Multi-objective Optimization Algorithm And Its Application In The Problem Of Public Bicycle Scheduling

As an important branch of mathematics,multi-objective optimization problems play an important role in the field of scientific research and engineering.In multi-objective optimization problems,multiple objectives are usually contradictory and restrict each other,the performance optimization of one objective often leads to the performance degradation of at least one other objective.Based on this,in recent years,multi-objective optimization algorithm,exact algorithm and heuristic optimization algorithm have gradually become popular methods to solve multi-objective optimization problems,and have been widely used in practical optimization scheduling problems.This paper mainly studies the related theories and implementation of multi-objective optimization algorithm,exact algorithm,heuristic optimization algorithm and public bicycle scheduling problem.The main contents and innovations are as follows:1.Research on the related theories of multi-objective optimization algorithms: firstly,based on the dual ascent method and the augmented Lagrange multiplier method,an alternating direction method of multipliers for solving multi-objective unconstrained optimization problems and multi-objective optimization problems with linear constraints is proposed;Secondly,on the basis of the original research,four improved indirect algorithms of multi-objective optimization are proposed,including linear weighted sum method based on ideal point,linear weighted sum method based on normalization,linear weighted sum method based on main objective and main objective method based on expected value.The relationship between multi-objective optimization problems and solutions of transformed single-objective optimization problems is discussed.2.Research on the related theories of exact algorithms: mainly for indefinite integer quadratic programming problem,a new branch and bound method is proposed.Based on DC decomposition and convex estimation,a lower bound technique is given,and the branching process adopts "hyper rectangular integer division" to improve the approximation degree of the algorithm,and the detailed steps of the algorithm and numerical experiments are given.3.In order to solve the public bicycle scheduling problem(referred to as the PBVSP problem),a multi-objective optimization model is established based on the minimization of the path length and the number of dispatched vehicles,and a hybrid heuristic optimization algorithm combining simulated annealing algorithm with genetic algorithm is proposed to solve the model.The algorithm uses the simulated annealing algorithm in the genetic algorithm to make judgment and selection,and proposes three improved chromosome crossover methods in the genetic algorithm.The experimental analysis shows that the improved algorithm can greatly improve the optimization effect and search efficiency.4.In order to solve the public bicycle scheduling problem with time window(referred to as the VSPTW problem),a multi-objective optimization model is established based on the minimization of vehicle running cost,the minimization of vehicle fixed cost and the minimization of penalty cost that does not meet the time window range,an objective optimization algorithm and an improved multi-objective optimization algorithm are used to solve the model.The experimental analysis shows that the optimization effect of the improved multi-objective optimization algorithm is better than that of the traditional multi-objective optimization algorithm.