Theory Of Particle Swarm Optimization For Interval Multi-objective Optimization Problems And Applications

Uncertain multi-objective optimization problems widely exist in real-world applications. Since they often contain multiple objectives with conflict as well as uncertain objective functions and constraints, it is difficult for traditional optimization algorithms to solve them. This dissertation studies theory and method of particle swarm optimization for multi-objective optimization problems with interval uncertainty, namely,interval multi-objective optimization problems,and applies parts of the proposed method into 2 typically real optimization problems.Considering an interval multi-objective optimization problem without constraints, two multi-objective particle swarm optimization algorithms (MOPSO) are presented. (1) The probability dominance relationship based MOPSO algorithm. In this algorithm, a probability dominance relationship is defined to compare qualities among particles with interval objective values. A method based on Sigma intervals is introduced to update the global best position of particle. Based on decision-maker's degree of tolerance, an updating method for the external archive is presented. Compared with those optimization approaches that transform interval objective values into precise ones, our algorithm requires less preference information from decision-makers. (2)The barebones MOPSO algorithm. This algorithm updates particle's position by a Gaussian sampling which bases on the global and local best position of particle, and tunes mutation probability and range based on iterative times of the algorithm simultaneously. To select the global best position for each particle and update the external archive, a new crowding distance measure is adopted to evaluate particles'density. Compared with the first algorithm, this one does not require inertia weight and acceleration coefficients, so it is an almost control parameter-free particle swarm optimization algorithm.Considering a multi-objective optimization problem with interval constraints, the barebones constrained MOPSO algorithm is proposed. First, a P-reliability measure is defined to evaluate satisfaction degree of a solution to constraints. Based on the constraint-risk coefficient specified by decision-makers, a constrained domination relationship is proposed to evaluate qualities of particles. A new updating method for the infeasible archive is designed based on particles'density and the Pareto dominance relationship. Furthermore, a dynamic selection strategy based on iterative times of the algorithm is also used to select the global best positions of particle from the infeasible archive. Compared with several typical algorithms, our algorithm improves PSO's capability to deal with the constrained multi-objective optimization problems.Finally, the dissertation applies parts of the aforementioned theories and methods into two real application problems. One problem is the multi-project location problem with interval benefits. To solve this problem, an improved particle swarm optimization with reverse mutation is presented. Considering features of the above problem with discrete variables, the equivalent probability matrix is used to transform discrete variables into continuous ones, and an encoding method for particle's position is also proposed to satisfy definition of the equivalent probability matrix as well as part constraints. Moreover, a reverse mutation is incorporated in our algorithm to improve particles'diversity. Another is the path planning problem of robot with uncertain dangers. To solve this problem, an improved constraint MOPSO algorithm is proposed. In this algorithm, a membership function with regard to danger degrees is defined to found model of the problem, a strategy combined with the simulated annealing method is proposed to update the local best position of particle, and a new updating method for particle position is proposed based on random sampling method and uniform mutation. In addition, based on collision times of path with obstacles, an improved constrained domination relationship is defined to evaluate qualities of particles.Feasibility and efficiency of the proposed five approaches/algorithms are validated by applying them into some numerical functions, 15-item-13-site location problems, and simulation environments of robot path planning. Research results of this dissertation enrich theory of the uncertain optimization, expand application domain of PSO, and provide beneficial guides for applying PSO in complicated uncertain systems.