Improved chemical reaction optimization for distributed flexible job shop problem with transportation times

Abstract

In this paper, we study a new variant of the Distributed Flexible Job shop Scheduling Problem introducing transportation time between machines as additional constraints. The problem is called Distributed Flexible Job shop Scheduling Problem with Transportation times and denoted by DFJSPT. In DFJSPT, each operation can be executed on one of the available machines in a set of geographically distributed factories. Each factory has a set of machines on which a set of jobs must be executed and the transport of jobs between machines is made by one or several transport robots. The DFJSPT combines three NP-Hard problems: The problem of assigning jobs to machines, the distribution problem of jobs to factories, and the robot routing problem. In this paper, we study the DFJSPT with a single robot in each factory and we propose an improved Chemical Reaction Optimization (CRO) metaheuristic to solve it in order to minimize the makespan to which we have made improvements in the classic CRO optimization phases in our algorithm. This phase consists of four functions: The crossover-Synthesis function, where we applied one point crossover known operator for the synthesis function, The mutation-OnWall function, where we applied the swap technique, The decomposition function, where we used the inversion mutation technique in this function and the Inter-Molecular, where we applied the two point crossover operator. We tested our approach on two different categories of instances that we designed on purpose, the first category is composed of instances of flexible job shop scheduling problem with transportation times to which we have integrated the constraints of jobs distribution between factories, the second category is composed of instances of distributed and flexible job shop scheduling problem to which we have integrated the constraints of Transportation times.