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The artificial bee colony (ABC) algorithm is a new branch of evolutionary algorithms (EAs) that is inspired by the collective foraging behavior of real honey bee colonies. Due to its foraging model and its solution search equation, ABC generally performs well in exploration but badly in exploitation. To address this concerning issue and obtain a good balance between exploration and exploitation, in this paper, we mainly introduce into the ABC an adaptive method for the population size (AMPS). AMPS is inspired by the natural principle that the size of a population is affected by the availability of food resources. When food resources are abundant, a population tends to expand; otherwise, a decrease in the availability of food resources leads to a shrinkage in the population size. Specifically, when the algorithm performs well in exploration, AMPS will shrink the population to enhance exploitation by periodically removing some inferior solutions that have low success rates. In contrast, AMPS will enlarge the population to improve exploration by introducing some reserved solutions. Furthermore, to make AMPS perform better, we design a new solution search equation for employed bees and onlooker bees. Moreover, we also improve the probability model of the onlooker bees. By embedding our three proposed algorithmic components into ABC, we propose a novel ABC variant, called APABC. To demonstrate the performance of APABC, we compare APABC with some state-of-the-art ABC variants and some other non-ABC methods on 22 scalable benchmark functions and 30 CEC2014 test functions. The simulation results show that APABC is better than or at least competitive with the competitors in terms of its solution quality, robustness and convergence speed. [ABSTRACT FROM AUTHOR]

The diversity of solutions is of great importance for multi-objective evolutionary algorithms. In this paper, a new multi-objective particle swarm optimization algorithm based on decomposition (MPSO/D) is proposed. Firstly, the objective space of a multi-objective problem is decomposed into a set of sub-regions based on a set of direction vectors. Then MPSO/D makes each sub-region have a solution to maintain the diversity. Secondly, considering the convergence of solutions, MPSO/D uses the crowding distance to calculate the fitness values of the reserved solutions for selection operator, and uses the neighboring particles of a particle to determine the global best historical position ( gbest ) of the particle. The proposed algorithm has been compared with NSGAII, MOEA/D and NNIA on sixteen test sets. The experimental results illustrate that the proposed algorithm outperforms NSGAII, MOEA/D and NNIA in terms of convergence and diversity. [ABSTRACT FROM AUTHOR]

This paper presents two mathematical models representing imprecise capacitated fixed-charge transportation problems for a two-stage supply chain network in Gaussian fuzzy type-2 environment. It is a two-stage transportation process from a manufacturing center to m potential distribution centers (DCs) and then from DCs to business centers of n retailers with particular demands. Retailers are situated at some distances apart. Here unit transportation costs, fixed charges, availabilities, and demands are imprecise and represented by Gaussian type-2 fuzzy numbers. The proposed models are formulated as profit maximization problems in such a way that some DCs are selected in order to satisfy the demands at all retailers. The type-2 fuzziness has been removed by using generalized credibility measure developed with the help of CV-based reduction method and hence the models are reduced to chance constrained programming problems with different credibility labels. The deterministic models are then solved using both genetic algorithm (GA) based on Roulette wheel selection, arithmetic crossover with uniform mutation and modified particle swarm optimization (PSO), where the position of each particle is adjusted according to its own experience and that of its neighbors. Finally models are illustrated with some numerical data. Some sensitivity analyses on the proposed models are presented. [ABSTRACT FROM AUTHOR]