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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]

The balance between convergence and diversity is the cornerstone of evolutionary multiobjective optimization (EMO). The recently proposed stable matching-based selection provides a new perspective to handle this balance under the framework of decomposition multiobjective optimization. In particular, the one-one stable matching between subproblems and solutions, which achieves an equilibrium between their mutual preferences, is claimed to strike a balance between convergence and diversity. However, the original stable marriage model has a high risk of matching a solution with an unfavorable subproblem, which finally leads to an imbalanced selection result. In this paper, we introduce the concept of incomplete preference lists into the stable matching model to remedy the loss of population diversity. In particular, each solution is only allowed to maintain a partial preference list consisting of its favorite subproblems. We implement two versions of stable matching-based selection mechanisms with incomplete preference lists: one achieves a two-level one-one matching and the other obtains a many-one matching. Furthermore, an adaptive mechanism is developed to automatically set the length of the incomplete preference list for each solution according to its local competitiveness. The effectiveness and competitiveness of our proposed methods are validated and compared with several state-of-the-art EMO algorithms on 62 benchmark problems. [ABSTRACT FROM PUBLISHER]

Decomposition-based multiobjective evolutionary algorithms (MOEAs) have received increasing research interests due to their high performance for solving multiobjective optimization problems. However, scalarizing functions (SFs), which play a crucial role in balancing diversity and convergence in these kinds of algorithms, have not been fully investigated. This paper is mainly devoted to presenting two new SFs and analyzing their effect in decomposition-based MOEAs. Additionally, we come up with an efficient framework for decomposition-based MOEAs based on the proposed SFs and some new strategies. Extensive experimental studies have demonstrated the effectiveness of the proposed SFs and algorithm. [ABSTRACT FROM PUBLISHER]

Taking both convergence and diversity into consideration, this paper suggests a vector angle-based evolutionary algorithm for unconstrained (with box constraints only) many-objective optimization problems. In the proposed algorithm, the maximum-vector-angle-first principle is used in the environmental selection to guarantee the wideness and uniformity of the solution set. With the help of the worse-elimination principle, worse solutions in terms of the convergence (measured by the sum of normalized objectives) are allowed to be conditionally replaced by other individuals. Therefore, the selection pressure toward the Pareto-optimal front is strengthened. The proposed method is compared with other four state-of-the-art many-objective evolutionary algorithms on a number of unconstrained test problems with up to 15 objectives. The experimental results have shown the competitiveness and effectiveness of our proposed algorithm in keeping a good balance between convergence and diversity. Furthermore, it was shown by the results on two problems from practice (with irregular Pareto fronts) that our method significantly outperforms its competitors in terms of both the convergence and diversity of the obtained solution sets. Notably, the new algorithm has the following good properties: 1) it is free from a set of supplied reference points or weight vectors; 2) it has less algorithmic parameters; and 3) the time complexity of the algorithm is low. Given both good performance and nice properties, the suggested algorithm could be an alternative tool when handling optimization problems with more than three objectives. [ABSTRACT FROM PUBLISHER]

Evolutionary algorithms have shown their promise in coping with many-objective optimization problems. However, the strategies of balancing convergence and diversity and the effectiveness of handling problems with irregular Pareto fronts (PFs) are still far from perfect. To address these issues, this paper proposes an adaptive sorting-based evolutionary algorithm based on the idea of decomposition. First, we propose an adaptive sorting-based environmental selection strategy. Solutions in each subpopulation (partitioned by reference vectors) are sorted based on their convergence. Those with better convergence are further sorted based on their diversity, then being selected according to their sorting levels. Second, we provide an adaptive promising subpopulation sorting-based environmental selection strategy for problems which may have irregular PFs. This strategy provides additional sorting-based selection effort on promising subpopulations after the general environmental selection process. Third, we extend the algorithm to handle constraints. Finally, we conduct an extensive experimental study on the proposed algorithm by comparing with start-of-the-state algorithms. Results demonstrate the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper develops a decomposition-based coevolutionary algorithm for many-objective optimization, which evolves a number of subpopulations in parallel for approaching the set of Pareto optimal solutions. The many-objective problem is decomposed into a number of subproblems using a set of well-distributed weight vectors. Accordingly, each subpopulation of the algorithm is associated with a weight vector and is responsible for solving the corresponding subproblem. The exploration ability of the algorithm is improved by using a mating pool that collects elite individuals from the cooperative subpopulations for breeding the offspring. In the subsequent environmental selection, the top-ranked individuals in each subpopulation, which are appraised by aggregation functions, survive for the next iteration. Two new aggregation functions with distinct characteristics are designed in this paper to enhance the population diversity and accelerate the convergence speed. The proposed algorithm is compared with several state-of-the-art many-objective evolutionary algorithms on a large number of benchmark instances, as well as on a real-world design problem. Experimental results show that the proposed algorithm is very competitive. [ABSTRACT FROM AUTHOR]

