<abstract xmlns="http://www.w3.org/1999/xhtml"><p>As a metaheuristic, Particle Swarm Optimization (PSO) has been used to solve the Bi-level Multiobjective Programming Problem (BMPP). However, in the existing solving approach based on PSO for the BMPP, the upper level and the lower level problem are solved interactively by PSO. In this paper, we present a different solving approach based on PSO for the BMPP. Firstly, we replace the lower level problem of the BMPP with Kuhn-Tucker optimality conditions and adopt the perturbed Fischer-Burmeister function to smooth the complementary conditions. After that, we adopt PSO approach to solve the smoothed multiobjective programming problem. Numerical results show that our solving approach can obtain the Pareto optimal front of the BMPP efficiently.</p></abstract>

As a metaheuristic, Particle Swarm Optimization (PSO) has been used to solve the Bi-level Multiobjective Programming Problem (BMPP). However, in the existing solving approach based on PSO for the BMPP, the upper level and the lower level problem are solved interactively by PSO. In this paper, we present a different solving approach based on PSO for the BMPP. Firstly, we replace the lower level problem of the BMPP with Kuhn-Tucker optimality conditions and adopt the perturbed Fischer-Burmeister function to smooth the complementary conditions. After that, we adopt PSO approach to solve the smoothed multiobjective programming problem. Numerical results show that our solving approach can obtain the Pareto optimal front of the BMPP efficiently.

Particle Swarm Optimization Based on Smoothing Approach for Solving a Class of Bi-Level Multiobjective Programming Problem

Cybernetics and Information Technologies

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

As a metaheuristic, Particle Swarm Optimization (PSO) has been used to solve the Bi-level Multiobjective Programming Problem (BMPP). However, in the existing...

Particle Swarm Optimization Based on Smoothing Approach for Solving a Class of Bi-Level Multiobjective Programming Problem

Published Online: Oct 04, 2017

Page range: 59 - 74

DOI: https://doi.org/10.1515/cait-2017-0030

Keywords
Bi-level multiobjective programming problem, scalarization method, optimality conditions, smoothing method, particle swarm optimization

© 2017 Qingping He et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Particle Swarm Optimization Based on Smoothing Approach for Solving a Class of Bi-Level Multiobjective Programming Problem

Published Online: Oct 04, 2017

Page range: 59 - 74

DOI: https://doi.org/10.1515/cait-2017-0030

KeywordsBi-level multiobjective programming problem, scalarization method, optimality conditions, smoothing method, particle swarm optimization

© 2017 Qingping He et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Bi-level multiobjective programming problem, scalarization method, optimality conditions, smoothing method, particle swarm optimization