Research On Multi-Objective Particle Swarm Optimization Algorithm And Its Application

In real-world engineering applications,the problem that needs to optimize multiple objectives which are often in conflict with each other simultaneously is encountered,which is called multi-objective optimization problem(MOP).Different from the single-objective optimization problems(SOPs),a set of tradeoff solutions,known as Pareto optimal solutions,rather than a single optimal solution is usually adopted to represent the best possible compromises among objectives in a given MOP.In the past two decades,multi-objective optimization has attracted increasing interests in the evolutionary computation community,and a large number of multi-objective optimization algorithms have been developed on the basis of different population based meta-heuristics.Particle swarm optimization(PSO)is one of the most classical swarm intelligence algorithms.PSO has good potential in solving MOPs due to its concise formation,fast convergence,and flexible parameters.However,when applying PSO to optimize MOPs,there are several challenges,such as maintaining the archive,selecting the global and personal best solutions,and balancing the exploration and exploitation,to be considered.The main work of the thesis is concluded as follows:(1)It is important to balance convergence and diversity of the obtained approximate Pareto front during the evolutionary process for a MOP.Inverted generational distance(IGD)is a comprehensive indicator capable of measuring convergence and diversity of a solution set simultaneously.In this paper,a virtual Pareto front(vPF)is constructed from the external archive to play the role similar to a true Pareto Front and the virtual IGD(vIGD)can be calculated based on the vPF.Finally,a multi-objective particle swarm optimization based on the vIGD(MOPSO/vIGD)is proposed.The experimental results demonstrate that the proposed algorithm performs significantly better than several state-of-the-art MOPSOs and multi-objective optimization evolutionary algorithms(MOEAs)on the selected benchmark functions in terms of convergence and diversity of those obtained approximate Pareto fronts.(2)The leader selection strategy is the key component of designing a MOPOS.It is necessary to select different leaders with different tasks adaptively during the whole search process.In this paper,a novel evolutionary state estimation(ESE)mechanism is proposed to monitor the current evolutionary state,which is identified as exploitation or exploration state in this mechanism.Therefore,the different gBest selection strategies are designed based on the ESE.In the search process,different kinds of leaders,such as a convergence global best solution(c-gBest)and several diversity global solutions(d-gBests),are intended to be selected for particles under different evolutionary environments.The c-gBest is selected for improving the convergence when the population is in the exploitation state while the d-gBests are chosen for increasing the diversity in the exploration state.Also,a modified archive maintenance strategy based on some predefined reference points is proposed to maximize the diversity of the Pareto solutions in the external archive.An adaptive MOPSO based on ESE(AMOPSO/ESE)seamlessly integrates with the strategies described above is proposed in this paper.The experimental results demonstrate that the proposed algorithm performs better than the selected MOPSOs and MOEAs in terms of convergence and diversity of those obtained approximate Pareto fronts.(3)The resource schedule problem is used to check whether the proposed algorithms are able to solve real problem.Currently,single-objective optimization or transforming multiple objectives into one objective model using weighting coefficients are commonly used to optimize emergency resource schedule problems.In fact,multiple goals,such as time,fairness,and cost,should be taken into considerations together during earthquake emergency resource schedule.But it is very difficult to determine the weight coefficients among these goals.The three-objective optimization models with constraints are constructed according to earthquake emergency resource schedule problems in this paper.The adjusted multi-objective particle swarm optimization is adopted to solve the models for the Pareto optimal sets.At the same time,based on the decision behavior pattern of “macro first and micro later”,the two-level optimal solution set consisting of interest optimal solution set and neighborhood optimal solution set is proposed to represent Pareto front roughly,which can simplify the decision-making process.The simulation results show that the chosen algorithm can effectively obtain the resource schedule,and can conveniently guide the decision maker to choose an execution schedule from the candidate schedules in Pareto front.