Optimal Computing Budget Allocation for Particle Swarm Optimization in Stochastic Optimization

Abstract

Particle Swarm Optimization (PSO) is a popular metaheuristic for deterministic optimization. Originated in the interpretations of the movement of individuals in a bird flock or fish school, PSO introduces the concept of personal best and global best to simulate the pattern of searching for food by flocking and successfully translate the natural phenomena to the optimization of complex functions. Many real-life applications of PSO cope with stochastic problems. To solve a stochastic problem using PSO, a straightforward approach is to equally allocate computational effort among all particles and obtain the same number of samples of fitness values. This is not an efficient use of computational budget and leaves considerable room for improvement. This paper proposes a seamless integration of the concept of optimal computing budget allocation (OCBA) into PSO to improve the computational efficiency of PSO for stochastic optimization problems. We derive an asymptotically optimal allocation rule to intelligently determine the number of samples for all particles such that the PSO algorithm can efficiently select the personal best and global best when there is stochastic estimation noise in fitness values. We also propose an easy-to-implement sequential procedure. Numerical tests show that our new approach can obtain much better results using the same amount of computational effort.

Seismic Model Parameter Optimization for Building Structures

“…This work also briefly described the inertia weight parameter and the possible need for a constriction factor. PSO has so far been applied successfully in many areas [49][50][51][52], and some improved PSO versions have also been studied [52][53][54][55][56]. Basically, the PSO algorithm has been used to find an optimum search space in complex areas by interacting with people in a particle population [57].…”

Two-Dimensional Steady-State Boundary Shape Inversion of CGM-SPSO Algorithm on Temperature Information

“…where the point " " represents the point source point, we get formula (13) into formula (12) and use the nature of the function , and we can get…”

“…Inversion methods based on optimization techniques can be divided into gradient-based optimization algorithms and nongradient optimization algorithms. Gradient optimization algorithm mainly includes the conjugate gradient method [8] (CGM), Levenberg-Marquardt method [9] (L-MM) and the steepest descent method [9] (SDM), and nongradient optimization algorithm mainly includes genetic algorithm [10] (GA), neural network algorithm [11] (NNM), particle swarm optimization (PSO) [12], and so forth.…”

An Improved Convergence Particle Swarm Optimization Algorithm with Random Sampling of Control Parameters

“…PSO, proposed by Kennedy and Eberhart [1], is an evolutionary algorithm based on swarm intelligence which simulates birds or fish predation, and it has already attracted a lot of interest from scholars and researchers for the reason that PSO has simple structure, strong maneuverability, easy realization, and other characteristics. Up to now, PSO has been successfully applied in many areas [2][3][4][5][6], and meanwhile some improved versions of PSO have also been studied accordingly [7][8][9][10][11].…”