A Simulation Optimization Method For Solving Vehicle Routing Problems With Time Windows

Focusing on the low efficiency and complex model of conventional approaches for solving vehicle routing problems with time windows, the principle of simulation optimization based on heuristic transformation is presented. According to this principle, a simulation optimization method for solving vehicle routing problems with time windows based on heuristic transformation is proposed. Using adjacency matrix which corresponds to the distance matrix and requirement matrix to represent logistics distribution scheme, this paper develops a matrix model of vehicle routing problems with time windows. The relationship between simulation and optimization is realized through matrix analysis and transformation. Through analyzing the parameters matrix produced by simulation, using heuristics to produce improved search strategies and transform the adjacency matrix, the heuristic algorithm finds the best solution or content solution. The main studies in this paper are as follows:(1) Focusing on the relationship between simulation and optimization, the principle of simulation optimization with heuristic transformation is constructed. According to this principle, a simulation optimization method for solving vehicle problems based on heuristic transformation is proposed.(2) On the basis of the analysis of the attributes of VRPTW, an adjacent matrix is used to denote the scheme of VRPTW. Using the principle and method of matrix transformation, the matrix model of VRPTW is developed.(3) Through analyzing the time windows and distance matrix of the nodes, we construct a probability transferring matrix, which is used to produce the initial scheme of VRPTW.(4) By analyzing the cost matrix and probability transferring matrix, the heuristic that maximizes the number of minimal independency elements is used to develop the improved search strategies and find the best or content solution.(5) Finally, a system is designed to realize the method of simulation optimization based on heuristic transformation. The system gives outstanding solutions which are better than the best solutions of Benchmark Problems at present in the world.The thought of heuristic transformation and the method of matrix analysis and transformation can be utilized for solving such problems which are congener to VRPTW. Meanwhile, the new research direction about solving NP-hard problems by the method of matrix transformation does make sense.