Genetic Algorithm for Mixed Integer Nonlinear Bilevel Programming and Applications in Product Family Design

Abstract

Many leader-follower relationships exist in product family design engineering problems. We use bilevel programming (BLP) to reflect the leader-follower relationship and describe such problems. Product family design problems have unique characteristics; thus, mixed integer nonlinear BLP (MINLBLP), which has both continuous and discrete variables and multiple independent lower-level problems, is widely used in product family optimization. However, BLP is difficult in theory and is an NP-hard problem. Consequently, using traditional methods to solve such problems is difficult. Genetic algorithms (GAs) have great value in solving BLP problems, and many studies have designed GAs to solve BLP problems; however, such GAs are typically designed for special cases that do not involve MINLBLP with one or multiple followers. Therefore, we propose a bilevel GA to solve these particular MINLBLP problems, which are widely used in product family problems. We give numerical examples to demonstrate the effectiveness of the proposed algorithm. In addition, a reducer family case study is examined to demonstrate practical applications of the proposed BLGA.

Multi-Objective Bi-Level Programming for the Energy-Aware Integration of Flexible Job Shop Scheduling and Multi-Row Layout

“…Ma et al [32] proposed a hierarchical hybrid particle swarm optimization and differential evolution algorithm to solve the pricing and lot-sizing decision problem. Miao et al [33] developed a bi-level GA to solve the mixed integer nonlinear bi-level programming for the product family problem. As a representative intelligence algorithm, the genetic algorithm simulates the evolution process of survival of the fittest and approaches the excellent results gradually.…”