# Algorithm Portfolio for Individual-based Surrogate-Assisted Evolutionary Algorithms

## TL;DR

This paper introduces algorithm portfolios for surrogate-assisted evolutionary algorithms to improve performance on expensive optimization problems by adaptively selecting algorithms, outperforming individual algorithms under limited evaluations.

## Contribution

It proposes two portfolio frameworks, Par-IBSAEA and UCB-IBSAEA, using parallel execution and reinforcement learning for algorithm selection in costly problems.

## Key findings

- Portfolios outperform single algorithms on benchmark problems.
- UCB-IBSAEA effectively adapts algorithm choice during optimization.
- Significant reduction in computational resources needed for problem solving.

## Abstract

Surrogate-assisted evolutionary algorithms (SAEAs) are powerful optimisation tools for computationally expensive problems (CEPs). However, a randomly selected algorithm may fail in solving unknown problems due to no free lunch theorems, and it will cause more computational resource if we re-run the algorithm or try other algorithms to get a much solution, which is more serious in CEPs. In this paper, we consider an algorithm portfolio for SAEAs to reduce the risk of choosing an inappropriate algorithm for CEPs. We propose two portfolio frameworks for very expensive problems in which the maximal number of fitness evaluations is only 5 times of the problem's dimension. One framework named Par-IBSAEA runs all algorithm candidates in parallel and a more sophisticated framework named UCB-IBSAEA employs the Upper Confidence Bound (UCB) policy from reinforcement learning to help select the most appropriate algorithm at each iteration. An effective reward definition is proposed for the UCB policy. We consider three state-of-the-art individual-based SAEAs on different problems and compare them to the portfolios built from their instances on several benchmark problems given limited computation budgets. Our experimental studies demonstrate that our proposed portfolio frameworks significantly outperform any single algorithm on the set of benchmark problems.