Runtime Analysis of Simple Evolutionary Algorithms for the Chance-Constrained Makespan Scheduling Problem

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 an expected value with a variance under the influence of external factors, and these actual processing times may be correlated with covariances. Thus within this paper, we propose a chance-constrained version of the Makespan Scheduling problem and investigate the performance of Randomized Local Search and (1 + 1) EA for it. More specifically, we study two variants of the Chance-constrained Makespan Scheduling problem and analyze the expected runtime of the two algorithms to obtain an optimal or almost optimal solution to the instances of the two variants.