Pareto Dominance-based Multi-objective Evolutionary Algorithms Research Articles

An adaptive neighborhood based evolutionary algorithm with pivot- solution based selection for multi- and many-objective optimization

Pareto dominance-based multi-objective evolutionary algorithms (PDMOEAs) encounter scalability issues due to the lack of selection pressure as the dimensionality of objective space increases. In addition, PDMOEAs combat difficulties in achieving the proper balance between convergence and diversity. To overcome this issue, recently, additional convergence-related metrics have been proposed for PDMOEAs to improve their performance by enhancing the selection pressure towards the true Pareto front; however, these approaches have limitations.To address the drawbacks of the previous approaches, in this paper, we propose an adaptive neighborhood based evolutionary algorithm with pivot-solution based selection (Pi-MOEA) to tackle multi- and many-objective optimization problems. The proposed Pi-MOEA approach identifies a set of pivot-solutions to improve the convergence performance. An adaptive neighborhood is designed among the individuals, and the average ranking method is employed to identify the pivot-solutions within the neighborhood. In addition, to preserve the population diversity, density estimation based on Euclidean distance is adopted in Pi-MOEA. The performance of the Pi-MOEA is investigated extensively on 26 test problems from three popular benchmark problem suites by comparing them with seven state-of-the-art algorithms. The experimental results show that the Pi-MOEA algorithm performs considerably better when compared with state-of-the-art algorithms.

An Evolutionary Algorithm for Multi and Many-Objective Optimization With Adaptive Mating and Environmental Selection

Multi-objective evolutionary algorithms (MOEAs) have received immense recognition due to their effectiveness and efficiency in tackling multi-objective optimization problems (MOPs). Recently, numerous studies on MOEAs revealed that when handling many-objective optimization problems (MaOPs) that have more than three objectives, MOEAs encounter challenges and the behavior of MOEAs resembles a random walk in search space as the proportion of nondominated solutions increases subsequently. This phenomenon is commonly observed in most classical Pareto-dominance-based MOEAs (PDMOEAs) such as NSGA-II, SPEAII, as these algorithms face difficulties in guiding the search process towards the optimal Pareto front due to lack of selection pressure. From the literature, it is evident that incorporating sum of normalized objectives into the framework of MOEAs would enhance the converging capabilities. Hence, in this work, we propose a novel multi-objective optimization algorithm with adaptive mating and environmental selection (ad-MOEA) which effectively incorporates the concept of sum of objectives in the mechanisms of mating and environmental selection to control the convergence and diversity adaptively. To demonstrate the effectiveness of the proposed ad-MOEA, we have conducted experiments on 26 test problems that includes DTLZ, WFG and MaOP test suites. Along with the benchmark problem, we have analyzed the performance of the proposed approach on real-world problems. The experimental results demonstrate the effectiveness of the proposed method with respect to the state-of-art methods.

A new dominance-relation metric balancing convergence and diversity in multi- and many-objective optimization

Maintaining a good balance between convergence and diversity in many-objective optimization is a key challenge for most Pareto dominance-based multi-objective evolutionary algorithms. In most existing multi-objective evolutionary algorithms, a certain fixed metric is used in the selection operation, no matter how far the solutions are from the Pareto front. Such a selection scheme directly affects the performance of the algorithm, such as its convergence, diversity or computational complexity. In this paper, we use a more structured metric, termed augmented penalty boundary intersection, which acts differently on each of the non-dominated fronts in the selection operation, to balance convergence and diversity in many-objective optimization problems. In diversity maintenance, we apply a distance-based selection scheme to each non-dominated front. The performance of our proposed algorithm is evaluated on a variety of benchmark problems with 3 to 15 objectives and compared with five state-of-the-art multi-objective evolutionary algorithms. The empirical results demonstrate that our proposed algorithm has highly competitive performance on almost all test instances considered. Furthermore, the combination of a special mate selection scheme and a clustering-based selection scheme considerably reduces the computational complexity compared to most state-of-the-art multi-objective evolutionary algorithms.

