Research And Application Of Decomposition Multii Objecttivr Evolutionary Algorithm Dased On Differential Neighborhood Strategy

In practical engineering and scientific research,multi-objective optimization issues has been a hot topic because of humans always follow the optimization principle of “maximizing benefits and minimizing costs”.The multi-objective optimization problem aims to optimize the multiple goals of conflicting and constraining at the same time,and obtain a set of approximate Pareto optimal solution sets for the decision maker to select the optimal solution.The multi-objective evolutionary algorithm based on decomposition(MOEA/D)becomes a research hotspot with advantages of a strong search capability in solving multi-objective optimization problems,high-efficiency fitness evaluation,good convergence,short running time,low complexity and so on.However,the proportion of non-dominated solutions in the population rises rapidly with the target dimension increases,and the number of solutions required to approach the entire Pareto frontier increases exponentially,with the same time,making the ability of the algorithm to search globally optimal solutions drop sharply;furthermore,the pressure on the selection of excellent solutions for the algorithm is insufficient when there are multi-objective optimization problems with complex Pareto solution sets resulting in it is easy to fall into a local optimum.,there are some problems when MOEA/D solves such multi-objective optimization problems,such as insufficient solution quality,slow convergence rate,less convergence,unreasonable resource allocation and so on.In view of the above difficulties,this paper proposes a differential neighborhood strategy which is based on computational resources of the algorithm,by analyzing the effect of different sizes of neighborhoods on the performance of the algorithm.It allocates thecomputational resources of the algorithm effectively to improve the performance of the algorithm.The main research contents are as follows:(1)The performance of the decomposition-based multi-objective evolutionary algorithm is easily affected by the neighborhood of a subproblem.When the neighborhood is too large,the new solutions generated by the population propagation deviate from the Pareto set and the frequency of comparison between new solutions and old solutions in the neighborhood is increased for the updating subproblems.Consequently,the computational complexity of the algorithm is increased.If the neighborhood is too small,the algorithm easily falls into the local optimum.To solve this problem,a decomposed multi-objective evolutionary algorithm based on differentiated neighborhood strategy(MOEA/D-DN)is proposed.The suitable parameters are selected by analyzing the influence of different neighborhood sizes on the algorithm performance and different sizes of neighborhood for each subproblem are set according to the angle between their weight vectors and the central vector.Thus,the resource of algorithm is allocated more rationally and the velocity of searching for the optimal solution is also improved.(2)Apply MOEA/D-DN to vehicle routing problems with hard time windows.The algorithm decomposes the multi-objective vehicle routing problem into a number of single-objective optimization subproblems by using decomposition strategy,and generates uniformly distributed weight vectors in the target space,so that each weight vector is bound to an individual,and optimizing these sub-problems simultaneously.It allows individuals to converge towards the Pareto front along the direction of the weight vector,allocates reasonable computing resources to each sub-problem through a differentiated neighborhood strategy,and increases the selection pressure of the algorithm for better solutions,providing decision makers with better options.