Resource allocation problems with expensive function evaluations

• Published in: European journal of operational research Vol. 306; no. 3; pp. 1170 - 1185
• Main Authors: ten Eikelder, S.C.M., van Amerongen, J.H.M.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2023
• Subjects: Black-box optimization; Expensive function evaluations; Nonlinear programming; Radiation therapy; Resource allocation problem; Expensive function evaluations; Nonlinear programming; Radiation therapy; Resource allocation problem; Black-box optimization
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2022.07.048

•A formulation of resource allocation problems with expensive function evaluations.•Two novel solution methods exploiting cost function separability.•Extensive numerical experiments, including two radiation therapy applications.•The novel solution methods outperform existing derivative free optimization solvers. 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.