), is highly configurable. The global optimum of MFRB is calculated mathematically for experimental comparisons. Experimental results on G24, G24v, G24w, and MFRB show that the DSPSO with the ensemble of strategies performs significantly better than the original DSPSO and other typical algorithms.

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This paper introduces necessary and sufficient conditions that surrogate functions must satisfy to properly define frontiers of nondominated solutions in multiobjective optimization (MOO) problems. These new conditions work directly on the objective space, and thus are agnostic about how the solutions are evaluated. Therefore, real objectives or user-designed objectives’ surrogates are allowed, opening the possibility of linking independent objective surrogates. To illustrate the practical consequences of adopting the proposed conditions, we use Gaussian processes (GPs) as surrogates endowed with monotonicity soft constraints and with an adjustable degree of flexibility, and compare them to regular GPs and to a frontier surrogate method in the literature that is the closest to the method proposed in this paper. Results show that the necessary and sufficient conditions proposed here are finely managed by the constrained GP, guiding to high-quality surrogates capable of suitably synthesizing an approximation to the Pareto frontier in challenging instances of MOO, while an existing approach that does not take the theory proposed in consideration defines surrogates which greatly violate the conditions to describe a valid frontier.

Meme automaton is an adaptive entity that autonomously acquires an increasing level of capability and intelligence through embedded memes evolving independently or via social interactions. This paper begins a study on memetic multiagent system (MeMAS) toward human-like social agents with memetic automaton. We introduce a potentially rich meme-inspired design and operational model, with Darwin’s theory of natural selection and Dawkins’ notion of a meme as the principal driving forces behind interactions among agents, whereby memes form the fundamental building blocks of the agents’ mind universe. To improve the efficiency and scalability of MeMAS, we propose memetic agents with structured memes in this paper. Particularly, we focus on meme selection design where the commonly used elitist strategy is further improved by assimilating the notion of like-attracts-like in the human learning. We conduct experimental study on multiple problem domains and show the performance of the proposed MeMAS on human-like social behavior.

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Taking both convergence and diversity into consideration, this paper suggests a vector angle-based evolutionary algorithm for unconstrained (with box constraints only) many-objective optimization problems. In the proposed algorithm, the maximum-vector-angle-first principle is used in the environmental selection to guarantee the wideness and uniformity of the solution set. With the help of the worse-elimination principle, worse solutions in terms of the convergence (measured by the sum of normalized objectives) are allowed to be conditionally replaced by other individuals. Therefore, the selection pressure toward the Pareto-optimal front is strengthened. The proposed method is compared with other four state-of-the-art many-objective evolutionary algorithms on a number of unconstrained test problems with up to 15 objectives. The experimental results have shown the competitiveness and effectiveness of our proposed algorithm in keeping a good balance between convergence and diversity. Furthermore, it was shown by the results on two problems from practice (with irregular Pareto fronts) that our method significantly outperforms its competitors in terms of both the convergence and diversity of the obtained solution sets. Notably, the new algorithm has the following good properties: 1) it is free from a set of supplied reference points or weight vectors; 2) it has less algorithmic parameters; and 3) the time complexity of the algorithm is low. Given both good performance and nice properties, the suggested algorithm could be an alternative tool when handling optimization problems with more than three objectives.

Evolutionary Computation, Ahead of Print.