FP-ABC: Fuzzy-Pareto dominance driven artificial bee colony algorithm for many-objective software module clustering

Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mid-eighties in an attempt to stochastically solve problems of this generic class. During the past decade, a variety, of multiobjective EA (MOEA) techniques have been proposed and applied to many scientific and engineering applications. Our discussion's intent is to rigorously define multiobjective optimization problems and certain related concepts, present an MOEA classification scheme, and evaluate the variety of contemporary MOEAs. Current MOEA theoretical developments are evaluated; specific topics addressed include fitness functions, Pareto ranking, niching, fitness sharing, mating restriction, and secondary populations. Since the development and application of MOEAs is a dynamic and rapidly growing activity, we focus on key analytical insights based upon critical MOEA evaluation of current research and applications. Recommended MOEA designs are presented, along with conclusions and recommendations for future work.

In recent years, multi-objective evolutionary algorithms (MOEAs) have been widely used to handle various water resources problems. One challenge within MOEAs’ applications is a lack of understanding on how various operators alter a MOEA’s behavior to achieve its final performance (i.e., MOEAs are black-boxes to practitioners), and hence it is difficult to select the most appropriate operators to ensure the MOEA’s best performance for a given real-world problem. To address this issue, this study proposes the use of the run-time measure metrics to reveal the underlying searching behavior of the MOEA’s operators. The proposed methodology is demonstrated by the non-dominated sorting genetic algorithm II (NSGA-II, a widely used MOEA in water resources) with five commonly used crossover operators applied to six water distribution system design problems. Results show that the simulated binary crossover (SBX) and the simplex crossover (SPX) operators possess great ability in extending the front and finding Pareto-front solutions, respectively, while the naive crossover (NVX) strategy exhibits the overall worst performance in identifying optimal fronts. The obtained understanding on the operators’ searching behavior not only offers guidance for selecting appropriate operators for real-world water resources problems, but also builds fundamental knowledge for developing more advanced MOEAs in future.

Swarm intelligence is briefly defined as the collective behavior of decentralized and self-organized swarms. Self-organization and labor division are the two key components of swarm intelligence. Artificial Bee Colony (ABC) algorithm is one of the most recent swarm intelligence-based algorithms. The behavior of bees in ABC algorithm satisfies the self-organization features, but there is no specific labor division mechanism in ABC algorithm. In this work, we propose an improved ABC algorithm called labor division artificial bee colony (LDABC) algorithm by incorporating the labor division mechanism into ABC algorithm, which is achieved by individual specialization and role plasticity. We specify three different search methods for employed bees, onlooker bees and scout bees to realize individual specialization, these search methods are related to food source quality, enable bees to maximize exploitation of food source. Role plasticity is achieved by combining with cellular automata, where the roles of bees are not static but vary with their surrounding environment, enable bees not to limit to one search method. The different search modes and the flexibility of the search behaviors make our algorithm achieve a better balance between exploration and exploitation. The experimental results tested on 13 benchmark functions and CEC-2013 test functions demonstrate a competitive performance.

The artificial bee colony (ABC) algorithm is an important branch of evolutionary algorithms and has been shown to be competitive with other algorithms for solving optimisation problems. However, there are always some insufficiencies in ABC algorithm such as lower convergence speed and easily get trapped in the local optima. To increase depth search capabilities of onlooker bees and ensure scout bees do not discard the current optimal solution, we proposed a modified ABC algorithm (denoted as ORABC) based on the optimisation strategy and retained strategy of the best individual in this paper. Compared with ABC algorithm, ABC* (added retained strategy to ABC) and ORABC algorithm, experiments are conducted on a set of numerical benchmark functions. The numerical simulation results demonstrate that ORABC algorithm improves the convergence characteristics of ABC algorithm and provides very remarkable performance in solving complex numerical optimisation problems compared to original algorithm.

