Hybrid particle swarm optimization and differential evolution algorithm for bi-level programming problem and its application to pricing and lot-sizing decisions

2013 ◽  
Vol 26 (3) ◽  
pp. 471-483 ◽  
Author(s):  
Weimin Ma ◽  
Miaomiao Wang ◽  
Xiaoxi Zhu
Keyword(s):  
Particle Swarm Optimization ◽  
Differential Evolution ◽  
Programming Problem ◽  
Lot Sizing ◽  
Differential Evolution Algorithm ◽  
Particle Swarm ◽  
Swarm Optimization ◽  
Hybrid Particle ◽  
Hybrid Particle Swarm Optimization ◽  
Evolution Algorithm

scholarly journals Multi-Objective Optimization of Planetary Gearbox with Adaptive Hybrid Particle Swarm Differential Evolution Algorithm

2021 ◽  
Vol 11 (3) ◽  
pp. 1107
Author(s):  
Miloš Sedak ◽  
Božidar Rosić
Keyword(s):  
Particle Swarm Optimization ◽  
Differential Evolution ◽  
Differential Evolution Algorithm ◽  
Particle Swarm ◽  
Multi Objective Optimization ◽  
Swarm Optimization ◽  
Planetary Gearbox ◽  
Multi Objective ◽  
Mutation Operators ◽  
Evolution Algorithm

This paper considers the problem of constrained multi-objective non-linear optimization of planetary gearbox based on hybrid metaheuristic algorithm. Optimal design of planetary gear trains requires simultaneous minimization of multiple conflicting objectives, such as gearbox volume, center distance, contact ratio, power loss, etc. In this regard, the theoretical formulation and numerical procedure for the calculation of the planetary gearbox power efficiency has been developed. To successfully solve the stated constrained multi-objective optimization problem, in this paper a hybrid algorithm between particle swarm optimization and differential evolution algorithms has been proposed and applied to considered problem. Here, the mutation operators from the differential evolution algorithm have been incorporated into the velocity update equation of the particle swarm optimization algorithm, with the adaptive population spacing parameter employed to select the appropriate mutation operator for the current optimization condition. It has been shown that the proposed algorithm successfully obtains the solutions of the non-convex Pareto set, and reveals key insights in reducing the weight, improving efficiency and preventing premature failure of gears. Compared to other well-known algorithms, the numerical simulation results indicate that the proposed algorithm shows improved optimization performance in terms of the quality of the obtained Pareto solutions.

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