Abstract
Metaheuristics are smart problem solvers devoted to tackling particularly large optimization problems. During the last 20 years, they have largely been used to solve different problems from the academic as well as from the real-world. However, most of them have originally been designed for operating over real domain variables, being necessary to tailor its internal core, for instance, to be effective in a binary space of solutions. Various works have demonstrated that this internal modification, known as binarization, is not a simple task, since the several existing binarization ways may lead to very different results. This of course forces the user to implement and analyze a large list of binarization schemas for reaching good results. In this paper, we explore two efficient clustering methods, namely KMeans and DBscan to alter a metaheuristic in order to improve it, and thus do not require on the knowledge of an expert user for identifying which binarization strategy works better during the run. Both techniques have widely been applied to solve clustering problems, allowing us to exploit useful information gathered during the search to efficiently control and improve the binarization process. We integrate those techniques to a recent metaheuristic called Crow Search, and we conduct experiments where KMeans and DBscan are contrasted to 32 different binarization methods. The results show that the proposed approaches outperform most of the binarization strategies for a large list of well-known optimization instances.
Highlights
Optimization problems can be seen in different areas of the modern world, such as bridge reinforcement [1], load dispatch [2], location of emergency facilities [3], marketing [4], and social networks [5], among others
We propose to test our approach by solving the instances of the Set Covering Problem (SCP) [47] and the 0/1 Knapsack
The data is grouped as follows: instance: name of the instance, MIN: the minimum reached value, MAX: the maximum value reached, AVG: the average value, BKS: the best known solution, relative percentage deviation (RPD) it is defined by the Equation (3) and TIME: time of execution in seconds
Summary
Optimization problems can be seen in different areas of the modern world, such as bridge reinforcement [1], load dispatch [2], location of emergency facilities [3], marketing [4], and social networks [5], among others. We must identify and understand to which model the problem belongs. Discrete optimization has widely been used to define a large number of problems belonging to the NP-hard class [6]. Mathematics 2020, 8, 1070 to emphasize that the time to solve this type of problem increases exponentially according to its size. For this reason, we consider it totally prudent to solve these problems through metaheuristics [7,8], which deliver acceptable results in a limited period of time
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