Achieving balance between convergence and diversity is a key issue in evolutionary multiobjective optimization. Most existing methodologies, which have demonstrated their niche on various practical problems involving two and three objectives, face significant challenges in many-objective optimization. This paper suggests a unified paradigm, which combines dominance- and decomposition-based approaches, for many-objective optimization. Our major purpose is to exploit the merits of both dominance- and decomposition-based approaches to balance the convergence and diversity of the evolutionary process. The performance of our proposed method is validated and compared with four state-of-the-art algorithms on a number of unconstrained benchmark problems with up to 15 objectives. Empirical results fully demonstrate the superiority of our proposed method on all considered test instances. In addition, we extend this method to solve constrained problems having a large number of objectives. Compared to two other recently proposed constrained optimizers, our proposed method shows highly competitive performance on all the constrained optimization problems. [ABSTRACT FROM PUBLISHER]

The multiobjective evolutionary algorithm (MOEA) based on decomposition transforms a multiobjective optimization problem into a set of aggregated subproblems and then optimizes them collaboratively. Since these subproblems usually have different degrees of difficulty, resource allocation (RA) strategies have been reported to enhance performance, attempting to dynamically assign proper amounts of computational resources for the solution of each of these subproblems. However, existing schemes for decomposition-based MOEAs fully rely on the relative improvement of the aggregated functions to do this. This paper proposes a diversity-enhanced RA strategy for this kind of MOEA, depending on both relative improvement on aggregated function value and solution density around each subproblem to assign computational resources. Thus, one subproblem surrounded with fewer solutions in its neighboring area and more relative improvement on the aggregated function value will be allocated a higher probability for evolution. Our experimental results show the advantages of our proposed strategy over two popular RA strategies available for decomposition-based MOEAs, on tackling a set of complicated benchmark problems. [ABSTRACT FROM AUTHOR]

The decomposition-based multiobjective evolutionary algorithms (MOEAs) generally make use of aggregation functions to decompose a multiobjective optimization problem into multiple single-objective optimization problems. However, due to the nature of contour lines for the adopted aggregation functions, they usually fail to preserve the diversity in high-dimensional objective space even by using diverse weight vectors. To address this problem, we propose to maintain the desired diversity of solutions in their evolutionary process explicitly by exploiting the perpendicular distance from the solution to the weight vector in the objective space, which achieves better balance between convergence and diversity in many-objective optimization. The idea is implemented to enhance two well-performing decomposition-based algorithms, i.e., MOEA, based on decomposition and ensemble fitness ranking. The two enhanced algorithms are compared to several state-of-the-art algorithms and a series of comparative experiments are conducted on a number of test problems from two well-known test suites. The experimental results show that the two proposed algorithms are generally more effective than their predecessors in balancing convergence and diversity, and they are also very competitive against other existing algorithms for solving many-objective optimization problems. [ABSTRACT FROM PUBLISHER]

Multiobjective evolutionary algorithm based on decomposition (MOEA/D), which bridges the traditional optimization techniques and population-based methods, has become an increasingly popular framework for evolutionary multiobjective optimization. It decomposes a multiobjective optimization problem (MOP) into a number of optimization subproblems. Each subproblem is handled by an agent in a collaborative manner. The selection of MOEA/D is a process of choosing solutions by agents. In particular, each agent has two requirements on its selected solution: one is the convergence toward the efficient front, the other is the distinction with the other agents’ choices. This paper suggests addressing these two requirements by defining mutual-preferences between subproblems and solutions. Afterwards, a simple yet effective method is proposed to build an interrelationship between subproblems and solutions, based on their mutual-preferences. At each generation, this interrelationship is used as a guideline to select the elite solutions to survive as the next parents. By considering the mutual-preferences between subproblems and solutions (i.e., the two requirements of each agent), the selection operator is able to balance the convergence and diversity of the search process. Comprehensive experiments are conducted on several MOP test instances with complicated Pareto sets. Empirical results demonstrate the effectiveness and competitiveness of our proposed algorithm. [ABSTRACT FROM PUBLISHER]