On the evolutionary optimisation of many conflicting objectives

This inquiry explores the effectiveness of a class of modern evolutionary algorithms, represented by Non-dominated Sorting Genetic Algorithm (NSGA) components, for solving optimisation tasks with many conflicting objectives. Optimiser behaviour is assessed for a grid of mutation and recombination operator configurations. Performance maps are obtained for the dual aims of proximity to, and distribution across, the optimal trade-off surface. Performance sweet-spots for both variation operators are observed to contract as the number of objectives is increased. Classical settings for recombination are shown to be suitable for small numbers of objectives but correspond to very poor performance for higher numbers of objectives, even when large population sizes are used. Explanations for this behaviour are offered via the concepts of dominance resistance and active diversity promotion

GALAXY: A new hybrid MOEA for the Optimal Design of Water Distribution Systems

This is the final version of the article. Available from American Geophysical Union via the DOI in this record.The first author would like to appreciate the financial support given by both the University of Exeter and the China Scholarship Council (CSC) toward the PhD research. We also appreciate the three anonymous reviewers, who help improve the quality of this paper substantially. The source code of the latest versions of NSGA-II and ε-MOEA can be downloaded from the official website of Kanpur Genetic Algorithms Laboratory via http://www.iitk.ac.in/kangal/codes.shtml. The description of each benchmark problem used in this paper, including the input file of EPANET and the associated best-known Pareto front, can be accessed from the following link to the Centre for Water Systems (http://tinyurl.com/cwsbenchmarks/). GALAXY can be accessed via http://tinyurl.com/cws-galaxy

Multi-Objective Archiving

Most multi-objective optimisation algorithms maintain an archive explicitly or implicitly during their search. Such an archive can be solely used to store high-quality solutions presented to the decision maker, but in many cases may participate in the search process (e.g., as the population in evolutionary computation). Over the last two decades, archiving, the process of comparing new solutions with previous ones and deciding how to update the archive/population, stands as an important issue in evolutionary multi-objective optimisation (EMO). This is evidenced by constant efforts from the community on developing various effective archiving methods, ranging from conventional Pareto-based methods to more recent indicator-based and decomposition-based ones. However, the focus of these efforts is on empirical performance comparison in terms of specific quality indicators; there is lack of systematic study of archiving methods from a general theoretical perspective. In this paper, we attempt to conduct a systematic overview of multi-objective archiving, in the hope of paving the way to understand archiving algorithms from a holistic perspective of theory and practice, and more importantly providing a guidance on how to design theoretically desirable and practically useful archiving algorithms. In doing so, we also present that archiving algorithms based on weakly Pareto compliant indicators (e.g., epsilon-indicator), as long as designed properly, can achieve the same theoretical desirables as archivers based on Pareto compliant indicators (e.g., hypervolume indicator). Such desirables include the property limit-optimal, the limit form of the possible optimal property that a bounded archiving algorithm can have with respect to the most general form of superiority between solution sets.Comment: 21 pages, 4 figures, journa

An Approach for the Generation of Multi-Objective Algorithms Applied to the Integration and Test Order Problem

Multi-Objective Evolutionary Algorithms (MOEAs) have been successfully applied to solve hard real software engineering problems. However, to choose and design a MOEA is considered a difficult task, since there are several parameters and components to be configured. These aspects directly impact the generated solutions and the performance of MOEAs. In this sense, this paper proposes an approach for the automatic generation of MOEAs applied to the Integration and Test Order (ITO) problem. Such a problem refers to the generation of optimal sequences of units for integration testing. The approach includes a set of parameters and components of different MOEAs, and is implemented with two design algorithms: Grammatical Evolution (GE) and Iterated Racing (irace). Evaluation results are presented, comparing the MOEAs generated by both design algorithms. Furthermore, the generated MOEAs are compared to two well-known MOEAs used in the literature to solve the ITO problem. Results show that the MOEAs generated with GE and irace perform similarly, and both outperform traditional MOEAs. The approach can reduce efforts spent to design and configure MOEAs, and serves as basis for implementing solutions to other software engineering problems

