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State-transition simulated annealing algorithm for constrained and unconstrained multi-objective optimization problems Xiaoxia Han1

· Yingchao Dong2 · Lin Yue1 · Quanxi Xu1 · Gang Xie1 · Xinying Xu1

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Abstract In this article, a novel multi-objective optimization algorithm based on a state-transition simulated annealing algorithm (MOSTASA) is proposed, in which four state-transition operators for generating candidate solutions and the Pareto optimal solution is obtained by combining it with the concept of Pareto dominance and then storing it in a Pareto archive. To ensure the uniform distribution of the Pareto optimal solution, we define a crowded comparison operator to update the Pareto archive. Simulation experiments were conducted on several standard constrained and unconstrained multi-objective problems, in which convergence and spacing metrics were used to assess the performance of the MOSTASA. The test results manifest that the MOSTASA can converge to the true Pareto-optimal front, and the solution distribution is uniform. Compared to the performance of other multi-objective optimization algorithms, the proposed algorithm is more efficient and reliable. Keywords Multi-objective optimization · Pareto dominance · State transition · Simulated annealing algorithm

1 Introduction Many practical engineering problems need to consider the simultaneous optimization of multiple objectives, which often conflict. Improvement in the performance of one objective is often at the cost of sharp deterioration in the performance of others. Therefore, it is necessary to find effective and rapid methods to these problems. Solving multi-objective optimization problems (MOPs) involves a trade-off between conflicting objectives. Although traditional mathematical methods are effective in solving MOPs, their objective functions have the requirements of differentiability, continuity and sometimes linearity [1]. In addition, most mathematical methods can only generate one solution at a time [2]. In contrast, multi-objective evolutionary algorithms (MOEAs) [3–5] are population-based, have no  Xiaoxia Han

[email protected] 1

College of Electrical and Power Engineering, Department of Automation, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, China

2

School of Electronic and Information Engineering, Taiyuan University of Science and Technology, Taiyuan, Shanxi, 030024, China

restriction on the objective function and can identify multiple optimal solutions in just one run. In the past few decades, many MOEAs have been devised to solve MOPs. For example, the non-dominant genetic algorithm (NSGA) [6] was the first MOEA proposed to solve MOPs. An improved version of the NSGA (NSGA-II) [7] proposed by Deb et al. in 2000 provided a unified framework for MOEAs. NSGA-II adopts a fast non-dominant sequencing method and solves MOPs by combining the strategies of parent and offspring populations. There are also many other multi-objective optimization algorithm