Abstract
Opposition-based learning (OBL) has been widely used to improve many swarm intelligent optimization (SI) algorithms for continuous problems during the past few decades. When the SI optimization algorithms apply OBL to solve discrete problems, the construction and utilization of the opposite solution is the key issue. Ant colony optimization (ACO) generally used to solve combinatorial optimization problems is a kind of classical SI optimization algorithm. Opposition-based ACO which is combined in OBL is proposed to solve the symmetric traveling salesman problem (TSP) in this paper. Two strategies for constructing opposite path by OBL based on solution characteristics of TSP are also proposed. Then, in order to use information of opposite path to improve the performance of ACO, three different strategies, direction, indirection, and random methods, mentioned for pheromone update rules are discussed individually. According to the construction of the inverse solution and the way of using it in pheromone updating, three kinds of improved ant colony algorithms are proposed. To verify the feasibility and effectiveness of strategies, two kinds of ACO algorithms are employed to solve TSP instances. The results demonstrate that the performance of opposition-based ACO is better than that of ACO without OBL.
Highlights
As an important branch of computational intelligence, swarm intelligence (SI) [1] provides a competitive solution for dealing with large-scale, nonlinear, and complex problems, and has become an important research direction of artificial intelligence
AS and PS-Ant colony optimization (ACO) are employed as ACO algorithms to verify the feasibility of three opposition-based
Twenty-six traveling salesman problem (TSP) examples are divided into three main categories, the small-scale, the medium-scale, and the large-scale according to the number of cities, respectively
Summary
As an important branch of computational intelligence, swarm intelligence (SI) [1] provides a competitive solution for dealing with large-scale, nonlinear, and complex problems, and has become an important research direction of artificial intelligence. Besides the above primary improvement strategies considering model modification and algorithm combination, approaches based on machine learning are proposed in recent decades [29]. OBL is combined with ACS and applied to solve the TSP as an example for discrete problems in [42] to acquire the better solution. Besides TSP, the graph coloring problem is employed as a discrete optimization problem in [43], and an improved DE algorithm based on OBL is proposed, which introduces two different methods of opposition. Inspired by the idea of OBL, in this paper, a series of methods, focusing on the opposite solution construction and the pheromone updating rule, are proposed. Aiming to solve TSP, our proposed methods introduce OBL to ACO and enable ACO no longer limited to the local optimal solutions, avoid premature convergence, and improve its performances.
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