A global optimization paradigm based on change of measures

TL;DR

This paper introduces COMBEO, a novel global optimization framework based on change of measures, which enhances existing evolutionary algorithms with derivative-free directional updates and random perturbations for improved efficiency.

Contribution

The paper presents a new measure-based approach to global optimization that integrates ideas from particle swarm and differential evolution methods, offering a more rational and faster alternative.

Findings

Demonstrates faster convergence compared to existing methods

Provides a more accurate search process

Offers a flexible framework for exploration and exploitation

Abstract

A global optimization framework, acronymed COMBEO (Change OfMeasure Based Evolutionary Optimization), is proposed. An important aspect in the development is a set of derivative-free additive directional terms obtainable through a change of measures en route to the imposition of any stipulated conditions aimed at driving the realized design variables (particles) to the global optimum. The generalized setting offered by the new approach also enables several basic ideas, used with other global search methods such as the particle swarm or the differential evolution, to be rationally incorporated in the proposed setup via a change of measures. The global search may be further aided by imparting to the directional update terms additional layers of random perturbations such as scrambling and selection. Depending on the precise choice of the optimality conditions and the extent of random perturbation, the search can be readily rendered either greedy or more exploratory. As numerically demonstrated, the new proposal appears to provide for a more rational, more accurate and faster alternative to most available evolutionary optimization schemes, prominent amongst which are the differential evolution and the particle swarm methods.