An Order-based Algorithm for Minimum Dominating Set with Application in Graph Mining

Dominating set is a set of vertices of a graph such that all other vertices have a neighbour in the dominating set. We propose a new order-based randomised local search (RLS$_o$) algorithm to solve minimum dominating set problem in large graphs. Experimental evaluation is presented for multiple types of problem instances. These instances include unit disk graphs, which represent a model of wireless networks, random scale-free networks, as well as samples from two social networks and real-world graphs studied in network science. Our experiments indicate that RLS$_o$ performs better than both a classical greedy approximation algorithm and two metaheuristic algorithms based on ant colony optimisation and local search. The order-based algorithm is able to find small dominating sets for graphs with tens of thousands of vertices. In addition, we propose a multi-start variant of RLS$_o$ that is suitable for solving the minimum weight dominating set problem. The application of RLS$_o$ in graph mining is also briefly demonstrated

A novel multi-objective evolutionary algorithm based on space partitioning

To design an e ective multi-objective optimization evolutionary algorithms (MOEA), we need to address the following issues: 1) the sensitivity to the shape of true Pareto front (PF) on decomposition-based MOEAs; 2) the loss of diversity due to paying so much attention to the convergence on domination-based MOEAs; 3) the curse of dimensionality for many-objective optimization problems on grid-based MOEAs. This paper proposes an MOEA based on space partitioning (MOEA-SP) to address the above issues. In MOEA-SP, subspaces, partitioned by a k-dimensional tree (kd-tree), are sorted according to a bi-indicator criterion de ned in this paper. Subspace-oriented and Max-Min selection methods are introduced to increase selection pressure and maintain diversity, respectively. Experimental studies show that MOEA-SP outperforms several compared algorithms on a set of benchmarks

Multiobjective Reliability Allocation in Multi-State Systems: Decision Making by Visualization and Analysis of Pareto Fronts and Sets

ISBN 978-1-4471-2206-7Reliability-based design, operation and maintenance of multi-state systems lead to multiobjective (multicriteria) optimization problems whose solutions are represented in terms of Pareto Fronts and Sets. Among these solutions, the decision maker must choose the ones which best satisfy his\her preferences on the objectives of the problem. Visualization and analysis of the Pareto Fronts and Sets can help decision makers in this task. In this view, a recently introduced graphical representation, called Level Diagrams, is here used in support of the analysis of Pareto Fronts and Sets aimed at reducing the number of non-dominated solutions to be considered by the decision maker. Each objective and design parameter is represented on separate "synchronized" diagrams which position the Pareto front points according to their proximity to ideal preference points and on the basis of this representation a two-step front reduction procedure is proposed. An application to a redundancy allocation problem of literature concerning a multi-state system is used to illustrate the analysis

The First Proven Performance Guarantees for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) on a Combinatorial Optimization Problem

The Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is one of the most prominent algorithms to solve multi-objective optimization problems. Recently, the first mathematical runtime guarantees have been obtained for this algorithm, however only for synthetic benchmark problems. In this work, we give the first proven performance guarantees for a classic optimization problem, the NP-complete bi-objective minimum spanning tree problem. More specifically, we show that the NSGA-II with population size $N \ge 4((n-1) w_{\max} + 1)$ computes all extremal points of the Pareto front in an expected number of $O(m^2 n w_{\max} \log(n w_{\max}))$ iterations, where $n$ is the number of vertices, $m$ the number of edges, and $w_{\max}$ is the maximum edge weight in the problem instance. This result confirms, via mathematical means, the good performance of the NSGA-II observed empirically. It also shows that mathematical analyses of this algorithm are not only possible for synthetic benchmark problems, but also for more complex combinatorial optimization problems. As a side result, we also obtain a new analysis of the performance of the global SEMO algorithm on the bi-objective minimum spanning tree problem, which improves the previous best result by a factor of $|F|$, the number of extremal points of the Pareto front, a set that can be as large as $n w_{\max}$. The main reason for this improvement is our observation that both multi-objective evolutionary algorithms find the different extremal points in parallel rather than sequentially, as assumed in the previous proofs.Comment: Author-generated version of a paper appearing in the proceedings of IJCAI 202

Advances and applications in high-dimensional heuristic optimization

“Applicable to most real-world decision scenarios, multiobjective optimization is an area of multicriteria decision-making that seeks to simultaneously optimize two or more conflicting objectives. In contrast to single-objective scenarios, nontrivial multiobjective optimization problems are characterized by a set of Pareto optimal solutions wherein no solution unanimously optimizes all objectives. Evolutionary algorithms have emerged as a standard approach to determine a set of these Pareto optimal solutions, from which a decision-maker can select a vetted alternative. While easy to implement and having demonstrated great efficacy, these evolutionary approaches have been criticized for their runtime complexity when dealing with many alternatives or a high number of objectives, effectively limiting the range of scenarios to which they may be applied. This research introduces mechanisms to improve the runtime complexity of many multiobjective evolutionary algorithms, achieving state-of-the-art performance, as compared to many prominent methods from the literature. Further, the investigations here presented demonstrate the capability of multiobjective evolutionary algorithms in a complex, large-scale optimization scenario. Showcasing the approach’s ability to intelligently generate well-performing solutions to a meaningful optimization problem. These investigations advance the concept of multiobjective evolutionary algorithms by addressing a key limitation and demonstrating their efficacy in a challenging real-world scenario. Through enhanced computational efficiency and exhibited specialized application, the utility of this powerful heuristic strategy is made more robust and evident”--Abstract, page iv

GALAXY: A new hybrid MOEA for the Optimal Design of Water Distribution Systems

This is the final version of the article. Available from American Geophysical Union via the DOI in this record.The first author would like to appreciate the financial support given by both the University of Exeter and the China Scholarship Council (CSC) toward the PhD research. We also appreciate the three anonymous reviewers, who help improve the quality of this paper substantially. The source code of the latest versions of NSGA-II and ε-MOEA can be downloaded from the official website of Kanpur Genetic Algorithms Laboratory via http://www.iitk.ac.in/kangal/codes.shtml. The description of each benchmark problem used in this paper, including the input file of EPANET and the associated best-known Pareto front, can be accessed from the following link to the Centre for Water Systems (http://tinyurl.com/cwsbenchmarks/). GALAXY can be accessed via http://tinyurl.com/cws-galaxy

A Deterministic Algorithm for the Deployment of Wireless Sensor Networks

Wireless sensor networks are made up by communicating sensor nodes that gather and elaborate information from real world in a distributed and coordinated way in order to deliver an intelligent support to human activities. They are used in many fields such as national security, surveillance, health care, biological detection, and environmental monitoring. However, sensor nodes are characterized by limited wireless communication and computing capabilities as well as reduced on-board battery power. Therefore, they have to be carefully deployed in order to cover the areas to be monitored without impairing network lifetime. This paper presents a new deterministic algorithm to solve the coverage problem of well-known areas by means of wireless sensor networks. The proposed algorithm depends on a small set of parameters and can control sensor deployment within areas even in the presence of obstacles. Moreover, the algorithm makes it possible to control the redundancy degree that can be obtained in covering a region of interest so as to achieve a network deployment characterized by a minimum number of wireless sensor nodes