On the Runtime of Randomized Local Search and Simple Evolutionary Algorithms for Dynamic Makespan Scheduling

Evolutionary algorithms have been frequently used for dynamic optimization problems. With this paper, we contribute to the theoretical understanding of this research area. We present the first computational complexity analysis of evolutionary algorithms for a dynamic variant of a classical combinatorial optimization problem, namely makespan scheduling. We study the model of a strong adversary which is allowed to change one job at regular intervals. Furthermore, we investigate the setting of random changes. Our results show that randomized local search and a simple evolutionary algorithm are very effective in dynamically tracking changes made to the problem instance. Optimization problems in real-world applications often change due to a changing environment. Evolutionary algorithms, ant colony optimization and other bio-inspired search heuristics have been frequently applied to dynamically changing problems. An important approach to gain a theoretical understanding of evolutionary algorithms and other types of bio-inspired computation methods is the computational complexity analysis of these algorithms. During the last 20 years, a large body of results and methods has been built up. This includes the development of methods for the analysis of bio-inspired computing [4, 6, 7, 25] and results for some of the best-known combinatorial optimization problems such as the traveling salesperson problem [21], set cover [5, 26], and makespan scheduling [22, 23] as well as different multi-objective problems [8, 17, 19]. These studies often consider the algorithms called Randomized Local Search (RLS) and (1+1) EA, which we also investigate in this paper. Although these algorithms seem to be relatively simple, it should be noted that upper bounds on the expected optimization time of these algorithms can often be translated to population-based evolutionary algorithms with more complicated variation operators, e. g., crossover by increasing the upper bounds by only a linear factor with respect