Abstract
The artificial bee colony (ABC) algorithm has become one of the popular optimization metaheuristics and has been proven to perform better than many state-of-the-art algorithms for dealing with complex multiobjective optimization problems. However, the multiobjective artificial bee colony (MOABC) algorithm has not been integrated into the common multiobjective optimization frameworks which provide the integrated environments for understanding, reusing, implementation, and comparison of multiobjective algorithms. Therefore, a unified, flexible, configurable, and user-friendly MOABC algorithm framework is presented which combines a multiobjective ABC algorithm named RMOABC and the multiobjective evolution algorithms (MOEA) framework in this paper. The multiobjective optimization framework aims at the development, experimentation, and study of metaheuristics for solving multiobjective optimization problems. The framework was tested on the Walking Fish Group test suite, and a many-objective water resource planning problem was utilized for verification and application. The experiment's results showed the framework can deal with practical multiobjective optimization problems more effectively and flexibly, can provide comprehensive and reliable parameters sets, and can complete reference, comparison, and analysis tasks among multiple optimization algorithms.
Highlights
To balance the trade-offs between the exploration and exploitation capabilities of MOABC, we proposed a multiobjective artificial bee colony algorithm with regulation operators (RMOABC) in [19] to dynamically adjust the capabilities of exploration and exploitation in the algorithm’s evolution process. e local and global dynamic regulation operators were integrated with the guided artificial bee colony algorithm (GABC) algorithm. e mechanisms are to improve the ability of exploitation and guide the search of candidate solutions based on the information of global optimal solutions. e updated Equation (2) in the GABC algorithm was changed into the following equation: vij xij + k ∗ φij ∗ xij − xkj + r ∗ yj − xij, (3)
We intend to assess the performance of the RMOABC algorithm with six state-of-the-art multiobjective algorithms which were implemented within the multiobjective evolution algorithms (MOEA) framework, such as the Nondominated Sorted Genetic Algorithm-II (NSGA-II) [5], Nondominated Sorted Genetic Algorithm-III (NSGA-III) [64],Multiobjective ε-evolutionary Algorithm Based on ε Dominance (ε-MOEA) [65], Speedconstrained Multiobjective particle swarm optimization (PSO) (SMPSO) [66], Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) [67], and the third evolution step of Generalized Differential Evolution (GDE3) [68]. e experiments of simulation were taken on the UOF-MOABC framework which combines the MOEA framework with the RMOABC algorithm in the paper
All the considered nondominated solution sets from the seven algorithms appear to converge into the optimal front, the algorithms perform differently in terms of diversity maintenance, which can be seen from Figure 4. e final nondominated solutions set obtained by NSGA-II, NSGA-III, ε-MOEA, SMPSO, and MOEA/D are all not converged in the uniform distribution, and there are many apparent gaps in the range lines of the objective functions, which means the algorithms fail to reach some regions of the Pareto front. e solution sets of GDE3 and RMOABC seem to have a better uniformity and can almost cover all the regions of the Pareto front
Summary
Most of the multiobjective algorithms are proposed based on the Pareto Sort [2, 49] theory, so the optimization result is not usually a single solution but rather a set of solutions named as a Pareto nondominated set. A multiobjective optimization problem is to optimize a set of objectives subjected to some equality/ inequality constraints. E basic concepts of the multiobjective method based on the Pareto theory can be found in [50]. E artificial bee colony (ABC) algorithm is a meta-heuristic and swarm intelligence algorithm proposed by Karaboga [12]. It is inspired by the foraging behavior of honeybees. The ABC algorithm has become an effective means for solving complex nonlinear optimization problems
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