Search-based software engineering (SBSE) consists of the application of metaheuristic search techniques—such as genetic algorithms, simulated annealing, hill climbing, and tabu search—to software engineering problems. This idea is based on the observation that some software engineering activities can be thought of as optimization problems, and on the fact that techniques providing exact solutions are, very often, unable to adequately scale to large, real-world software engineering problems. Define fitness functions to guide an automated search for solutions, rather than attempting to construct solutions from scratch by hand. SBSE moves the engineer up the abstraction chain, from the tedious and expensive role of detailed solution construction, to the potentially more productive and more cost-effective area of fitness function design. This approach has been repeatedly demonstrated to have successful applications across the software engineering life cycle from requirements and project planning to maintenance and testing. This special issue focuses on applications of search SBSE to the maintenance phase of the life cycle. After software testing 2, software maintenance is the most widely studied application area for SBSE research. Work on SBSE applications to problems in software maintenance can be traced back to the pioneering work of the Mancoridis et al. 3, which led to the development of the Bunch tool for software re-modularization 4. In the past five years there has been a significant increase in SBSE applications to software maintenance and evolution. Search-based techniques have been applied to post-development code improvement problems, such as object-oriented refactoring 5, 6, and imperative language slicing and transformation 7. Other applications are related to software engineering economics and project management problems, such as release planning 8-12, effort, and cost estimation 13-16, and project staffing and planning 17-20. Last, but not the least, SBSE has been applied to deal with service-oriented architectures, for example for services QoS-aware composition 21, service-level agreement negotiation 22, and testing 23. A complete overview of SBSE with a discussion of future research trends can be found in the recent International Conference on Software Engineering (ICSE) ‘Future of Software Engineering’ paper 24. This issue of the Journal of Software Maintenance and Evolution: Research and Practice features three outstanding papers, dealing with different aspects of software maintenance and evolution: release planning and staffing, re-factoring, and component substitution. The paper ‘Optimized Staffing for Product Releases—Focused Search and its Application at Chartwell Technologies’ by Puneet Kapur, An Ngo-The, Günther Ruhe, and Andrew Smith presents an approach for optimizing the staffing for product releases. The problem they solve can be viewed as part of the more general release planning problem, which assigns features to releases such that technical, resource, risk, and budget constraints are met. In particular, the genetic search-based approach the authors propose aims at assigning human resources to software development tasks, taking them from a pool of developers having different levels of skills. The applicability of the proposed approach is demonstrated with an industrial case study. The paper ‘Search-Based Refactoring: an Empirical Study’ by Mark O'Keffe and Mel Ó Cinnéide presents an approach to automatically re-factor, using search-based techniques, object-oriented systems that undergo repeated addition of functionality. Such addition can, very often, deteriorate the quality of the system's underlying design. Their re-factoring is guided by the QMOOD quality model 25, and the paper compares different optimization techniques, such as Genetic Algorithms, Simulated Annealing, and Multiple Ascent Hill-Climbing. The results of experiments carried out on five software systems suggest that the latter technique outperforms the others. The paper ‘Search-based Many-to-one Component Substitution’ by Nicolas Desnos, Marianne Huchard, Guy Tremblay, Christelle Urtado, and Sylvain Vauttier presents a search-based approach that allows the replacement of an obsolete component with a composition of multiple components. When a component becomes obsolete, the approach searches for a minimal assembly of other components, exposing their functionality by means of ports that preserves the behavior of the original component. The proposed approach has been evaluated on a set of randomly generated components. We hope that readers will enjoy this special issue and find the selected papers insightful and inspiring. We would like to thank all the authors who presented papers for this special issue: there were many good quality papers, but unfortunately we could accept only three of them. Last, but not the least, we would like to thank the reviewers who provided timely, detailed and constructive feedbacks to the authors. Without their precious help this special issue would not have been possible.

INTRODUCTION: The artificial bee colony (ABC) algorithm is a nature-inspired technique used for solving different optimization problems. This paper presents a multi-hive ABC algorithm for solving constrained benchmark functions of CEC2006. The CEC2006 data set contains the global benchmark functions with different design variables, number and type of constraints. OBJECTIVES: The objective of the proposed work is to design and apply the GPGPU based multi-hive ABC algorithm to solve constrained optimization problems. METHODS: The proposed approach is a multi-population coarse-grained system implemented using General Purpose Graphics Processing Unit (GPGPU). The performance of the proposed approach is compared with the serial ABC algorithm for eleven benchmark functions and results in the literature. The multi-hive ABC algorithm has multiple hives, each running separate ABC algorithm on different cores of GPGPU. RESULTS: The proposed approach provides global best solutions in significantly reduced time for all benchmark functions. The speed-up obtained is approximately 7X to 9X. The GPGPU device utilization is approximately 57% to 91%. CONCLUSION: The GPGPU based multi-hive ABC algorithm is a found good with respect to best results, speed up factor and GPU utilization to solve constrained optimization problems.

In real-world multi-objective problems, each objective has a totally different scale. However, some frequently-used multi-objective evolutionary algorithms (MOEAs) have no objective space normalization mechanisms. The effect of objective space normalization on the performance of decomposition-based MOEAs (e.g., MOEA/D and NSGA-III) has already been examined for artificial test problems (e.g., DTLZ and WFG) in the literature. In this paper, we examine its practical usefulness for real-world multi-objective problems using various MOEAs. Our experimental results clearly show that objective space normalization is needed not only in decomposition-based MOEAs but also in hypervolume-based MOEAs. We also explain why objective space normalization is needed in these two types of MOEAs.

Multi-objective evolutionary algorithms (MOEAs) of the state of the art are created with the only purpose of dealing with the number of objective functions in a multi-objective optimization problem (MOP) and treat the decision variables of a MOP as a whole. However, when dealing with MOPs with a large number of decision variables (more than 100) their efficacy decreases as the number of decision variables of the MOP increases. On the other hand, problem decomposition, in terms of decision variables, has been found to be extremely efficient and effective for solving large scale optimization problems. Nevertheless, most of the currently available approaches for large scale optimization rely on models based on cooperative coevolution or linkage learning methods that use multiple subpopulations or preliminary analysis, respectively, which is computationally expensive (in terms of function evaluations) when used within MOEAs. In this work, we study the effect of what we call operational decomposition, which is a novel framework based on coevolutionary concepts to apply MOEAs’s crossover operator without adding any extra cost. We investigate the improvements that NSGA-III can achieve when combined with our proposed coevolutionary operators. This new scheme is capable of improving efficiency of a MOEA when dealing with large scale MOPs having from 200 up to 1200 decision variables.

Evolutionary Algorithm provides a framework that is largely applicable to particular problems including multiobjective optimization problems, basically for the ease of their implementation and their capability to perform efficient parallel search. Indeed, in some cases, expensive multiobjective optimization evaluations might be a challenge to restrict the number of explicit fitness evaluations in multiobjective evolutionary algorithms. Accordingly, this article presents a novel approach that tackles this problem so as to not only decrease the number of fitness evaluations but also to improve the performance. During evolution, our proposed approach selects fit individuals based on the knowledge acquired throughout the search, and performs explicit fitness evaluations on these individuals. A comprehensive comparative analysis of a wide range of well-established test problems, selected from both traditional and state-of-the-art benchmarks, has been presented. Afterward, the effectiveness of the obtained results is compared with some of the state-of-the-art methods using two well-known metrics- i.e. Hypervolume and Inverted Generational Distance (IGD). The experiments of our implemented approach is performed to illustrate that our proposal seems to be promising and would prove more efficient than other approaches in terms of both the performance and the computational cost.

A self adaptive hybrid enhanced artificial bee colony algorithm for continuous optimization problems

The Hausdorff distance d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> is a widely used tool to measure the distance between different objects in several research fields. Possible reasons for this might be that it is a natural extension of the well-known and intuitive distance between points and/or the fact that d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> defines in certain cases a metric in the mathematical sense. In evolutionary multiobjective optimization (EMO) the task is typically to compute the entire solution set-the so-called Pareto set-respectively its image, the Pareto front. Hence, d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> should, at least at first sight, be a natural choice to measure the performance of the outcome set in particular since it is related to the terms spread and convergence as used in EMO literature. However, so far, d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> does not find the general approval in the EMO community. The main reason for this is that d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> penalizes single outliers of the candidate set which does not comply with the use of stochastic search algorithms such as evolutionary strategies. In this paper, we define a new performance indicator, Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> , which can be viewed as an “averaged Hausdorff distance” between the outcome set and the Pareto front and which is composed of (slight modifications of) the well-known indicators generational distance (GD) and inverted generational distance (IGD). We will discuss theoretical properties of Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> (as well as for GD and IGD) such as the metric properties and the compliance with state-of-theart multiobjective evolutionary algorithms (MOEAs), and will further on demonstrate by empirical results the potential of Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> as a new performance indicator for the evaluation of MOEAs.

Archive-based multi-criteria Artificial Bee Colony algorithm for whole test suite generation

The Economic Load Dispatch (ELD) is considered to minimize the only fuel cost in power system planning and operation. Due to environmental issues, the emission amount released by thermal power generation should be considered in minimizing the total cost generation as well. This make the power dispatch problem become multi-objective problem that called Economic and Emission Load Dispatch (EELD). This paper investigates the performances of Artificial Bee colony (ABC) algorithm for determining optimal solution for EELD problem. In this paper, the EELD problem is formulated as a single objective problem by taking minimization of total cost and emission level as separated objective. The cost characteristic of thermal generator considered the effect of opening and closing of the valve for practical application. The ABC algorithm has been tested on standard test systems which is 10-generating unit test system in order to validate the effectiveness of proposed ABC algorithm. The results obtained have been compared with reported result by other methods in literature. From the result, it found that ABC algorithm is better than other methods for minimizing fuel cost of thermal power generation and obtained comparative results in reducing the emission level.

Introduction:Reliability analysis is a good tool to deal with the uncertainty and has been widely used in the engineering system. The first order reliability method (FORM) is generally used to calculate the reliability index but FORM is time-consuming and requires derivative computing.Methods:Artificial Bee Colony (ABC) algorithm is a very simple, robust and population-based stochastic optimization algorithm. In this study, an ABC-based reliability analysis was proposed to calculate the reliability index of engineering system through combining Artificial Bee Colony (ABC) algorithm with FORM. FORM was adopted to calculate the reliability index and design point. ABC is used to solve the constrained optimization about FORM. The procedure of ABC-based reliability analysis was presented in detail.Results and Conclusion:The proposed method was verified by two classic examples and then applied to geotechnical engineering. The results show that the ABC algorithm can effectively solve the global optimization problem in FORM. Results demonstrate that ABC-based reliability analysis is a good approach to obtain the reliability index and design point with a good accuracy so that it can be applied to analyze the reliability of a complex engineering system.

The selection of products for testing Software Product Lines (SPLs) is an optimization problem. The goal is to select a possible minimum set of products that satisfies testing criteria, such as, pairwise and mutation testing. Multi-objective Evolutionary Algorithms (MOEAs) have been successfully used to solve this problem and other ones related to software development. However, the use of MOEAs demands setting a number of control parameters and selection of genetic operators, to which the algorithm performance is often very sensitive. Adaptive Operator Selection (AOS) methods, such as Upper Confidence Bound (UCB) based ones can help in this task. UCB methods used with Multi-objective Evolutionary Algorithm Based on Decomposition with Dynamical Resource Allocation (MOEA/D-DRA) have presented promising results, but they are underexplored in the Search Based Software Engineering (SBSE) field. To contribute to this research area and to solve efficiently the product selection problem, this paper investigates the use of different AOS UCB-based methods with MOEA/D-DRA. The idea is to reduce effort spent by the tester. Some parameters and evolutionary operators can be automatically set. The approach is empirical evaluated using four instances and three UCB methods. The UCB methods present similar results and outperform the canonical version of MOEA/D-DRA.