Hyper-volume evolutionary algorithm

We propose a multi-objective evolutionary algorithm (MOEA), named the Hyper-volume Evolutionary Algorithm (HVEA). The algorithm is characterised by three components. First, individual fitness evaluation depends on the current Pareto front, specifically on the ratio of its dominated hyper-volume to the current Pareto front hyper-volume, hence giving an indication of how close the individual is to the current Pareto front. Second, a ranking strategy classifies individuals based on their fitness instead of Pareto dominance, individuals within the same rank are non-guaranteed to be mutually non-dominated. Third, a crowding assignment mechanism that adapts according to the individual’s neighbouring area, controlled by the neighbouring area radius parameter, and the archive of non-dominated solutions. We perform extensive experiments on the multiple 0/1 knapsack problem using different greedy repair methods to compare the performance of HVEA to other MOEAs including NSGA2, SEAMO2, SPEA2, IBEA and MOEA/D. This paper shows that by tuning the neighbouring area radius parameter, the performance of the proposed HVEA can be pushed towards better convergence, diversity or coverage and this could be beneficial to different types of problems

Rank-Based Learning and Local Model Based Evolutionary Algorithm for High-Dimensional Expensive Multi-Objective Problems

Surrogate-assisted evolutionary algorithms have been widely developed to solve complex and computationally expensive multi-objective optimization problems in recent years. However, when dealing with high-dimensional optimization problems, the performance of these surrogate-assisted multi-objective evolutionary algorithms deteriorate drastically. In this work, a novel Classifier-assisted rank-based learning and Local Model based multi-objective Evolutionary Algorithm (CLMEA) is proposed for high-dimensional expensive multi-objective optimization problems. The proposed algorithm consists of three parts: classifier-assisted rank-based learning, hypervolume-based non-dominated search, and local search in the relatively sparse objective space. Specifically, a probabilistic neural network is built as classifier to divide the offspring into a number of ranks. The offspring in different ranks uses rank-based learning strategy to generate more promising and informative candidates for real function evaluations. Then, radial basis function networks are built as surrogates to approximate the objective functions. After searching non-dominated solutions assisted by the surrogate model, the candidates with higher hypervolume improvement are selected for real evaluations. Subsequently, in order to maintain the diversity of solutions, the most uncertain sample point from the non-dominated solutions measured by the crowding distance is selected as the guided parent to further infill in the uncertain region of the front. The experimental results of benchmark problems and a real-world application on geothermal reservoir heat extraction optimization demonstrate that the proposed algorithm shows superior performance compared with the state-of-the-art surrogate-assisted multi-objective evolutionary algorithms. The source code for this work is available at https://github.com/JellyChen7/CLMEA

Hybrid non-dominated sorting genetic algorithm with adaptive operators selection

Multiobjective optimization entails minimizing or maximizing multiple objective functions subject to a set of constraints. Many real world applications can be formulated as multi-objective optimization problems (MOPs), which often involve multiple conflicting objectives to be optimized simultaneously. Recently, a number of multi-objective evolutionary algorithms (MOEAs) were developed suggested for these MOPs as they do not require problem specific information. They find a set of non-dominated solutions in a single run. The evolutionary process on which they are based, typically relies on a single genetic operator. Here, we suggest an algorithm which uses a basket of search operators. This is because it is never easy to choose the most suitable operator for a given problem. The novel hybrid non-dominated sorting genetic algorithm (HNSGA) introduced here in this paper and tested on the ZDT (Zitzler-Deb-Thiele) and CEC’09 (2009 IEEE Conference on Evolutionary Computations) benchmark problems specifically formulated for MOEAs. Numerical results prove that the proposed algorithm is competitive with state-of-the-art MOEAs