Optimising a nonlinear utility function in multi-objective integer programming

TL;DR

This paper presents a new algorithm for optimizing nonlinear utility functions in multi-objective integer programming, leveraging bounds, known solutions, and linear relaxations to efficiently find optimal solutions.

Contribution

It introduces a general optimization algorithm for multiple objectives, combining bounds, utility inversion, and integer programming techniques, demonstrated on a tri-objective problem.

Findings

Effective optimization of nonlinear utility functions in multi-objective integer programming.

Algorithm applicable to any number of objectives, demonstrated on three objectives.

Utilizes known solutions and relaxations to improve efficiency.

Abstract

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem.