The fixed set search applied to the power dominating set problem

Abstract

In this article, we focus on solving the power dominating set problem and its connected version. These problems are frequently used for finding optimal placements of phasor measurement units in power systems. We present an improved integer linear program (ILP) for both problems. In addition, a greedy constructive algorithm and a local search are developed. A greedy randomised adaptive search procedure (GRASP) algorithm is created to find near optimal solutions for large scale problem instances. The performance of the GRASP is further enhanced by extending it to the novel fixed set search (FSS) metaheuristic. Our computational results show that the proposed ILP has a significantly lower computational cost than existing ILPs for both versions of the problem. The proposed FSS algorithm manages to find all the optimal solutions that have been acquired using the ILP. In the last group of tests, it is shown that the FSS can significantly outperform the GRASP in both solution quality and computational cost.

A GRASP Approach for Solving Large-Scale Electric Bus Scheduling Problems

“…Another issue relates to disturbances in public transport (see [47] for a survey and [48] for some conceptional work) as they can even arise with special features related to EBs (see, e.g., [49]). Finally, the Fixed Set Search metaheuristic [50], which adds a learning mechanism to GRASP, can be applied to try to increase the quality of found solutions for the problem of interest.…”

Special issue on new trends and challenges of bio‐inspired computational intelligence algorithms in massively complex systems

“…2. Jovanovic and Voss (2020) have developed a greedy randomized adaptive search procedure (GRASP) optimized with the novel fixed set search (FSS) meta-heuristic to solve the power dominating set problem and its connected version. These problems frequently occur in finding optimal placements of phasor measurement units in power systems.…”

“…The contributions of these papers are summarized as follows: The paper by García‐Ortega, García‐Sánchez, & Merelo‐Guervós (2020) proposes and evaluates a methodology to automatically synthesize sets of high‐level elements of a film (called tropes), in a way that maximizes the potential rating of a film that conforms to them. The authors use machine learning to create a surrogate model that maps film ratings from tropes, trained with the data extracted and processed from huge film databases from the Internet, and then they apply a genetic algorithm that uses that surrogate model as evaluator to optimize the combination of tropes in a film. Jovanovic and Voss (2020) have developed a greedy randomized adaptive search procedure (GRASP) optimized with the novel fixed set search (FSS) meta‐heuristic to solve the power dominating set problem and its connected version. These problems frequently occur in finding optimal placements of phasor measurement units in power systems.…”

A Clustering Routing Algorithm Based on Improved Ant Colony Optimization Algorithms for Underwater Wireless Sensor Networks

“…That is the reason why they cannot obtain the optimal solution sometimes. Hence, researchers proposed many metaheuristics extending greedy algorithms, which can be applied to a wide range of different problems [38][39][40][41]. The greedy randomized adaptive search procedure (GRASP) was presented by Feo et al in [38], where the present problem can be solved in every iteration.…”

“…Each iteration has two stages: stage one provides the initial solution and stage two aims to find the improved solution by applying the local search procedure to the solution provided by stage one. The fixed set search (FSS) was proposed by Jovanovic et al in [39], which adds the learning method to the GRASP and is thus more effective than the GRASP in the solution quality as well as the computational cost. In the work of Arnaout in [40], the worm optimization (WO), on the basis of the worm behaviors, was proposed to solve unrelated parallel machine schedule problems, which can find the optimal solution as well as reduce the makespan.…”