# Multi-objective scheduling on two dedicated processors

## TL;DR

This paper addresses a complex multi-objective scheduling problem on two dedicated processors by adapting genetic algorithms, proposing three methods, and evaluating their effectiveness with new bounds and quality metrics.

## Contribution

It introduces three genetic algorithm-based methods for multi-objective scheduling on two processors, with adapted bounds and metrics for evaluating solution quality.

## Key findings

- The proposed algorithms are effective in solving the problem.
- The adapted bounds help evaluate and compare algorithm performance.
- NSGA-II performs well in generating high-quality Pareto fronts.

## Abstract

We study a multi-objective scheduling problem on two dedicated processors. The aim is to minimize simultaneously the makespan, the total tardiness and the total completion time. This NP-hard problem requires the use of well-adapted methods. For this, we adapted genetic algorithms to multi-objective case. Three methods are presented to solve this problem. The first is aggregative, the second is Pareto and the third is non-dominated sorting genetic algorithm II (NSGA-II). We proposed some adapted lower bounds for each criterion to evaluate the quality of the found results on a large set of instances. Indeed, these bounds also make it possible to determine the dominance of one algorithm over another based on the different results found by each of them. We used two metrics to measure the quality of the Pareto front: the hypervolume indicator (HV) and the number of solutions in the optimal front (ND). The obtained results show the effectiveness of the proposed algorithms.