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Decomposition-based evolutionary algorithms using predefined reference points have shown good performance in many-objective optimization. Unfortunately, almost all experimental studies have focused on problems having regular Pareto fronts (PFs). Recently, it has been shown that the performance of such algorithms is deteriorated when facing irregular PFs, such as degenerate, discontinuous, inverted, strongly convex, and/or strongly concave fronts. The main issue is that the predefined reference points may not all intersect with the PF. Therefore, many researchers have proposed to update the reference points with the aim of adapting them to the discovered Pareto shape. Unfortunately, the adaptive update does not really solve the issue for two main reasons. On the one hand, there is a considerable difficulty to set the time and the frequency of updates. On the other hand, it is not easy to define how to update the search directions for an unknown PF shape. This article proposes to approximate irregular PFs using a set of predefined normal-boundary intersection (NBI) directions. The main motivation behind this article is that when using a set of well-distributed NBI directions, all these directions intersect with the PF regardless of its shape, except for the case of discontinuous and/or degenerate fronts. To handle the latter cases, a simple interaction mechanism between the decision maker (DM) and the algorithm is used. In fact, the DM is asked if the number of NBI directions needs to be increased in some stages of the evolutionary process. If so, the resolution of the NBI directions that intersect the PF is increased to properly cover discontinuous and/or degenerate PFs. Our experimental results on benchmark problems with regular and irregular PFs, having up to fifteen objectives, show the merits of our algorithm when compared to eight of the most representative state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Multiobjective evolutionary algorithms (MOEAs) have proven their effectiveness and efficiency in solving problems with two or three objectives. However, recent studies show that MOEAs face many difficulties when tackling problems involving a larger number of objectives as their behavior becomes similar to a random walk in the search space since most individuals are nondominated with respect to each other. Motivated by the interesting results of decomposition-based approaches and preference-based ones, we propose in this paper a new decomposition-based dominance relation to deal with many-objective optimization problems and a new diversity factor based on the penalty-based boundary intersection method. Our reference point-based dominance (RP-dominance), has the ability to create a strict partial order on the set of nondominated solutions using a set of well-distributed reference points. The RP-dominance is subsequently used to substitute the Pareto dominance in nondominated sorting genetic algorithm-II (NSGA-II). The augmented MOEA, labeled as RP-dominance-based NSGA-II, has been statistically demonstrated to provide competitive and oftentimes better results when compared against four recently proposed decomposition-based MOEAs on commonly-used benchmark problems involving up to 20 objectives. In addition, the efficacy of the algorithm on a realistic water management problem is showcased. [ABSTRACT FROM AUTHOR]

Recently, a new metaheuristic called chemical reaction optimization was proposed. This search algorithm, inspired by chemical reactions launched during collisions, inherits several features from other metaheuristics such as simulated annealing and particle swarm optimization. This fact has made it, nowadays, one of the most powerful search algorithms in solving mono-objective optimization problems. In this paper, we propose a multiobjective variant of chemical reaction optimization, called nondominated sorting chemical reaction optimization, in an attempt to exploit chemical reaction optimization features in tackling problems involving multiple conflicting criteria. Since our approach is based on nondominated sorting, one of the main contributions of this paper is the proposal of a new quasi-linear average time complexity quick nondominated sorting algorithm; thereby making our multiobjective algorithm efficient from a computational cost viewpoint. The experimental comparisons against several other multiobjective algorithms on a variety of benchmark problems involving various difficulties show the effectiveness and the efficiency of this multiobjective version in providing a well-converged and well-diversified approximation of the Pareto front. [ABSTRACT FROM PUBLISHER]

We propose in this paper to consider code-smells detection as a distributed optimization problem. The idea is that different methods are combined in parallel during the optimization process to find a consensus regarding the detection of code-smells. To this end, we used Parallel Evolutionary algorithms (P-EA) where many evolutionary algorithms with different adaptations (fitness functions, solution representations, and change operators) are executed, in a parallel cooperative manner, to solve a common goal which is the detection of code-smells. An empirical evaluation to compare the implementation of our cooperative P-EA approach with random search, two single population-based approaches and two code-smells detection techniques that are not based on meta-heuristics search. The statistical analysis of the obtained results provides evidence to support the claim that cooperative P-EA is more efficient and effective than state of the art detection approaches based on a benchmark of nine large open source systems where more than 85 percent of precision and recall scores are obtained on a variety of eight different types of code-smells. [ABSTRACT FROM PUBLISHER]

Evolutionary multiobjective optimization (EMO) methodologies have gained popularity in finding a representative set of Pareto optimal solutions in the past decade and beyond. Several techniques have been proposed in the specialized literature to ensure good convergence and diversity of the obtained solutions. However, in real world applications, the decision maker is not interested in the overall Pareto optimal front since the final decision is a unique solution. Recently, there has been an increased emphasis in addressing the decision-making task in searching for the most preferred alternatives. In this paper, we introduce a new variant of the Pareto dominance relation, called r-dominance, which has the ability to create a strict partial order among Pareto-equivalent solutions. This fact makes such a relation able to guide the search toward the interesting parts of the Pareto optimal region based on the decision maker's preferences expressed as a set of aspiration levels. After integrating the new dominance relation in the NSGA-II methodology, the efficacy and the usefulness of the modified procedure are assessed through two to ten-objective test problems a priori and interactively. Moreover, the proposed approach provides competitive and better results when compared to other recently proposed preference-based EMO approaches. [ABSTRACT FROM PUBLISHER]