LCS & GBML Central

Under mild conditions, the Pareto front (Pareto set) of a continuous $boldsymbol m$ -objective optimization problem forms an ( $boldsymbol {m-1}$ )-dimensional piecewise continuous manifold. Based on this property, this paper proposes a self-organizing multiobjective evolutionary algorithm. At each generation, a self-organizing mapping method with ( $boldsymbol {m-1}$ ) latent variables is applied to establish the neighborhood relationship among current solutions. A solution is only allowed to mate with its neighboring solutions to generate a new solution. To reduce the computational overhead, the self-organizing training step and the evolution step are conducted in an alternative manner. In other words, the self-organizing training is performed only one single step at each generation. The proposed algorithm has been applied to a number of test instances and compared with some state-of-the-art multiobjective evolutionary methods. The results have demonstrated its advantages over other approaches.

Operating mode scheduling is crucial for the lifetime of wireless sensor networks (WSNs). However, the growing scale of networks has made such a scheduling problem more challenging, as existing set cover and evolutionary algorithms become unable to provide satisfactory efficiency due to the curse of dimensionality. In this paper, a Kuhn–Munkres (KM) parallel genetic algorithm is developed to solve the set cover problem and is applied to the lifetime maximization of large-scale WSNs. The proposed algorithm schedules the sensors into a number of disjoint complete cover sets and activates them in batch for energy conservation. It uses a divide-and-conquer strategy of dimensionality reduction, and the polynomial KM algorithm a are hence adopted to splice the feasible solutions obtained in each subarea to enhance the search efficiency substantially. To further improve global efficiency, a redundant-trend sensor schedule strategy was developed. Additionally, we meliorate the evaluation function through penalizing incomplete cover sets, which speeds up convergence. Eight types of experiments are conducted on a distributed platform to test and inform the effectiveness of the proposed algorithm. The results show that it offers promising performance in terms of the convergence rate, solution quality, and success rate.

For many-objective optimization problems (MaOPs), in which the number of objectives is greater than three, the performance of most existing evolutionary multi-objective optimization algorithms generally deteriorates over the number of objectives. As some MaOPs may have redundant or correlated objectives, it is desirable to reduce the number of the objectives in such circumstances. However, the Pareto solution of the reduced MaOP obtained by most of the existing objective reduction methods, based on objective selection, may not be the Pareto solution of the original MaOP. In this paper, we propose an objective extraction method (OEM) for MaOPs. It formulates the reduced objective as a linear combination of the original objectives to maximize the conflict between the reduced objectives. Subsequently, the Pareto solution of the reduced MaOP obtained by the proposed algorithm is that of the original MaOP, and the proposed algorithm can thus preserve the dominance structure as much as possible. Moreover, we propose a novel framework that features both simple and complicated Pareto set shapes for many-objective test problems with an arbitrary number of essential objectives. Within this framework, we can control the importance of essential objectives. As there is no direct performance metric for the objective reduction algorithms on the benchmarks, we present a new metric that features simplicity and usability for the objective reduction algorithms. We compare the proposed OEM with three objective reduction methods, i.e., REDGA, L-PCA, and NL-MVU-PCA, on the proposed test problems and benchmark DTLZ5 with different numbers of objectives and essential objectives. Our numerical studies show the effectiveness and robustness of the proposed approach.

This paper introduces an original algebraic approach to differential evolution (DE) algorithms for combinatorial search spaces. An abstract algebraic differential mutation for generic combinatorial spaces is defined by exploiting the concept of a finitely generated group. This operator is specialized for the permutations space by means of an original randomized bubble sort algorithm. Then, a discrete DE algorithm is derived for permutation problems and it is applied to the permutation flowshop scheduling problem with the total flowtime criterion. Other relevant components of the proposed algorithm are: a crossover operator for permutations, a novel biased selection strategy, a heuristic-based initialization, and a memetic restart procedure. Extensive experimental tests have been performed on a widely accepted benchmark suite in order to analyze the dynamics of the proposed approach and to compare it with the state-of-the-art algorithms. The experimental results clearly show that the proposed algorithm reaches state-of-the-art performances and, most remarkably, it is able to find some new best known results. Furthermore, the experimental analysis on the impact of the algorithmic components shows that the two main contributions of this paper, i.e., the discrete differential mutation and the biased selection operator, greatly contribute to the overall performance of the algorithm.

