Evolutionary Many-Objective Algorithm Using Decomposition-Based Dominance Relationship

A multitask optimization algorithm based on elite individual transfer

Evolutionary multitasking algorithms aim to solve several optimization tasks simultaneously, and they can improve the efficiency of various tasks evolution through the knowledge transfer between different optimization tasks. Evolutionary multitasking algorithms have been applied to various applications and achieved certain results. However, how to transfer knowledge between tasks is still a problem worthy of research. Aiming to improve the positive transfer between tasks and reduce the negative transfer, we propose a single-objective multitask optimization algorithm based on elite individual transfer, namely MSOET. In this paper, whether to execute knowledge transfer between tasks depends on a certain probability. Meanwhile, in order to enhance the effectiveness and the global search ability of the algorithm, the current population and the elite individual in the transfer population are further utilized as the learning sources to construct a Gaussian distribution model, and the offspring is generated by the Gaussian distribution model to achieve knowledge transfer between tasks. We compared the proposed MSOET with ten multitask optimization algorithms, and the experimental results verify the algorithm's excellent performance and strong robustness.

A Rough-to-Fine Evolutionary Multiobjective Optimization Algorithm

This article presents a rough-to-fine evolutionary multiobjective optimization algorithm based on the decomposition for solving problems in which the solutions are initially far from the Pareto-optimal set. Subsequently, a tree is constructed by a modified k -means algorithm on N uniform weight vectors, and each node of the tree contains a weight vector. Each node is associated with a subproblem with the help of its weight vector. Consequently, a subproblem tree can be established. It is easy to find that the descendant subproblems are refinements of their ancestor subproblems. The proposed algorithm approaches the Pareto front (PF) by solving a few subproblems in the first few levels to obtain a rough PF and gradually refining the PF by involving the subproblems level-by-level. This strategy is highly favorable for solving problems in which the solutions are initially far from the Pareto set. Moreover, the proposed algorithm has lower time complexity. Theoretical analysis shows the complexity of dealing with a new candidate solution is O(M logN) , where M is the number of objectives. Empirical studies demonstrate the efficacy of the proposed algorithm.

Resetting Weight Vectors in MOEA/D for Multiobjective Optimization Problems With Discontinuous Pareto Front

When a multiobjective evolutionary algorithm based on decomposition (MOEA/D) is applied to solve problems with discontinuous Pareto front (PF), a set of evenly distributed weight vectors may lead to many solutions assembling in boundaries of the discontinuous PF. To overcome this limitation, this article proposes a mechanism of resetting weight vectors (RWVs) for MOEA/D. When the RWV mechanism is triggered, a classic data clustering algorithm DBSCAN is used to categorize current solutions into several parts. A classic statistical method called principal component analysis (PCA) is used to determine the ideal number of solutions in each part of PF. Thereafter, PCA is used again for each part of PF separately and virtual targeted solutions are generated by linear interpolation methods. Then, the new weight vectors are reset according to the interrelationship between the optimal solutions and the weight vectors under the Tchebycheff decomposition framework. Finally, taking advantage of the current obtained solutions, the new solutions in the decision space are updated via a linear interpolation method. Numerical experiments show that the proposed MOEA/D-RWV can achieve good results for bi-objective and tri-objective optimization problems with discontinuous PF. In addition, the test on a recently proposed MaF benchmark suite demonstrates that MOEA/D-RWV also works for some problems with other complicated characteristics.

A New Many-Objective Evolutionary Algorithm Based on Generalized Pareto Dominance

In the past several years, it has become apparent that the effectiveness of Pareto-dominance-based multiobjective evolutionary algorithms deteriorates progressively as the number of objectives in the problem, given by M , grows. This is mainly due to the poor discriminability of Pareto optimality in many-objective spaces (typically M ≥ 4 ). As a consequence, research efforts have been driven in the general direction of developing solution ranking methods that do not rely on Pareto dominance (e.g., decomposition-based techniques), which can provide sufficient selection pressure. However, it is still a nontrivial issue for many existing non-Pareto-dominance-based evolutionary algorithms to deal with unknown irregular Pareto front shapes. In this article, a new many-objective evolutionary algorithm based on the generalization of Pareto optimality (GPO) is proposed, which is simple, yet effective, in addressing many-objective optimization problems. The proposed algorithm used an "( M-1 ) + 1" framework of GPO dominance, ( M-1 )-GPD for short, to rank solutions in the environmental selection step, in order to promote convergence and diversity simultaneously. To be specific, we apply M symmetrical cases of ( M-1 )-GPD, where each enhances the selection pressure of M-1 objectives by expanding the dominance area of solutions, while remaining unchanged for the one objective left out of that process. Experiments demonstrate that the proposed algorithm is very competitive with the state-of-the-art methods to which it is compared, on a variety of scalable benchmark problems. Moreover, experiments on three real-world problems have verified that the proposed algorithm can outperform the others on each of these problems.

