Parameterized analysis of multiobjective evolutionary algorithms and the weighted vertex cover problem

Evolutionary multiobjective optimization for the classical vertex cover problem has been analysed in Kratsch and Neumann (2013) in the context of parameterized complexity analysis. This article extends the analysis to the weighted vertex cover problem in which integer weights are assigned to the vertices and the goal is to find a vertex cover of minimum weight. Using an alternative mutation operator introduced in Kratsch and Neumann (2013), we provide a fixed parameter evolutionary algorithm with respect to OPT, the cost of an optimal solution for the problem. Moreover, we present a multiobjective evolutionary algorithm with standard mutation operator that keeps the population size in a polynomial order by means of a proper diversity mechanism, and therefore, manages to find a 2-approximation in expected polynomial time. We also introduce a population-based evolutionary algorithm which finds a (1+ɛ)-approximation in expected time O(n·2min{n,2(1-ɛ)OPT}+n3).Mojgan Pourhassan, Feng Shi and Frank Neuman

Finding Near-Optimal Independent Sets at Scale

The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in huge sparse networks. A recent exact algorithm has shown that large networks can be solved exactly by employing a branch-and-reduce technique that recursively kernelizes the graph and performs branching. However, one major drawback of their algorithm is that, for huge graphs, branching still can take exponential time. To avoid this problem, we recursively choose vertices that are likely to be in a large independent set (using an evolutionary approach), then further kernelize the graph. We show that identifying and removing vertices likely to be in large independent sets opens up the reduction space---which not only speeds up the computation of large independent sets drastically, but also enables us to compute high-quality independent sets on much larger instances than previously reported in the literature.Comment: 17 pages, 1 figure, 8 tables. arXiv admin note: text overlap with arXiv:1502.0168

Partitioning networks into cliques: a randomized heuristic approach

In the context of community detection in social networks, the term community can be grounded in the strict way that simply everybody should know each other within the community. We consider the corresponding community detection problem. We search for a partitioning of a network into the minimum number of non-overlapping cliques, such that the cliques cover all vertices. This problem is called the clique covering problem (CCP) and is one of the classical NP-hard problems. For CCP, we propose a randomized heuristic approach. To construct a high quality solution to CCP, we present an iterated greedy (IG) algorithm. IG can also be combined with a heuristic used to determine how far the algorithm is from the optimum in the worst case. Randomized local search (RLS) for maximum independent set was proposed to find such a bound. The experimental results of IG and the bounds obtained by RLS indicate that IG is a very suitable technique for solving CCP in real-world graphs. In addition, we summarize our basic rigorous results, which were developed for analysis of IG and understanding of its behavior on several relevant graph classes

Optimal Recombination in Genetic Algorithms

This paper surveys results on complexity of the optimal recombination problem (ORP), which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We consider efficient reductions of the ORPs, allowing to establish polynomial solvability or NP-hardness of the ORPs, as well as direct proofs of hardness results

Improving the Interpretability of Classification Rules Discovered by an Ant Colony Algorithm: Extended Results

The vast majority of Ant Colony Optimization (ACO) algorithms for inducing classification rules use an ACO-based procedure to create a rule in an one-at-a-time fashion. An improved search strategy has been proposed in the cAnt-MinerPB algorithm, where an ACO-based procedure is used to create a complete list of rules (ordered rules)-i.e., the ACO search is guided by the quality of a list of rules, instead of an individual rule. In this paper we propose an extension of the cAnt-MinerPB algorithm to discover a set of rules (unordered rules). The main motivations for this work are to improve the interpretation of individual rules by discovering a set of rules and to evaluate the impact on the predictive accuracy of the algorithm. We also propose a new measure to evaluate the interpretability of the discovered rules to mitigate the fact that the commonly-used model size measure ignores how the rules are used to make a class prediction. Comparisons with state-of-the-art rule induction algorithms, support vector machines and the cAnt-MinerPB producing ordered rules are also presented