Abstract
Inspired by the mechanism of generation and restriction among five elements in Chinese traditional culture, we present a novel Multi-Objective Five-Elements Cycle Optimization algorithm (MOFECO). During the optimization process of MOFECO, we use individuals to represent the elements. At each iteration, we first divide the population into several cycles, each of which contains several individuals. Secondly, for every individual in each cycle, we judge whether to update it according to the force exerted on it by other individuals in the cycle. In the case of an update, a local or global update is selected by a dynamically adjustable probability P s ; otherwise, the individual is retained. Next, we perform combined mutation operations on the updated individuals, so that a new population contains both the reserved and updated individuals for the selection operation. Finally, the fast non-dominated sorting method is adopted on the current population to obtain an optimal Pareto solution set. The parameters’ comparison of MOFECO is given by an experiment and also the performance of MOFECO is compared with three classic evolutionary algorithms Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi-Objective Particle Swarm Optimization algorithm (MOPSO), Pareto Envelope-based Selection Algorithm II (PESA-II) and two latest algorithms Knee point-driven Evolutionary Algorithm (KnEA) and Non-dominated Sorting and Local Search (NSLS) on solving test function sets Zitzler et al’s Test suite (ZDT), Deb et al’s Test suite (DTLZ), Walking Fish Group (WFG) and Many objective Function (MaF). The experimental results indicate that the proposed MOFECO can approach the true Pareto-optimal front with both better diversity and convergence compared to the five other algorithms.
Highlights
In real-world applications, commonly Multiple-Objective Optimization (MOO) problems are applied to many situations such as biology, engineering, medical and economics, and so forth [1].Usually this kind of optimization problem contains multiple objectives which conflict with each other, no single optimal solution can be derived
In Five-Elements Cycle Optimization algorithm (FECO), the elements are generally divided into q different cycles and each cycle has L elements, where the value of L × q is equivalent to the population size in the evolution algorithm and each element represents an individual in the population
Optimization algorithm (MOFECO) for solving MOO problems is proposed in this paper and the validity of the Multi-Objective Five-Elements Cycle Optimization algorithm (MOFECO) has been verified by using the test function sets ZDT, DTLZ, Walking Fish Group (WFG) and Many objective Function (MaF)
Summary
In real-world applications, commonly Multiple-Objective Optimization (MOO) problems are applied to many situations such as biology, engineering, medical and economics, and so forth [1]. In the past few decades, Evolutionary Algorithms (EAs), and some population-based meta-heuristic algorithms, have been verified to effectively solve MOO problems and they can get an optimal Pareto solution set in one run [2]. The application of EAs to MOO problems has received considerable attention, which led to the emergence of a new research issue named Multi-Objective Evolutionary Algorithms (MOEAs). Multi-Objective Evolutionary Algorithm based on an enhanced Inverted Generational Distance metric (MOEA/IGD-NS) [18], and so forth, show great potential for solving MOO problems. Based on the scheme of FECM, we propose a new meta-heuristic algorithm that can effectively solve MOO problems, named the Multi-Objective. The rest of this paper is composed of the following 5 parts: Section 2 describes the basic concepts of MOO problems and some related research on MOEAs; Section 3 elaborates the related work of FECO and explains the motivation of the proposed algorithm MOFECO; Section 4 illustrates the principle of the proposed algorithm; Section 5 makes a parameter analysis and experimentally verifies the performance of MOFECO algorithm compared with the other five MOEAs; Section 6 draws the conclusion of this paper
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