Showing papers by "Christian Blum published in 2020"

Search Trajectory Networks of Population-based Algorithms in Continuous Spaces

Abstract: We introduce search trajectory networks (STNs) as a tool to analyse and visualise the behaviour of population-based algorithms in continuous spaces. Inspired by local optima networks (LONs) that model the global structure of search spaces, STNs model the search trajectories of algorithms. Unlike LONs, the nodes of the network are not restricted to local optima but instead represent a given state of the search process. Edges represent search progression between consecutive states. This extends the power and applicability of network-based models to understand heuristic search algorithms. We extract and analyse STNs for two well-known population-based algorithms: particle swarm optimisation and differential evolution when applied to benchmark continuous optimisation problems. We also offer a comparative visual analysis of the search dynamics in terms of merged search trajectory networks.

Solution Merging in Matheuristics for Resource Constrained Job Scheduling

Abstract: Matheuristics have been gaining in popularity for solving combinatorial optimisation problems in recent years. This new class of hybrid method combines elements of both mathematical programming for intensification and metaheuristic searches for diversification. A recent approach in this direction has been to build a neighbourhood for integer programs by merging information from several heuristic solutions, namely construct, solve, merge and adapt (CMSA). In this study, we investigate this method alongside a closely related novel approach—merge search (MS). Both methods rely on a population of solutions, and for the purposes of this study, we examine two options: (a) a constructive heuristic and (b) ant colony optimisation (ACO); that is, a method based on learning. These methods are also implemented in a parallel framework using multi-core shared memory, which leads to improving the overall efficiency. Using a resource constrained job scheduling problem as a test case, different aspects of the algorithms are investigated. We find that both methods, using ACO, are competitive with current state-of-the-art methods, outperforming them for a range of problems. Regarding MS and CMSA, the former seems more effective on medium-sized problems, whereas the latter performs better on large problems.

BARRAKUDA: A Hybrid Evolutionary Algorithm for Minimum Capacitated Dominating Set Problem

Abstract: The minimum capacitated dominating set problem is an NP-hard variant of the well-known minimum dominating set problem in undirected graphs. This problem finds applications in the context of clustering and routing in wireless networks. Two algorithms are presented in this work. The first one is an extended version of construct, merge, solve and adapt, while the main contribution is a hybrid between a biased random key genetic algorithm and an exact approach which we labeled Barrakuda. Both algorithms are evaluated on a large set of benchmark instances from the literature. In addition, they are tested on a new, more challenging benchmark set of larger problem instances. In the context of the problem instances from the literature, the performance of our algorithms is very similar. Moreover, both algorithms clearly outperform the best approach from the literature. In contrast, Barrakuda is clearly the best-performing algorithm for the new, more challenging problem instances.

On Solving a Generalized Constrained Longest Common Subsequence Problem

Abstract: Given a set of two input strings and a pattern string, the constrained longest common subsequence problem deals with finding a longest string that is a subsequence of both input strings and that contains the given pattern string as a subsequence. This problem has various applications, especially in computational biology. In this work we consider the \(\mathcal {NP}\)–hard case of the problem in which more than two input strings are given. First, we adapt an existing A\(^*\) search from two input strings to an arbitrary number m of input strings (\(m \ge 2\)). With the aim of tackling large problem instances approximately, we additionally propose a greedy heuristic and a beam search. All three algorithms are compared to an existing approximation algorithm from the literature. Beam search turns out to be the best heuristic approach, matching almost all optimal solutions obtained by A\(^*\) search for rather small instances.

NuCDS: An Efficient Local Search Algorithm for Minimum Connected Dominating Set

Abstract: The minimum connected dominating set (MCDS) problem is an important extension of the minimum dominating set problem, with wide applications, especially in wireless networks. Despite its practical importance, there are few works on solving MCDS for massive graphs, mainly due to the complexity of maintaining connectivity. In this paper, we propose two novel ideas, and develop a new local search algorithm for MCDS called NuCDS. First, a hybrid dynamic connectivity maintenance method is designed to switch alternately between a novel fast connectivity maintenance method based on spanning tree and its previous counterpart. Second, we define a new vertex property called safety to make the algorithm more considerate when selecting vertices. Experiments show that NuCDS significantly outperforms the state-of-the-art MCDS algorithms on both massive graphs and classic benchmarks.

A New Approach for Making Use of Negative Learning in Ant Colony Optimization

Abstract: The overwhelming majority of ant colony optimization approaches from the literature is exclusively based on learning from positive examples. Natural examples from biology, however, indicate the potential usefulness of negative learning. Several research works have explored this topic over the last two decades in the context of ant colony optimization, with limited success. In this work we present an alternative proposal for the incorporation of negative learning in ant colony optimization. The results obtained for the capacitated minimum dominating set problem indicate that this approach can be quite useful. More specifically, our extended ant colony algorithm clearly outperforms the standard approach. Moreover, we were able to improve the current state-of-the-art results in 10 out of 36 cases.

On the Use of Decision Diagrams for Finding Repetition-Free Longest Common Subsequences

Abstract: We consider the repetition-free longest common subsequence (RFLCS) problem, where the goal is to find a longest sequence that appears as subsequence in two input strings and in which each character appears at most once. Our approach is to transform a RFLCS instance to an instance of the maximum independent set (MIS) problem which is subsequently solved by a mixed integer linear programming solver. To reduce the size of the underlying conflict graph of the MIS problem, a relaxed decision diagram is utilized. An experimental evaluation on two benchmark instance sets shows the advantages of the reduction of the conflict graphs in terms of shorter total computation times and the number of instances solved to proven optimality. A further advantage of the created relaxed decision diagrams is that heuristic solutions can be effectively derived. For some instances that could not be solved to proven optimality, new state-of-the-art results were obtained in this way.