Nested optimization method combining complex method and ant colony optimization to solve JSSP with complex associated processes

摘要

Job Shop Scheduling Problem (JSSP) is one of classic combinatorial optimization problems and has a long research history. Modern job shop has following characteristics: increasingly complicated processes, small batch and personalized requirement, which lead to complex correlations among processes. Complex correlations of processes, involving nested correlations besides serial and parallel correlations, propose a new task for JSSP research. Decomposing JSSP into two nested sub problems of order of arranging processes and machine arrangement, this research integrates the traditional thought of complex method into the ant colony optimization (ACO) to develop a nested optimization method in order to solve the new task. This paper is divided into four parts: first, the model of JSSP with complex associated processes is constructed and the difficulties to solve which are analyzed and listed; second, the definition of "order of arranging processes" is originally proposed, based on which the mathematical model available for the complex method is developed, taking process starting time as design variables of the first level optimization. The steps of the first level optimization and the secondary nested flow chart are detailed with the demonstration of the effectiveness of the complex method's iteration mechanism; third, based on the representation of features the order of arranging processes obtained by the first level optimization combined with the first-in first-out rule owns, the corresponding modified ACO algorithm, involving pheromone positive perception and reverse spreading mechanism, is put forward to realize the second level optimization, which result is taken as the objective function value of the complex vertex to realize the secondary nested optimization strategy; finally, taking plentiful JSSP with complex associated processes as study cases, a serial of comparative experiments are done respectively adopting the genetic algorithm, ACO algorithm, particle swarm optimization algorithm, some combinations of heuristic algorithms respectively in the nested two levels, and the proposed nested optimization method, and experiment results attest the reliability and superiority of the proposed method.