A Modified Vortex Search Algorithm for Numerical Function Optimization

Abstract

The Vortex Search (VS) algorithm is one of the recently proposed metaheuristic algorithms which was inspired from the vortical flow of the stirred fluids. Although the VS algorithm is shown to be a good candidate for the solution of certain optimization problems, it also has some drawbacks. In the VS algorithm, candidate solutions are generated around the current best solution by using a Gaussian distribution at each iteration pass. This provides simplicity to the algorithm but it also leads to some problems along. Especially, for the functions those have a number of local minimum points, to select a single point to generate candidate solutions leads the algorithm to being trapped into a local minimum point. Due to the adaptive step-size adjustment scheme used in the VS algorithm, the locality of the created candidate solutions is increased at each iteration pass. Therefore, if the algorithm cannot escape a local point as quickly as possible, it becomes much more difficult for the algorithm to escape from that point in the latter iterations. In this study, a modified Vortex Search algorithm (MVS) is proposed to overcome above mentioned drawback of the existing VS algorithm. In the MVS algorithm, the candidate solutions are generated around a number of points at each iteration pass. Computational results showed that with the help of this modification the global search ability of the existing VS algorithm is improved and the MVS algorithm outperformed the existing VS algorithm, PSO2011 and ABC algorithms for the benchmark numerical function set.Comment: 18 pages, 7 figure

Robust Estimators in Geodetic Networks Based on a New Metaheuristic: Independent Vortices Search

“…The reader can find more details in [49]. Thus, the algorithms tested were: Artificial Bee Colony (ABC) [23,24];Vortex Search algorithm (VS) [32];Modified Vortex Search algorithm (MVS) [33];Hybrid Vortex Search algorithm (HVS) [49]; and,Independent Vortices Search (IVS).…”

“…The configurations of the MHs obeyed the following parameters: 5,000,000 FE as processing limit, 50 candidates per center for vortex algorithms, and 50 bees in ABC (25 food sources). In addition, we tested the MVS and IVS with five vortices, as presented in [33], and 40 vortices. Preliminary tests showed better results from 20 to 60 vortices, so we adopted an intermediate value of 40.…”

“…For the numerical optimization, we developed the Independent Vortices Search (IVS), based on the Vortex Search algorithm (VS) [32] and its modification, the Modified Vortex Search algorithm (MVS) [33]. While VS works with one vortex, MVS can explore many vortices at once, exchanging information.…”

“…The third modification considers maintaining the amount of candidates per vortex when L>1 (where L is the total number of vortices). In the MVS proposal [33], the experiments presented five centers and divided the number of candidates between them. IVS, however, fixes the quantity of candidates for each vortex.…”

“…Therefore, this work has two main goals: First, developing better MHs by presenting the Independent Vortices Search (IVS) based on the Vortex Search method [32], which brings advances to mitigate the limitations found in the original algorithm [33]. We compare its performance with the original method, other modifications, and a competing algorithm.…”