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A multi-objective mixed-discrete particle swarm optimization with multi-domain diversity preservation

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Abstract

Among population-based optimization algorithms guided by meta-heuristics, Particle Swarm Optimization (PSO) has gained significant popularity in the past two decades, particularly due to its ease of implementation and fast convergence capabilities. This paper seeks to translate the beneficial features of PSO from solving typical continuous single-objective problems to solving multi-objective mixed-discrete problems, which is relatively a new ground for PSO application. The original Mixed-Discrete PSO (MDPSO) algorithm, which included an exclusive diversity preservation technique to significantly mitigate premature particle clustering, has been shown to be a powerful single-objective solver for highly constrained MINLP problems. This papers makes fundamental advancements to MDPSO, enabling it to solve complex multi-objective problems with mixed-discrete design variables. Specifically, in the velocity update equation for any particle, the explorative term is modified to point towards a stochastically selected non-dominated solution at that iteration − thereby adopting the concept of multi-leader swarms. The fractional domain in the diversity preservation technique, which was previously defined in terms of the best global particle, is now formulated as a function of the extreme members in the set of intermediate Pareto optimal solutions. With this advancement, diversity preservation not only mitigates premature particle stagnation, but also promotes more uniform coverage of the Pareto frontier. The multi-objective MDPSO algorithm is tested using a set of benchmark problems and a wind farm layout optimization problem. To illustrate the competitive benefits of the new MO-MDPSO algorithm, the results are compared with those given by other popular multi-objective solvers such as NSGA-II and SPEA.

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Notes

  1. Wherever color is mentioned in any figure, please refer to the electronic version.

  2. This is the boundary of the feasible region in the objective space also containing the actual Pareto frontier

  3. Solutions of ZDT4 are far away from the feasible region, so the result of ZDT4 is not provided.

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Acknowledgements

Support from the National Science Foundation Awards CMMI-1100948 and CMMI-1437746 is gratefully acknowledged. Any opinions, findings, conclusions, or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the NSF.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Syracuse University, Syracuse, NY, 13244, USA

    Weiyang Tong

  2. Department of Aerospace Engineering, Mississippi State, MS, 39762, USA

    Souma Chowdhury & Achille Messac

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  1. Weiyang Tong
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  2. Souma Chowdhury
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  3. Achille Messac
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Corresponding author

Correspondence to Achille Messac.

Additional information

Parts of this manuscript have been presented at the ASME 2014 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE), in August 17-20, 2014, at Buffalo, New York - Paper Number: DETC2014-35572.

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Tong, W., Chowdhury, S. & Messac, A. A multi-objective mixed-discrete particle swarm optimization with multi-domain diversity preservation. Struct Multidisc Optim 53, 471–488 (2016). https://doi.org/10.1007/s00158-015-1319-8

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