Analysis of Evolutionary Algorithms in Dynamic and Stochastic Environments

Many real-world optimization problems occur in environments that change dynamically or involve stochastic components. Evolutionary algorithms and other bio-inspired algorithms have been widely applied to dynamic and stochastic problems. This survey gives an overview of major theoretical developments in the area of runtime analysis for these problems. We review recent theoretical studies of evolutionary algorithms and ant colony optimization for problems where the objective functions or the constraints change over time. Furthermore, we consider stochastic problems under various noise models and point out some directions for future research.Comment: This book chapter is to appear in the book "Theory of Randomized Search Heuristics in Discrete Search Spaces", which is edited by Benjamin Doerr and Frank Neumann and is scheduled to be published by Springer in 201

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.Comment: Conference version appears at IJCAI 201

Populations can be essential in tracking dynamic optima

Real-world optimisation problems are often dynamic. Previously good solutions must be updated or replaced due to changes in objectives and constraints. It is often claimed that evolutionary algorithms are particularly suitable for dynamic optimisation because a large population can contain different solutions that may be useful in the future. However, rigorous theoretical demonstrations for how populations in dynamic optimisation can be essential are sparse and restricted to special cases. This paper provides theoretical explanations of how populations can be essential in evolutionary dynamic optimisation in a general and natural setting. We describe a natural class of dynamic optimisation problems where a sufficiently large population is necessary to keep track of moving optima reliably. We establish a relationship between the population-size and the probability that the algorithm loses track of the optimum

Combinatorial optimization and the analysis of randomized search heuristics

Randomized search heuristics have widely been applied to complex engineering problems as well as to problems from combinatorial optimization. We investigate the runtime behavior of randomized search heuristics and present runtime bounds for these heuristics on some well-known combinatorial optimization problems. Such analyses can help to understand better the working principle of these algorithms on combinatorial optimization problems as well as help to design better algorithms for a newly given problem. Our analyses mainly consider evolutionary algorithms that have achieved good results on a wide class of NP-hard combinatorial optimization problems. We start by analyzing some easy single-objective optimization problems such as the minimum spanning tree problem or the problem of computing an Eulerian cycle of a given Eulerian graph and prove bounds on the runtime of simple evolutionary algorithms. For the minimum spanning tree problem we also investigate a multi-objective model and show that randomized search heuristics find minimum spanning trees easier in this model than in a single-objective one. Many polynomial solvable problems become NP-hard when a second objective has to be optimized at the same time. We show that evolutionary algorithms are able to compute good approximations for such problems by examining the NP-hard multi-objective minimum spanning tree problem. Another kind of randomized search heuristic is ant colony optimization. Up to now no runtime bounds have been achieved for this kind of heuristic. We investigate a simple ant colony optimization algorithm and present a first runtime analysis. At the end we turn to classical approximation algorithms. Motivated by our investigations of randomized search heurisitics for the minimum spanning tree problem, we present a multi-objective model for NP-hard spanning tree problems and show that the model can help to speed up approximation algorithms for this kind of problems