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In particle swarm optimization (PSO), the inertia weight is an important parameter for controlling its search capability. There have been intensive studies of the inertia weight in continuous optimization, but little attention has been paid to the binary case. This paper comprehensively investigates the effect of the inertia weight on the performance of binary PSO (BPSO), from both theoretical and empirical perspectives. A mathematical model is proposed to analyze the behavior of BPSO, based on which several lemmas and theorems on the effect of the inertia weight are derived. Our research findings suggest that in the binary case, a smaller inertia weight enhances the exploration capability while a larger inertia weight encourages exploitation. Consequently, this paper proposes a new adaptive inertia weight scheme for BPSO. This scheme allows the search process to start first with exploration and gradually move toward exploitation by linearly increasing the inertia weight. The experimental results on 0/1 knapsack problems show that the BPSO with the new increasing inertia weight scheme performs significantly better than that with the conventional decreasing and constant inertia weight schemes. This paper verifies the efficacy of increasing inertia weight in BPSO.

In general, an ${M}$ -objective continuous optimization problem has an ( $ {M-1}$ )-dimensional Pareto front in the objective space. If its dimension is smaller than ( $ {M-1}$ ), it is called a degenerate Pareto front. Deb–Thiele–Laumanns–Zitzler (DTLZ)5 and Walking Fish Group (WFG)3 have often been used as many-objective continuous test problems with degenerate Pareto fronts. However, it was noted that DTLZ5 has a nondegenerate part of the Pareto front. Constraints have been proposed to remove the nondegenerate part. In this letter, first we show that WFG3 also has a nondegenerate part. Then, we derive constraints to remove the nondegenerate part. Finally, we show that the existence of the nondegenerate part makes WFG3 an interesting test problem through computational experiments.

It is known that Pareto dominance has its own weaknesses as the selection criterion in evolutionary multiobjective optimization. Algorithms based on Pareto criterion (PC) can suffer from problems such as slow convergence to the optimal front and inferior performance on problems with many objectives. Non-Pareto criterion (NPC), such as decomposition-based criterion and indicator-based criterion, has already shown promising results in this regard, but its high selection pressure may lead to the algorithm to prefer some specific areas of the problem’s Pareto front, especially when the front is highly irregular. In this paper, we propose a bi-criterion evolution (BCE) framework of the PC and NPC, which attempts to make use of their strengths and compensates for each other’s weaknesses. The proposed framework consists of two parts: PC evolution and NPC evolution. The two parts work collaboratively, with an abundant exchange of information to facilitate each other’s evolution. Specifically, the NPC evolution leads the PC evolution forward and the PC evolution compensates the possible diversity loss of the NPC evolution. The proposed framework keeps the freedom on the implementation of the NPC evolution part, thus making it applicable for any non-Pareto-based algorithm. In the PC evolution, two operations, population maintenance and individual exploration, are presented. The former is to maintain a set of representative nondominated individuals and the latter is to explore some promising areas that are undeveloped (or not well-developed) in the NPC evolution. Experimental results have shown the effectiveness of the proposed framework. The BCE works well on seven groups of 42 test problems with various characteristics, including those in which Pareto-based algorithms or non-Pareto-based algorithms struggle.

This paper discusses a special technique, called conditionally matching rules (CMRs), for the representation of transition functions of cellular automata (CA) and its application to the evolutionary design of complex multistate CA. The problem of designing replicating loops in 2-D CA and the square calculation in 1-D CA will be treated as case studies. It will be shown that the evolutionary algorithm in combination with CMRs is able to successfully solve these tasks and provide some innovative results compared to existing solutions. In particular, a novel replication scheme will be presented that exhibits a higher replication speed in comparison with the existing replicating loops. As regards the square calculation, some results have been obtained that allow a substantial reduction of the number of steps of the cellular automaton against the currently known solution. The utilization of the CMRs in the proposed experiments represents the first case of a successful automatic evolutionary design of complex CA for solving nontrivial problems in which the existing conventional approaches have failed.

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