Vine copula-based EDA for dynamic multiobjective optimization
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RESEARCH PAPER
Vine copula‑based EDA for dynamic multiobjective optimization Abdelhakim Cheriet1 Received: 7 April 2020 / Revised: 22 October 2020 / Accepted: 30 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Dynamic Multiobjective Problems cover a set of real-world problems that have many conflicting objectives. These problems are challenging and well known by the dynamic nature of their objective functions, constraint functions, and problem parameters which often change over time. In fact, dealing with these problems has not been investigated in detail using the Estimation of Distribution Algorithms (EDAs). Thus, we propose in this paper an EDA-based on Vine Copulas algorithm to deal with Dynamic Multiobjective Problems (DMOPs). Vines Copulas are graphical models that represent multivariate dependence using bivariate copulas. The proposed Copula-based Estimation of Distribution Algorithm, labeled Dynamic Vine-Copula Estimation of Distribution Algorithm (DynVC-EDA), is used to implement two search strategies. The first strategy is an algorithm that uses the model as a memory to save the status of the best solutions obtained during the current generation. The second strategy is a prediction-based algorithm that uses the history of the best solutions to predict a new population when a change occurs. The proposed algorithms are tested using a set of benchmarks provided with CEC2015 and the Gee-Tan-Abbass. Statistical findings show that the DynVC-EDA is competitive to the state-of-the-art methods in dealing with dynamic multiobjective optimization. Keywords Evolutionary algorithm · Copula · Vine-copula · EDA · Dynamic multiobjective optimization
1 Introduction In various fields of science and technology, optimization problems have two or more objectives that should be optimized simultaneously. These problems are called Multiobjective Optimization Problems (MOPs) [14], and their solution involves the design of algorithms that are different from those adopted for solving single-objective optimization problems. In the absence of reference information, there is no unique or straightforward way to determine if a given solution is better than others in multiobjective optimization. The notion of optimality most commonly adopted in such context is the one called Pareto optimality. Pareto optimality leads to trade-offs among the objectives in MOPs. Thus, the solution of MOPs is usually a set of acceptable trade-off optimal solutions called Pareto optimal set. Compared to traditional * Abdelhakim Cheriet Abdelhakim.cheriet@univ‑ouargla.dz 1
Department of Computer Science and Information Technologies, Kasdi Merbah University of Ouargla, Ouargla, Algeria
algorithms, evolutionary algorithms (EAs) have shown good results in solving problems in many research areas, including engineering, biology, robotics [51], classification and clustering [2, 3], machine learning [5], information retrievals [4] and optimization. Namely, Non-dominated Sorting Genetic Algorithm (NSGA2) [18], Strength Par
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