Pareto Dominance-Based Algorithms With Ranking Methods for Many-Objective Optimization

In Pareto dominance-based multi-objective evolutionary algorithms (PDMOEAs), Pareto dominance fails to provide the essential selection pressure required to drive the search toward convergence in many-objective optimization problems (MaOPs). Recently, the idea of using secondary criterion, such as knee points and so on to enhance the convergence, is becoming popular. In this paper, we propose to employ popular ranking methods—average rank (AR) and weighted sum (WS) of objectives, which are capable of accelerating the convergence as secondary criterion. After nondominated sorting, based on the secondary criterion employed (AR or WS) and a niche radius, nondominated solutions are assigned a rank referred to as priority rank (PR). In other words, among a set of nondominated solutions, solutions that are diverse and best within a neighborhood in terms of ranking method (AR or WS) employed are assigned a better PR. During mating and environmental selections, giving preference to solutions with least PR enables the selection of solutions that are diverse and can improve the convergence speed of MOEA without the need for additional diversity maintenance mechanisms. The performances of proposed PDMOEAs with ranking methods are compared with the state-of-the-art methods to demonstrate the significance of ranking methods in accelerating the convergence. PDMOEA with AR as secondary criterion is referred to as PDMOEA-AR while PDMOEA with WS as secondary criterion is referred to as PDMOEA-WS. From the experimental results, it has been observed that PDMOEAs with ranking methods (PDMOEA-AR and PDMOEA-WS) outperform the state-of-the-art algorithms on benchmark MaOPs, such as DTLZ and WFG. In addition, it has been observed that PDMOEA-AR performs better on a wide variety of MaOPs with diverse characteristics whereas PDMOEA-WS is particularly suitable for only a subclass of MaOPs. In other words, the range-independent nature of AR makes PDMOEA-AR a general-purpose algorithm, which performs better on a wide variety of problems.

A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization

Many-objective optimization has posed a great challenge to the classical Pareto dominance-based multiobjective evolutionary algorithms (MOEAs). In this paper, an evolutionary algorithm based on a new dominance relation is proposed for many-objective optimization. The proposed evolutionary algorithm aims to enhance the convergence of the recently suggested nondominated sorting genetic algorithm III by exploiting the fitness evaluation scheme in the MOEA based on decomposition, but still inherit the strength of the former in diversity maintenance. In the proposed algorithm, the nondominated sorting scheme based on the introduced new dominance relation is employed to rank solutions in the environmental selection phase, ensuring both convergence and diversity. The proposed algorithm is evaluated on a number of well-known benchmark problems having 3–15 objectives and compared against eight state-of-the-art algorithms. The extensive experimental results show that the proposed algorithm can work well on almost all the test functions considered in this paper, and it is compared favorably with the other many-objective optimizers. Additionally, a parametric study is provided to investigate the influence of a key parameter in the proposed algorithm.

MOEA/D with biased weight adjustment inspired by user preference and its application on multi-objective reservoir flood control problem

Related to the safety of public lives and property in the lower area of reservoirs, flood control is a priority for most large reservoirs. Considering both dam safety and downstream flood control, reservoir flood control is a multi-objective problem (MOP). To meet the needs of irrigation and generating electricity after the flood, the decision maker usually has his/her preferred final scheduling water level. To deal with this kind of MOP with user-preference information, we incorporate user-preference information into the framework of MOEA/D (multi-objective evolutionary algorithm-based decomposition). The widely used preference information is mainly composed of reference points and preference directions. Compared with the Pareto dominance-based multi-objective evolutionary algorithms (MOEAs), MOEA/D can naturally include two kinds of preference information since MOEA/D is directly based on the reference point and the preference direction. The weight vector of a subproblem in MOEA/D is just its preference. Aiming to obtain uniformly distributed solutions on the objective space, one of innovation points in this paper is using modified Tchebycheff decomposition instead of Tchebycheff decomposition as the decomposition method. To focus the search on the interesting regions of decision maker, the other innovation point in this paper is to integrate biased subproblem (weight vector) adjustment into the framework of MOEA/D. The distribution of subproblems (weight vectors) are adjusted periodically so that the subproblems are re-distributed adaptively to search the interesting regions. Some subproblems, which are far away from the preference regions, are deleted. And then some new subproblems, which are expected to search the preference regions, are added into the current evolutionary population. The efficiency and the effectiveness of the proposed algorithm are assessed through multi-objective reservoir flood control problem and two- to ten-objective test problems.