Research On Evolutionary Algorithms For Multi-objective Optimization

Multi-objective optimization approaches have been widely used in the field of engineering applications. Many researchers have been attracted by the research on solving multi-objective optimization problems based on evolutionary algorithms. The key technique issues and applications of multi-objective optimization evolutionary algorithms are studied in this dissertation, and the main research work is concluded as follows:(1) A multi-objective optimization evolutionary algorithm incorporating preference information is proposed. A preference handling method to quantify the relative importance between pairs of objectives is proposed, and the influence of the parameters on the results of the preference handling is discussed. A new outranking relation called "strength superior" is constructed based on fuzzy logic to compare candidate solutions instead of the commonly used Pareto dominance relation. The relationship between these two outranking relations is analyzed theoretically. A novel strategy of fitness evaluation is designed based on the "strength superior" relation. The preference information of the decision maker is incorporated into the algorithm interactively vie the graphical user interface in order to guide the algorithm to find the solutions located in the desired regions. The computational complexity of the algorithm is analyzed. The proposed algorithm is applied to a parameter optimization problem in the control system for a manipulator with 5 objectives. Simulation results indicate that the proposed algorithm can deal with high dimensional multi-objective optimization problems effectively, and it can reduce the burden of the decision maker.(2) A multi-objective optimization evolutionary algorithm keeping diversity of the population is proposed. A metric based on entropy to measure the diversity of the population in the case of multi-objective space is proposed. The evolving state of current population is associated with the running mechanism of the algorithm by the diversity metric. It explores new individuals in the vicinity of elitist individuals located in the sparse region, controls the number of elitist individuals, adjusts the formation of the population in the new generation adaptively according to the diversity metric, and converts between the two searching modes which are exploitation of elitist individuals and exploration of new individuals so as to prevent the algorithm from stagation or premature. The computational complexity of the algorithm is analyzed. Simulation results in a complex multi-modal function and a mechanical design problem indicate that the proposed algorithm has good performance of convergence and distribution.(3) For the decomposable problem, a cooperative co-evolutionary algorithm for multi-objective optimization is proposed. n subpopulations are set to evolve n decision variables of the problem respectively. Considering the characteristics of multi-objective optimization problems, a novel form of collaboration among subpopulations which can increase the diversity of the candidate solutions is designed. The computational complexity of the algorithm is analyzed. Simulation results in a suite of standard test functions indicate that the proposed algorithm has high searching efficiency. For the undecomposable problem, a multi-objective optimization co-evolutionary algorithm with dynamically varying number of subpopulations is proposed. A new criterion judging the stagnation of the population in evolutionary algorithms in the existence of multiple objectives is presented, and the conditions of adding and deleting subpopulations and the stopping criterion of the algorithm are induced. The computational complexity of the algorithm is analyzed. Simulation results in a suite of standard test functions indicate that the proposed algorithm can save computational resources as many as possible while ensuring the performance of convergence and diversity of the algorithm.(4) The applications of multi-objective optimization evolutionary algorithms are studied. The multi-objective optimization model of the inverse kinematics problem of the redundant manipulator is constructed. For the characteristic of this problem, a new way to produce individuals which can ensure the satisfaction of the constraints is adopted in the proposed multi-objective optimization evolutionary algorithm keeping diversity of the population. The improved algorithm is employed to solve the inverse kinematics problem of the redundant manipulator with 3 objectives. The multi-objective optimization model of the single robot path planning problem is constructed. For the characteristics of this problem, the heuristic method based on domain knowledge is employed in the initialization, and three intelligent evolutionary operators are adopted in the proposed multi-objective optimization evolutionary algorithm keeping diversity of the population, which make the algorithm optimize multiple objectives of the problem simultaneously. The multi-objective optimization model of the multi-robot path planning problem is constructed. A coordinated strategy among robots is presented. The paths of multiple robots are planned based on the proposed cooperative co-evolutionary algorithm for multi-objective optimization.