A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in Many-Objective Optimization Problems

Singh, Hemant Kumar; Isaacs, Amitay; Ray, Tapabrata

doi:10.1109/tevc.2010.2093579

Cited by 226 publications

(113 citation statements)

References 18 publications

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“…In our approach, refactoring solutions are evaluated using a set of 15 software quality metrics. We evaluated our approach on seven large open source systems [28][29] [30][31] [32]. The experimental results indicate that NSGA-III outperforms other many-objective algorithms (IBEA [31] and MOEA/D [30]), NSGA-II and mono-objective evolutionary algorithms [19] [23].…”

Section: Discussionmentioning

confidence: 99%

High dimensional search-based software engineering

Mkaouer

Kessentini

Bechikh

et al. 2014

Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation

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There is a growing need for scalable search-based software engineering approaches that address software engineering problems where a large number of objectives are to be optimized. Software refactoring is one of these problems where a refactoring sequence is sought that optimizes several software metrics. Most of the existing refactoring work uses a large set of quality metrics to evaluate the software design after applying refactoring operations, but current search-based software engineering approaches are limited to using a maximum of five metrics. We propose for the first time a scalable search-based software engineering approach based on a newly proposed evolutionary optimization method NSGA-III where there are 15 different objectives to be optimized. In our approach, automated refactoring solutions are evaluated using a set of 15 distinct quality metrics. We evaluated this approach on seven large open source systems and found that, on average, more than 92% of code smells were corrected. Statistical analysis of our experiments over 31 runs shows that NSGA-III performed significantly better than two other many-objective techniques (IBEA and MOEA/D), a multiobjective algorithm (NSGA-II) and two mono-objective approaches, hence demonstrating that our NSGA-III approach represents the new state of the art in fully-automated refactoring.

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Section: Discussionmentioning

confidence: 99%

High dimensional search-based software engineering

Mkaouer

Kessentini

Bechikh

et al. 2014

Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation

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“…(2) Dimensionality reduction: A novel technique for dimensionality reduction is proposed in which the true dimensionality of a problem is identified using a key set of solutions (corners) on the Pareto front. An algorithm to identify the set of corners, Pareto Corner Search Evolutionary Algorithm (PCSEA) [1], is proposed; followed by analysis of the obtained corner solutions by omitting each objective sequentially. The proposed method is able to estimate the dimensionality using merely a small fraction of evaluations required by other contemporary techniques.…”

Section: Large Scale Optimization (Many Objectives)mentioning

confidence: 99%

Development of optimization methods to deal with current challenges in engineering design optimization

Singh

2014

AIC

Self Cite

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Abstract.Presented herein is a summary of PhD thesis entitled "Development of optimization methods to deal with current challenges in engineering design optimization" by the author. The thesis is available online at http://handle.unsw.edu.au/1959.4/ 51426. Keywords: Artificial intelligence, constraint handling, many-objective optimization, large scale optimization Background and motivationIn engineering design, optimization is customary, and often indispensable. Typical cases include minimization of drag for vehicles, minimization of weight for structures like buildings and bridges, maximization of power and lift for aircraft and rockets, minimization of fuel consumption for engines, etc. Therefore it comes as no surprise that development of fast and efficient optimization algorithms for engineering design is an actively pursued research area.In recent decades, metaheuristic algorithms have proven to be efficient, robust and versatile methods for numerical optimization. However, they usually need to evaluate a large number of candidate designs to find near optimum solutions. This becomes prohibitive for engineering optimization problems in which each design evaluation may require computationally expensive analysis and, consequently, the optimization process may take much longer time than affordable.Considering that the number of design evaluations is a critical factor in overall optimization time, it is imperative to develop techniques to search for the optimum design using fewest evaluations possible. With this singular goal, this thesis investigates a range of domains in which existing metaheuristic optimization approaches can be improved.Engineering problems are often highly non-linear, discontinuous, and non-differentiable, which rules out (or restricts) the applicability of analytical techniques for solving them. However, they exhibit additional attributes that prove challenging even to the existing metaheuristic techniques, thus making the search difficult and, consequently, creating a necessity for carrying out large numbers of evaluations. These include: (a) Constraints -constraints render a fraction (often a large fraction) of the search space infeasible, making it hard to find the optimum and at times even a feasible design; (b) Large number of objectivesPareto-dominance sorting, a commonly used technique in multi-objective optimization algorithms, is inadequate to solve problems with large numbers of objectives, a fact well reported in literature; (c) Large number of variables -the search space grows exponentially with the number of variables, which results in a corresponding increase in computational effort; and (d) Multiple models -for certain problems, there may be multiple candidate models to choose a solution from, with none of them being an obviously preferred one. In such a case, one may need to explore each one of them to find the global best.In this thesis, studies are conducted on each of these domains individually. Shortcomings of the existing 0921-7126/16/$35.00

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“…We recall Singh et al's [4] definition of corner points which at first sight appear to be good candidates for extremal points lying on the edge of a mutually non-dominating set. They consider the minimisation of M functions fi(x) where x is a vector of decision variables.…”

Section: From Corners To Edgesmentioning

confidence: 99%

“…For example, the individuals that maximise or minimise any single objective provide natural reference points [3]. Singh et al [4] have given a procedure for finding the corners in multi-objective optimisation problems. In this paper we extend these ideas by examining what is meant by the edge of a mutually non-dominating set.…”

Section: Introductionmentioning

confidence: 99%

Edges of mutually non-dominating sets

Everson

Walker

Fieldsend

2013

Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation

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Multi-objective optimisation yields an estimated Pareto front of mutually non-dominating solutions, but with more than three objectives understanding the relationships between solutions is challenging. Natural solutions to use as landmarks are those lying near to the edges of the mutually nondominating set. We propose four definitions of edge points for many-objective mutually non-dominating sets and examine the relations between them.The first defines edge points to be those that extend the range of the attainment surface. This is shown to be equivalent to finding points which are not dominated on projection onto subsets of the objectives. If the objectives are to be minimised, a further definition considers points which are not dominated under maximisation when projected onto objective subsets. A final definition looks for edges via alternative projections of the set.We examine the relations between these definitions and their efficacy for synthetic concave-and convex-shaped sets, and on solutions to a prototypical many-objective optimisation problem, showing how they can reveal information about the structure of the estimated Pareto front.

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A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in Many-Objective Optimization Problems

Cited by 226 publications

References 18 publications

High dimensional search-based software engineering

High dimensional search-based software engineering

Development of optimization methods to deal with current challenges in engineering design optimization

Edges of mutually non-dominating sets

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