Improved binary artificial fish swarm algorithm for the 0–1 multidimensional knapsack problems

The 0–1 multidimensional knapsack problem (MKP) arises in many fields of optimization and is NP-hard. Several exact as well as heuristic methods exist. Recently, an artificial fish swarm algorithm has been developed in continuous global optimization. The algorithm uses a population of points in space to represent the position of fish in the school. In this paper, a binary version of the artificial fish swarm algorithm is proposed for solving the 0–1 MKP. In the proposed method, a point is represented by a binary string of 0/1 bits. Each bit of a trial point is generated by copying the corresponding bit from the current point or from some other specified point, with equal probability. Occasionally, some randomly chosen bits of a selected point are changed from 0 to 1, or 1 to 0, with an user defined probability. The infeasible solutions are made feasible by a decoding algorithm. A simple heuristic add_item is implemented to each feasible point aiming to improve the quality of that solution. A periodic reinitialization of the population greatly improves the quality of the solutions obtained by the algorithm. The proposed method is tested on a set of benchmark instances and a comparison with other methods available in literature is shown. The comparison shows that the proposed method gives a competitive performance when solving this kind of problems.Fundação para a Ciência e a Tecnologia (FCT

A Review of the Family of Artificial Fish Swarm Algorithms: Recent Advances and Applications

The Artificial Fish Swarm Algorithm (AFSA) is inspired by the ecological behaviors of fish schooling in nature, viz., the preying, swarming, following and random behaviors. Owing to a number of salient properties, which include flexibility, fast convergence, and insensitivity to the initial parameter settings, the family of AFSA has emerged as an effective Swarm Intelligence (SI) methodology that has been widely applied to solve real-world optimization problems. Since its introduction in 2002, many improved and hybrid AFSA models have been developed to tackle continuous, binary, and combinatorial optimization problems. This paper aims to present a concise review of the family of AFSA, encompassing the original ASFA and its improvements, continuous, binary, discrete, and hybrid models, as well as the associated applications. A comprehensive survey on the AFSA from its introduction to 2012 can be found in [1]. As such, we focus on a total of {\color{blue}123} articles published in high-quality journals since 2013. We also discuss possible AFSA enhancements and highlight future research directions for the family of AFSA-based models.Comment: 37 pages, 3 figure

Heuristic-based firefly algorithm for bound constrained nonlinear binary optimization

Firefly algorithm (FA) is a metaheuristic for global optimization. In this paper,we address the practical testing of aheuristic-based FA (HBFA) for computing optimaof discrete nonlinear optimization problems,where the discrete variables are of binary type. An important issue in FA is the formulation of attractiveness of each firefly which in turn affects its movement in the search space. Dynamic updating schemes are proposed for two parameters, one from the attractiveness term and the other from the randomization term. Three simple heuristics capable of transforming real continuous variables into binary ones are analyzed. A new sigmoid ‘erf’ function is proposed. In the context of FA, three different implementations to incorporate the heuristics for binary variables into the algorithm are proposed. Based on a set of benchmark problems, a comparison is carried out with other binary dealing metaheuristics. The results demonstrate that the proposed HBFA is efficient and outperforms binary versions of differential evolution (DE) and particle swarm optimization (PSO). The HBFA also compares very favorably with angle modulated version of DE and PSO. It is shown that the variant of HBFA based on the sigmoid ‘erf’ function with ‘movements in continuous space’ is the best, both in terms of computational requirements and accuracy.Fundação para a Ciência e a Tecnologia (FCT

Firefly Algorithm: Recent Advances and Applications

Nature-inspired metaheuristic algorithms, especially those based on swarm intelligence, have attracted much attention in the last ten years. Firefly algorithm appeared in about five years ago, its literature has expanded dramatically with diverse applications. In this paper, we will briefly review the fundamentals of firefly algorithm together with a selection of recent publications. Then, we discuss the optimality associated with balancing exploration and exploitation, which is essential for all metaheuristic algorithms. By comparing with intermittent search strategy, we conclude that metaheuristics such as firefly algorithm are better than the optimal intermittent search strategy. We also analyse algorithms and their implications for higher-dimensional optimization problems.Comment: 15 page

A survey of swarm intelligence for dynamic optimization: algorithms and applications

Swarm intelligence (SI) algorithms, including ant colony optimization, particle swarm optimization, bee-inspired algorithms, bacterial foraging optimization, firefly algorithms, fish swarm optimization and many more, have been proven to be good methods to address difficult optimization problems under stationary environments. Most SI algorithms have been developed to address stationary optimization problems and hence, they can converge on the (near-) optimum solution efficiently. However, many real-world problems have a dynamic environment that changes over time. For such dynamic optimization problems (DOPs), it is difficult for a conventional SI algorithm to track the changing optimum once the algorithm has converged on a solution. In the last two decades, there has been a growing interest of addressing DOPs using SI algorithms due to their adaptation capabilities. This paper presents a broad review on SI dynamic optimization (SIDO) focused on several classes of problems, such as discrete, continuous, constrained, multi-objective and classification problems, and real-world applications. In addition, this paper focuses on the enhancement strategies integrated in SI algorithms to address dynamic changes, the performance measurements and benchmark generators used in SIDO. Finally, some considerations about future directions in the subject are given