A Multiobjective Evolutionary Algorithm Based on Objective-Space Localization Selection

This article proposes a simple yet effective multiobjective evolutionary algorithm (EA) for dealing with problems with irregular Pareto front. The proposed algorithm does not need to deal with the issues of predefining weight vectors and calculating indicators in the search process. It is mainly based on the thought of adaptively selecting multiple promising search directions according to crowdedness information in local objective spaces. Concretely, the proposed algorithm attempts to dynamically delete an individual of poor quality until enough individuals survive into the next generation. In this environmental selection process, the proposed algorithm considers two or three individuals in the most crowded area, which is determined by the local information in objective space, according to a probability selection mechanism, and deletes the worst of them from the current population. Thus, these surviving individuals are representative of promising search directions. The performance of the proposed algorithm is verified and compared with seven state-of-the-art algorithms [including four general multi/many-objective EAs and three algorithms specially designed for dealing with problems with irregular Pareto-optimal front (PF)] on a variety of complicated problems with different numbers of objectives ranging from 2 to 15. Empirical results demonstrate that the proposed algorithm has a strong competitiveness power in terms of both the performance and the algorithm compactness, and it can well deal with different types of problems with irregular PF and problems with different numbers of objectives.

Distributed Multiobjective Optimization for Network Resource Allocation of Multiagent Systems

In this article, a distributed multiobjective optimization problem is formulated for the resource allocation of network-connected multiagent systems. The framework encompasses a group of distributed decision makers in the subagents, where each of them possesses a local preference index. Novel distributed algorithms are proposed to solve such a problem in a distributed manner. The weighted L_p preference index is utilized in each agent since it can provide a robust Pareto solution to the problem. By using distributed fixed-time optimization methods, the L_p preference index is constructed online without specifying the unknown parameters. Then, it is proved that the problem admits a unique Pareto solution. By exploiting consensus and gradient descent techniques, asymptotic convergence to the optimal solution is established via Lyapunov theories. Distinct from most of the current works, the proposed framework does not require any prior information in the formulation process, and private data can be well protected using this distributed approach. Numerical examples are included to validate the effectiveness of the proposed algorithms.

An Indicator-Based Many-Objective Evolutionary Algorithm With Boundary Protection

Many-objective optimization problems (MaOPs) pose a big challenge to the traditional Pareto-based multiobjective evolutionary algorithms (MOEAs). As the number of objectives increases, the number of mutually nondominated solutions explodes and MOEAs become invalid due to the loss of Pareto-based selection pressure. Indicator-based many-objective evolutionary algorithms (MaOEAs) have been proposed to address this issue by enhancing the environmental selection. Indicator-based MaOEAs are easy to implement and of good versatility, however, they are unlikely to maintain the population diversity and coverage very well. In this article, a new indicator-based MaOEA with boundary protection, namely, MaOEA-IBP, is presented to relieve this weakness. In MaOEA-IBP, a worst elimination mechanism based on the I_ϵ⁺ indicator and boundary protection strategy is devised to enhance the balance of population convergence, diversity, and coverage. Specifically, a pair of solutions with the smallest I_ϵ⁺ value are first identified from the population. If one solution dominates the other, the dominated solution is eliminated. Otherwise, one solution is eliminated by the boundary protection strategy. MaOEA-IBP is compared with four indicator-based algorithms (i.e., I _SDE⁺ , SRA, MaOEAIGD, and ARMOEA) and other five state-of-the-art MaOEAs (i.e., KnEA, MaOEA-CSS, 1by1EA, RVEA, and EFR-RR) on various benchmark MaOPs. The experimental results demonstrate that MaOEA-IBP can achieve competitive performance with the compared algorithms.

An Elite Gene Guided Reproduction Operator for Many-Objective Optimization

Traditional reproduction operators in many-objective evolutionary algorithms (MaOEAs) seem to not be so effective to tackle many-objective optimization problems (MaOPs). This is mainly because the population size cannot be set to an arbitrarily large value if the computational efficiency is of concern. In such a case, the distance between the parents becomes remarkably large and, consequently, it is not easy to reproduce a superior offspring in high-dimensional objective space. To alleviate this problem, an elite gene-guided (EGG) reproduction operator is proposed to tackle MaOPs in this article. In this operator, an elite gene pool is built by collecting the knee points from the current population. Then, the offspring is produced by exchanging the genes with this elite gene pool under an exchange rate, aiming to reserve more promising genes into the next generation. In order to provide new genes for the population, other genes will be disturbed under a disturbance rate. The settings and functional analysis of the exchange rate and disturbance rate are studied using several experiments. The proposed EGG operator is easy to implement and can be embedded to any MaOEA. As examples, we show the embedding of the proposed EGG operator into four competitive MaOEAs, that is, MOEA/D, NSGA-III, θ -DEA, and SPEA2-SDE provide some advantages over simulated binary crossover, differential evolution, and an evolutionary path-based reproduction operator on solving a number of benchmark problems with 3 to 15 objectives.

Multiobjective Optimization and Local Merge for Clustering Attributed Graphs

Methods for detecting the community structure in complex networks have mainly focused on network topology, neglecting the rich content information often associated with nodes. In the last few years, the compositional dimension contained in many real-world networks has been recognized fundamental to find network divisions which better reflect group organization. In this paper, we propose a multiobjective genetic framework which integrates the topological and compositional dimensions to uncover community structure in attributed networks. The approach allows to experiment different structural measures to search for densely connected communities, and similarity measures between attributes to obtain high intracommunity feature homogeneity. An efficient and efficacious post-processing local merge procedure enables the generation of high quality solutions, as confirmed by the experimental results on both synthetic and real-world networks, and the comparison with several state-of-the-art methods.