# Algorithms for Generating Pareto Fronts of Multi-objective Integer and Mixed-Integer Programming Problems

## TL;DR

This paper adapts algorithms originally for continuous problems to approximate Pareto fronts in multi-objective integer and mixed-integer programming, demonstrating effectiveness on complex problems including rocket injector design.

## Contribution

It introduces adapted algorithms for multi-objective integer and mixed-integer problems and analyzes scalarization techniques to improve Pareto front approximation.

## Key findings

- Algorithms successfully approximate Pareto fronts for integer problems.
- Effective handling of multi-objective mixed-integer problems demonstrated.
- New four-objective algorithm applied to rocket injector design.

## Abstract

Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms which were originally devised for continuous problems can be successfully adapted to approximate the Pareto front for integer, and mixed-integer, multi-objective optimization problems. Relationships amongst various scalarization techniques are established to motivate the choice of a particular scalarization in these algorithms. The proposed algorithms are tested by means of two-, three- and four-objective integer and mixed-integer problems, and comparisons are made. In particular, a new four-objective algorithm is used to solve a rocket injector design problem with a discrete variable, which is a challenging mixed-integer programming problem.