A Multiobjective Optimization Evolutionary Algorithm and Its Application

This paper presents a genetic algorithm for vector optimization, PAND-ES (Pareto Adaptive Normal Distribution Evolution Strategy). The approximate Pareto set is being clarified and completed over successive generations. The method uses normal distribution, but generating sample points in the parameter space is performed without covariance matrix calculating. The algorithm is simple to implement and demonstrates high convergence rate. The proposed algorithm is applied to the problem of multiobjective optimization of electron beam longitudinal motion in a linear accelerator. A representative Pareto set is obtained. Beam dynamics investigation shows the Pareto-optimal solutions to be promising. The vector optimization results are validated using the NSGA-II algorithm (Nondominated Sorting Genetic Algorithm II). However, the latter was found to be slower both in generation formation and convergence speed compared to the PAND-ES algorithm.