An approximate It\^o-SDE based simulated annealing algorithm for multivariate design optimization problems

TL;DR

This paper introduces a novel simulated annealing variant using Itô stochastic differential equations and spline interpolation to efficiently solve high-dimensional, non-convex design optimization problems, demonstrated on two diverse applications.

Contribution

It develops a new optimization algorithm combining ISDE and spline interpolation, improving global search efficiency in complex, high-dimensional spaces.

Findings

Efficient exploration of large search spaces.

Successful application to high-dimensional and finite element models.

Enhanced ability to find global optima in complex problems.

Abstract

This research concerns design optimization problems involving numerous design parameters and large computational models. These problems generally consist in non-convex constrained optimization problems in large and sometimes complex search spaces. The classical simulated annealing algorithm rapidly loses its efficiency in high search space dimension. In this paper a variant of the classical simulated annealing algorithm is constructed by incorporating (1) an It\^o stochastic differential equation generator (ISDE) for the transition probability and (2) a polyharmonic splines interpolation of the cost function. The control points are selected iteratively during the research of the optimum. The proposed algorithm explores efficiently the design search space to find the global optimum of the cost function as the best control point. The algorithm is illustrated on two applications. The first application consists in a simple function in relatively high dimension. The second is related to a Finite Element model.