Optimisation via Slice Sampling

TL;DR

This paper introduces a simulation-based optimisation method using slice sampling for multi-modal functions, leveraging energy potentials and auxiliary variables to identify global modes, demonstrated on standard test functions.

Contribution

It presents a novel slice sampling approach for optimisation that effectively handles multi-modal functions by using energy potentials and auxiliary variables.

Findings

Successfully applied to functions with multiple modes and complex landscapes

Demonstrates flexibility across diverse test functions

Implemented in R package McmcOpt

Abstract

In this paper, we develop a simulation-based approach to optimisation with multi-modal functions using slice sampling. Our method specifies the objective function as an energy potential in a Boltzmann distribution and then we use auxiliary exponential slice variables to provide samples for a variety of energy levels. Our slice sampler draws uniformly over the augmented slice region. We identify the global modes by projecting the path of the chain back to the underlying space. Four standard test functions are used to illustrate the methodology: Rosenbrock, Himmelblau, Rastrigin, and Shubert. These functions demonstrate the flexibility of our approach as they include functions with long ridges (Rosenbrock), multi-modality (Himmelblau, Shubert) and many local modes dominated by one global (Rastrigin). The methods described here are implemented in the {\tt R} package {\tt McmcOpt}.