Research On Multi-Objective Particle Swarm Optimization Algorithm And Applications

Multi-objective optimization is an important subject in both scientific studies and engineering applications.As an efficient heuristic algorithm running in parallel,the particle swarm optimization(PSO)algorithm has its advantages in solving multi-objective optimization problems.In this dissertation,a research has been made on multi-objective particle swarm optimization(MOPSO)algorithms.The main contributions are summarized as follows:(1)Most of the existing MOPSO algorithms are sensitive to the values of control parameters.To overcome this limitation,a MOPSO algorithm requiring less control parameters is proposed.To achieve the balance between exploration and exploitation,the particles are updated adaptively using a Gaussian sampling based on the global best position and personal best position of particles.Making use of the spatial information of adjacent particles,a clustering technique based on the difference of individuals' objective values is proposed.To produce well-distributed solutions while guiding the search toward the Pareto front,the proposed clustering technique is used for the update of the external repository,from which the the global best positions are selected.A time-varying mutation operator is incorporated in order to avoid trapping in a local optima.The time complexity of the proposed algorithm is analyzed.Simulation results on several benchmark test problems indicate that the proposed algorithm achieves better convergence and distribution under the same number of fitness function evaluations.(2)Most of the existing MOPSO algorithms scale poorly when dealing with more than 3 objective functions.To overcome this limitation,a r-dominance based MOPSO algorithm is proposed.The r-dominance is adopted to compare particles instead of the commonly used Pareto dominance relation,thus guiding the search toward the interesting parts of the Pareto optimal region based on the decision maker's preferences expressed as a reference point.This not only enriches the search capacities of the algorithm when the number of objectives increases but also lightens the decision burden.Restricting the search space using a preference mechanism,however,may cause a lack of population diversity.To avoid this phenomena,the value of the non-r-dominance threshold is varied in an improved way.Furthermore,the external repository is updated by incorporating the crowding distance in the variable space to avoid trapping in a local optima.Simulation results on several benchmark test problems indicate that the proposed algorithm outperforms three other existing algorithms in terms of convergence,diversity and distribution over the reference point.(3)Most of the existing MOPSO algorithms have difficulties handling uncertainty given as intervals.To deal with this kind of problems,a fuzzy dominance based MOPSO algorithm is proposed.With the help of fuzzy set theory,an order relation of interval-valued objective functions is defined by using the membership function.Applying this,a fuzzy dominance relation substituting the standard Pareto dominance relation is developed for comparing particles.The influence of the confidence level on the construction of non-dominated solution sets is discussed theoretically.In order of keep population diversity,the crowding distance is extended to the handle interval-valued objective functions.The effect of different confidence level values on the performance of the algorithm is validated experimentally.Simulation results on several interval-valued benchmark test problems indicate that the proposed algorithm is effective in handling multi-objective optimization problems with uncertainty given as intervals.(4)The application of MOPSO algorithms in the reliability optimization problem is investigated.To solve the redundancy allocation problem formulated as a multi-objective optimization problem,the proposed MOPSO algorithm which requires less control parameters is modified.The particles are initialized in a heuristic way.A combination of modification and penalty strategy is adopted to handle the constraints.Additionally,the mutation operator is applied for not only particles but also members in the external repository.Two illustrative examples are presented to show the feasibility and effectiveness of the proposed approach.Next,the redundancy allocation problem with uncertainty given as intervals is considered.To deal with the problem modeled in an interval environment,the proposed fuzzy-dominance based MOPSO algorithm is modified.An integer encoding scheme as well as the heuristic way of initialization is adopted.A constraint-handling strategy for interval-valued objectives is incorporated.The effectiveness of the proposed approach has been demonstrated through three numerical examples...