Wanru Gao

Runtime analysis for maximizing population diversity in single-objective optimization

Recently Ulrich and Thiele [14] have introduced evolutionary algorithms for the mixed multi-objective problem of maximizing fitness as well as diversity in the decision space. Such an approach allows to generate a diverse set of solutions which are all of good quality. With this paper, we contribute to the theoretical understanding of evolutionary algorithms for maximizing the diversity in a population that contains several solutions of high quality. We study how evolutionary algorithms maximize the diversity of a population where each individual has to have fitness beyond a given threshold value. We present a first runtime analysis in this area and study the classical problems called \emph{\OM} and \emph{\LO}. Our results give first rigorous insights on how evolutionary algorithms can be used to produce a maximal diverse set of solutions in which all solutions have quality above a certain threshold value.

Speeding up evolutionary multi-objective optimisation through diversity-based parent selection

Parent selection in evolutionary algorithms for multi-objective optimization is usually performed by dominance mechanisms or indicator functions that prefer non-dominated points, while the reproduction phase involves the application of diversity mechanisms or other methods to achieve a good spread of the population along the Pareto front. We propose to refine the parent selection on evolutionary multi-objective optimization with diversity-based metrics. The aim is to focus on individuals with a high diversity contribution located in poorly explored areas of the search space, so the chances of creating new non-dominated individuals are better than in highly populated areas. We show by means of rigorous runtime analysis that the use of diversity-based parent selection mechanisms in the Simple Evolutionary Multi-objective Optimiser (SEMO) and Global SEMO for the well known bi-objective functions OneMinMax and Lotz can significantly improve their performance. Our theoretical results are accompanied by additional experiments that show a correspondence between theory and empirical results.

Runtime Analysis of Evolutionary Diversity Maximization for OneMinMax

Diversity mechanisms are key to the working behaviour of evolutionary multi-objective algorithms. With this paper, we contribute to the theoretical understanding of such mechanisms by means of rigorous runtime analysis. We consider the OneMinMax problem for which it has been shown in [11] that a standard benchmark algorithm called SIBEA is not able to obtain a population with optimal hypervolume distribution in expected polynomial time if the population size is relatively small. We investigate the same setting as in [11] and show that SIBEA is able to achieve a good approximation of the optimal hypervolume distribution very efficiently. Furthermore, we study OneMinMax in the context of search-based diversity optimization and examine the time until SIBEA with a search-based diversity mechanism has obtained a population of maximal diversity covering the whole Pareto front.

Maintaining 2-Approximations for the Dynamic Vertex Cover Problem Using Evolutionary Algorithms

Evolutionary algorithms have been frequently used to deal with dynamic optimization problems, but their success is hard to understand from a theoretical perspective. With this paper, we contribute to the theoretical understanding of evolutionary algorithms for dynamic combinatorial optimization problems. We examine a dynamic version of the classical vertex cover problem and analyse evolutionary algorithms with respect to their ability to maintain a 2-approximation. Analysing the different evolutionary algorithms studied by Jansen et al. (2013), we point out where two previously studied approaches are not able to maintain a 2-approximation even if they start with a solution of that quality. Furthermore, we point out that the third approach is very effective in maintaining 2-approximations for the dynamic vertex cover problem.

Feature-Based Diversity Optimization for Problem Instance Classification

Understanding the behaviour of heuristic search methods is a challenge. This even holds for simple local search methods such as 2-OPT for the Traveling Salesperson problem. In this paper, we present a general framework that is able to construct a diverse set of instances that are hard or easy for a given search heuristic. Such a diverse set is obtained by using an evolutionary algorithm for constructing hard or easy instances that are diverse with respect to different features of the underlying problem. Examining the constructed instance sets, we show that many combinations of two or three features give a good classification of the TSP instances in terms of whether they are hard to be solved by 2-OPT.

Randomized greedy algorithms for covering problems

Greedy algorithms provide a fast and often also effective solution to many combinatorial optimization problems. However, it is well known that they sometimes lead to low quality solutions on certain instances. In this paper, we explore the use of randomness in greedy algorithms for the minimum vertex cover and dominating set problem and compare the resulting performance against their deterministic counterpart. Our algorithms are based on a parameter y which allows to explore the spectrum between uniform and deterministic greedy selection in the steps of the algorithm and our theoretical and experimental investigations point out the benefits of incorporating randomness into greedy algorithms for the two considered combinatorial optimization problems.

Discrepancy-based evolutionary diversity optimization

Diversity plays a crucial role in evolutionary computation. While diversity has been mainly used to prevent the population of an evolutionary algorithm from premature convergence, the use of evolutionary algorithms to obtain a diverse set of solutions has gained increasing attention in recent years. Diversity optimization in terms of features on the underlying problem allows to obtain a better understanding of possible solutions to the problem at hand and can be used for algorithm selection when dealing with combinatorial optimization problems such as the Traveling Salesperson Problem. We consider discrepancy-based diversity optimization approaches for evolving diverse sets of images as well as instances of the Traveling Salesperson problem where a local search is not able to find near optimal solutions. Our experimental investigations comparing three diversity optimization approaches show that a discrepancy-based diversity optimization approach using a tie-breaking rule based on weighted differences to surrounding feature points provides the best results in terms of the star discrepancy measure.

Design and analysis of diversity-based parent selection schemes for speeding up evolutionary multi-objective optimisation

Abstract Parent selection in evolutionary algorithms for multi-objective optimisation is usually performed by dominance mechanisms or indicator functions that prefer non-dominated points. We propose to refine the parent selection on evolutionary multi-objective optimisation with diversity-based metrics. The aim is to focus on individuals with a high diversity contribution located in poorly explored areas of the search space, so the chances of creating new non-dominated individuals are better than in highly populated areas. We show by means of rigorous runtime analysis that the use of diversity-based parent selection mechanisms in the Simple Evolutionary Multi-objective Optimiser (SEMO) and Global SEMO for the well known bi-objective functions OneMinMax and LOTZ can significantly improve their performance. Our theoretical results are accompanied by experimental studies that show a correspondence between theory and empirical results and motivate further theoretical investigations in terms of stagnation. We show that stagnation might occur when favouring individuals with a high diversity contribution in the parent selection step and provide a discussion on which scheme to use for more complex problems based on our theoretical and experimental results.

Scaling up Local Search for Minimum Vertex Cover in Large Graphs by Parallel Kernelization

We investigate how well-performing local search algorithms for small or medium size instances can be scaled up to perform well for large inputs. We introduce a parallel kernelization technique that is motivated by the assumption that graphs in medium to large scale are composed of components which are on their own easy for state-of-the-art solvers but when hidden in large graphs are hard to solve. To show the effectiveness of our kernelization technique, we consider the well-known minimum vertex cover problem and two state-of-the-art solvers called NuMVC and FastVC. Our kernelization approach reduces an existing large problem instance significantly and produces better quality results on a wide range of benchmark instances and real world graphs.

Fixed-Parameter Single Objective Search Heuristics for Minimum Vertex Cover

We consider how well-known branching approaches for the classical minimum vertex cover problem can be turned into randomized initialization strategies with provable performance guarantees and investigate them by experimental investigations. Furthermore, we show how these techniques can be built into local search components and analyze a basic local search variant that is similar to a state-of-the-art approach called NuMVC. Our experimental results for the two local search approaches show that making use of more complex branching strategies in the local search component can lead to better results on various benchmark graphs.