A COMPUTATIONAL MODEL OF THE COLLECTIVE BEHAVIOR OF A GROUP OF ANIMALS: EFFECTIVE BIO HEURISTICS FOR SOLVING APPLIED GLOBAL OPTIMIZATION PROBLEMS

Abstract

A promising solution to global optimization problems are metaheuristics inspired by nature, which
are non-deterministic algorithms that explore the search space, solutions, learning in the search process,
not tied to a specific task, although they do not guarantee accurate solutions. The purpose of this study is to develop an effective algorithm for solving applied problems of global optimization of multidimensional
single-modal and multimodal functions found in engineering design, image processing and computer vision,
energy and energy management, data analysis and machine learning, robotics. To achieve this goal, the article
proposes a computational model of the collective behavior of a group of animals and an effective algorithm
for differential vector motion. The model includes various patterns of behavior in a group of animals:
to hold the current position; to move towards the nearest neighbors or, conversely, from the nearest neighbors;
to move randomly; to compete for a position. The collective memory stores information about the location
of the dominant individuals of the group and the direction of movement of the group, the best positions of
agents, taking into account the mechanisms of competition and dominance in the group. The algorithm was
experimentally tested on seven known multidimensional single-modal and multimodal functions. The results
were compared with a genetic algorithm, a particle swarm algorithm, and a gravitational search for differential
evolution. The proposed algorithm showed better results than competing algorithms on all test functions.
This is due to the better balance of the new algorithm between the rate of convergence and the diversification
of the solution search space. Verification of the results obtained using the Wilcoxon sum of ranks T-test for
independent samples showed that the results of the algorithm are statistically significant. A comparison was
also made with one of the most effective continuous optimization algorithms of BFGS - a quasi-Newtonian
iterative numerical optimization algorithm designed to find the local extremum of single-modal functions. The
results were comparable for multidimensional functions. The algorithm was also compared with the
multistart method in the problem of global optimization of multi-extreme functions and proved its advantage
in terms of time and accuracy of the solutions found.