A Two-phase evolutionary algorithm framework for multi-objective optimization
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A Two-phase evolutionary algorithm framework for multi-objective optimization Siyu Jiang1 · Zefeng Chen2 Accepted: 28 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper proposes a two-phase evolutionary algorithm framework for solving multi-objective optimization problems (MOPs), which allows different users to flexibly handle MOPs with different existing algorithms. In the first phase, a specific multi-objective evolutionary algorithm (MOEA) with a smaller population size is adopted to fast obtain a population converging to the true Pareto front. Then, in the second phase, a simple environmental selection mechanism based on a measure function and a well-designed crowdedness function is used to promote the uniformity of population in the objective space. Based on the proposed framework, we form four instantiations by embedding four distinct MOEAs into the first phase of the proposed framework. In the experimental study, different experiments are conducted on a variety of well-known benchmark problems from 3 to 10 objectives, and experimental results demonstrate the effect of the proposed framework. Furthermore, compared with several state-of-the-art multi-objective evolutionary algorithms, the four instantiations of the proposed framework have better performance and can obtain well-distributed solution sets. In short, the proposed framework has the strong ability to promote the performance of existing algorithms. Keywords Multi-objective optimization · Evolutionary algorithm · Convergence · Diversity
1 Introduction
Without loss of generality, an MOP can be formally defined as follows:
As an important kind of optimization problem, multiobjective optimization problems (MOPs) involve the simultaneous optimization of multiple conflicting objectives. Generally, MOPs with at least four objectives are known as many-objective optimization problems (MaOPs) [1]. MOPs widely exist in real-world applications, e.g, car controller optimization [2], automotive engine calibration [3], water resource system planning/control [4, 5], optimizing performance of wireless sensor networks [6], infrastructure deployment in vehicular communication networks [7], optimal product selection for software product lines [8] and so on.
min F(x) = f1 (x), · · · , fm (x)
Zefeng Chen
[email protected] 1
Guangzhou Key Laboratory of Multilingual Intelligent Processing, School of Information Science and Technology, Guangdong University of Foreign Studies, Guangzhou, 510006, PR China
2
School of Computer Science and Engineering, Nanyang Technological University, Singapore, Singapore
s.t. x ∈ X,
(1)
where X ⊂ R n is the decision space, x is the decision variable, F(x) ∈ R m consists of m ≥ 2 functions and R m is the objective space. Since, the objectives fi (x), i = 1, · · · , m, in (1) are often mutually conflicting, there is no a solution x that can minimize all objectives simultaneously. Instead, these conflicting objectives give rise to a set of trade-off optimal solutions. Fo
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