Heterogeneous swarm optimization algorithm for continuous optimization: optimization by cooperation between ants and bees

Abstract

Optimization problems are easily found in our real lives including various fields such as finance, physics, chemistry, engineering, manufacturing, and so on. Most of these problems are discontinuous or non-differentiable types that limit to be solved by the classic method in mathematics, such as a gradient descent or a quasi-Newton method, as well as complex types. Metaheuristic approaches do not need the gradient or Hessian matrix, having the advantage to optimize and being widely used and studied to solve real-life optimization problems. Metaheuristics, however, have an issue to solve of balancing between diversification and intensification, in which a metaheuristic algorithm should use some strategy to diversify the search in such a way that on the one hand it does not get stuck into local optima (diversification), on the other it is able to converge once the global optimum has been found (intensification).

There are many metaheuristic approaches inspired from nature, recently the researches based on the swarm intelligence which is inspired from the movement of a swarm such as ant colonies, bird flocking, bee colonies, and fish schooling are studied actively. As the representative optimization methods for Continuous Optimization Problems (CnOPs), there are Ant Colony Optimization for continuous domains (ACO$_\mathbb{R}$) and Artificial Bee Colony (ABC) optimization algorithms which are inspired from the foraging behavior of real ants and honeybees respectively. The excellence of these algorithms have already been proven in many earlier studies on these algorithms.

ACO$_\mathbb{R}$ appears a strength in the ability of the intensification to converge once the global optimum has been found, and the algorithm increases only a very small number of Function Evaluations (NFEs) at every iteration in comparison with other algorithms, showing stable and relatively rapid convergence. ACO$_\mathbb{R}$, however, is very sensitive about changing the control parameters,...