Search

The performance of the Gravitational Search Algorithm (GSA) depends on the gravitational constant G, which controls the balance of exploration and exploitation abilities. Improving the setting of this parameter has attracted many researchers. In this paper, we analyzed the GSA stability using the von Neumann stability criterion. First, we modeled the iterative process by a second-order differential equation and derived the first and second-order stability conditions. Then, based on these criteria, we suggested a new law to adjust the initial value of the parameter G, depending on the distance between objects and then on the search space. Some supporting simulations were carried out using different update laws of the gravitational constant (e.g., exponential, log-sigmoid, linear, and chaotic) on CEC 2017 benchmark functions in different search space dimensions. The achieved results show that the new setting leads to significantly better outcomes in high-dimensional search spaces (greater than 20). A comparison with other metaheuristics (Particle Swarm Optimization, Artificial Bee Colony, and Grey Wolf Optimizer) reveals that the new setting proffers GSA competitiveness. Tests on 23 real-world problems (CEC 2011 benchmark problems and the iron ores sintering problem) further proved all the merits of the proposed parameter setting. [ABSTRACT FROM AUTHOR]

In complexity theory, there is a widely studied grouping of optimization problems that belongs to the non-deterministic polynomial-time hard set. One of them is the set covering problem, known as one of Karp's 21 NP -complete problems, and it consists of finding a subset of decision variables for satisfying a set of constraints at the minimum feasible cost. However, due to the nature of the problem, this cannot be solved using traditional complete algorithms for hard instances. In this work, we present an improved binary version of the monkey search algorithm for solving the set covering problem. Originally, this approximate method was naturally inspired by the cognitive behavior of monkeys for climbing mountains. We propose a new climbing process with a better exploratory capability and a new cooperation procedure to reduce the number of unfeasible solutions. For testing this approach, we present a detailed computational results section, where we illustrate how this variation of the monkey search algorithm is capable of reaching various global optimums for a well-known instance set from the Beasley's OR-Library and how it outperforms many other heuristics and meta-heuristics addressed in the literature. Moreover, we add a complete statistical analysis to show the effectiveness of the proposed approach with respect to the original version. [ABSTRACT FROM AUTHOR]