A genetic algorithm extended modified sub-gradient algorithm for cell formation problem with alternative routings

• Published in: International journal of production research Vol. 50; no. 15; pp. 4025 - 4037
• Main Authors: Ozcelik, Feristah, Saraç, Tugba
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.08.2012; Taylor & Francis; Taylor & Francis LLC
• Subjects: Algorithms; alternative routings; Applied sciences; Calculus of variations and optimal control; cell formation problem; cellular manufacturing; Exact sciences and technology; Genetic algorithms; Inventory control, production control. Distribution; Lagrange multiplier; Manufacturing cells; Mathematical analysis; Mathematical models; Mathematics; modified sub-gradient algorithm; Operational research and scientific management; Operational research. Management science; Optimization; Optimization algorithms; Placing; Sciences and techniques of general use; Separation; Solvers; Studies; Voids; Production system; Subgradient optimization; modified sub-gradient algorithm; Routing; Grouping; genetic algorithms; Modeling; Search algorithm; Genetic algorithm; Augmented Lagrangian; Cellular manufacturing; Problem solving; alternative routings; Convexity; Cell system; cell formation problem; Localization
• ISSN: 0020-7543; 1366-588X
• DOI: 10.1080/00207543.2011.588264

This paper addresses the cell formation problem with alternative part routes. The problem is considered in the aspect of the natural constraints of real-life production systems such as cell size, separation and co-location constraints. Co-location constraints were added to the proposed model in order to deal with the necessity of grouping certain machines in the same cell for technical reasons, and separation constraints were included to prevent placing certain machines in close vicinity. The objective is to minimise the weighted sum of the voids and the exceptional elements. A hybrid algorithm is proposed to solve this problem. The proposed algorithm hybridises the modified sub-gradient (MSG) algorithm with a genetic algorithm. MSG algorithm solves the sharp augmented Lagrangian dual problems, where zero duality gap property is guaranteed for a wide class of optimisation problems without convexity assumption. Generally, the dual problem is solved by using GAMS solvers in the literature. In this study, a genetic algorithm has been used for solving the dual problem at the first time. The experimental results show the advantage of combining the MSG algorithm and the genetic algorithm. Although the MSG algorithm, whose dual problem is solved by GAMS solver, and the genetic algorithm cannot find feasible solutions, hybrid algorithm generates feasible solutions for all of the test problems.