Resource allocation problems with expensive function evaluations

TL;DR

This paper addresses the challenge of solving resource allocation problems with costly function evaluations by proposing new heuristics and exact methods that reduce evaluation counts, demonstrating superior performance over existing solvers.

Contribution

It introduces novel solution approaches for integer resource allocation problems with expensive evaluations, applicable to convex and non-convex costs, and validates them through extensive experiments.

Findings

Methods reduce number of function evaluations

Solutions outperform existing derivative-free optimizers

Effective on both synthetic and real-world instances

Abstract

The resource allocation problem is among the classical problems in operations research, and has been studied extensively for decades. However, current solution approaches are not able to efficiently handle problems with expensive function evaluations, which can occur in a variety of applications. We study the integer resource allocation problem with expensive function evaluations, for both convex and non-convex separable cost functions. We present several solution methods, both heuristics and exact methods, that aim to limit the number of function evaluations. The methods are compared in numerical experiments using both randomly generated instances and instances from two resource allocation problems occurring in radiation therapy planning. Results show that the presented solution methods compare favorably against existing derivative free optimization solvers.