Runtime Performance of Evolutionary Algorithms for the Chance-constrained Makespan Scheduling Problem

TL;DR

This paper introduces a chance-constrained version of the Makespan Scheduling problem considering stochastic processing times and analyzes the runtime performance of classical evolutionary algorithms on these variants.

Contribution

It proposes a new stochastic scheduling problem model and provides theoretical and experimental analysis of classical algorithms' performance on it.

Findings

Analyzed the computational complexity of the variants.

Derived expected runtime bounds for the algorithms.

Provided experimental results on algorithm performance.

Abstract

The Makespan Scheduling problem is an extensively studied NP-hard problem, and its simplest version looks for an allocation approach for a set of jobs with deterministic processing times to two identical machines such that the makespan is minimized. However, in real life scenarios, the actual processing time of each job may be stochastic around the expected value with a variance, under the influence of external factors, and the actual processing times of these jobs may be correlated with covariances. Thus within this paper, we propose a chance-constrained version of the Makespan Scheduling problem and investigate the theoretical performance of the classical Randomized Local Search and (1+1) EA for it. More specifically, we first study two variants of the Chance-constrained Makespan Scheduling problem and their computational complexities, then separately analyze the expected runtime of the two algorithms to obtain an optimal solution or almost optimal solution to the instances of the two variants. In addition, we investigate the experimental performance of the two algorithms for the two variants.