An evolutionary algorithm with double-level archives for multiobjective optimization

Existing multiobjective evolutionary algorithms (MOEAs) tackle a multiobjective problem either as a whole or as several decomposed single-objective sub-problems. Though the problem decomposition approach generally converges faster through optimizing all the sub-problems simultaneously, there are two issues not fully addressed, i.e., distribution of solutions often depends on a priori problem decomposition, and the lack of population diversity among sub-problems. In this paper, a MOEA with double-level archives is developed. The algorithm takes advantages of both the multiobjective-problemlevel and the sub-problem-level approaches by introducing two types of archives, i.e., the global archive and the sub-archive. In each generation, self-reproduction with the global archive and cross-reproduction between the global archive and sub-archives both breed new individuals. The global archive and sub-archives communicate through cross-reproduction, and are updated using the reproduced individuals. Such a framework thus retains fast convergence, and at the same time handles solution distribution along Pareto front (PF) with scalability. To test the performance of the proposed algorithm, experiments are conducted on both the widely used benchmarks and a set of truly disconnected problems. The results verify that, compared with state-of-the-art MOEAs, the proposed algorithm offers competitive advantages in distance to the PF, solution coverage, and search speed

Evolutionary Multiobjective Optimization Driven by Generative Adversarial Networks (GANs)

Recently, increasing works have proposed to drive evolutionary algorithms using machine learning models. Usually, the performance of such model based evolutionary algorithms is highly dependent on the training qualities of the adopted models. Since it usually requires a certain amount of data (i.e. the candidate solutions generated by the algorithms) for model training, the performance deteriorates rapidly with the increase of the problem scales, due to the curse of dimensionality. To address this issue, we propose a multi-objective evolutionary algorithm driven by the generative adversarial networks (GANs). At each generation of the proposed algorithm, the parent solutions are first classified into real and fake samples to train the GANs; then the offspring solutions are sampled by the trained GANs. Thanks to the powerful generative ability of the GANs, our proposed algorithm is capable of generating promising offspring solutions in high-dimensional decision space with limited training data. The proposed algorithm is tested on 10 benchmark problems with up to 200 decision variables. Experimental results on these test problems demonstrate the effectiveness of the proposed algorithm

An adaptation reference-point-based multiobjective evolutionary algorithm

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.It is well known that maintaining a good balance between convergence and diversity is crucial to the performance of multiobjective optimization algorithms (MOEAs). However, the Pareto front (PF) of multiobjective optimization problems (MOPs) affects the performance of MOEAs, especially reference point-based ones. This paper proposes a reference-point-based adaptive method to study the PF of MOPs according to the candidate solutions of the population. In addition, the proportion and angle function presented selects elites during environmental selection. Compared with five state-of-the-art MOEAs, the proposed algorithm shows highly competitive effectiveness on MOPs with six complex characteristics

Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm with the interleaved multi-start scheme

The Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm (MO-GOMEA) has been shown to be a promising solver for multi-objective combinatorial optimization problems, obtaining an excellent scalability on both standard benchmarks and real-world applications. To attain optimal performance, MO-GOMEA requires its two parameters, namely the population size and the number of clusters, to be set properly with respect to the problem instance at hand, which is a non-trivial task for any EA practitioner. In this article, we present a new version of MO-GOMEA in combination with the so-called Interleaved Multi-start Scheme (IMS) for the multi-objective domain that eliminates the manual setting of these two parameters. The new MO-GOMEA is then evaluated on multiple benchmark problems in comparison with two well-known multi-objective evolutionary algorithms (MOEAs): Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D). Experiments suggest that MO-GOMEA with the IMS is an easy-to-use MOEA that retains the excellent performance of the original MO-GOMEA

Multi-objective evolutionary algorithms for data clustering

In this work we investigate the use of Multi-Objective metaheuristics for the data-mining task of clustering. We �first investigate methods of evaluating the quality of clustering solutions, we then propose a new Multi-Objective clustering algorithm driven by multiple measures of cluster quality and then perform investigations into the performance of different Multi-Objective clustering algorithms. In the context of clustering, a robust measure for evaluating clustering solutions is an important component of an algorithm. These Cluster Quality Measures (CQMs) should rely solely on the structure of the clustering solution. A robust CQM should have three properties: it should be able to reward a \good" clustering solution; it should decrease in value monotonically as the solution quality deteriorates and, it should be able to evaluate clustering solutions with varying numbers of clusters. We review existing CQMs and present an experimental evaluation of their robustness. We find that measures based on connectivity are more robust than other measures for cluster evaluation. We then introduce a new Multi-Objective Clustering algorithm (MOCA). The use of Multi-Objective optimisation in clustering is desirable because it permits the incorporation of multiple measures of cluster quality. Since the definition of what constitutes a good clustering is far from clear, it is beneficial to develop algorithms that allow for multiple CQMs to be accommodated. The selection of the clustering quality measures to use as objectives for MOCA is informed by our previous work with internal evaluation measures. We explain the implementation details and perform experimental work to establish its worth. We compare MOCA with k-means and find some promising results. We�find that MOCA can generate a pool of clustering solutions that is more likely to contain the optimal clustering solution than the pool of solutions generated by k-means. We also perform an investigation into the performance of different implementations of MOEA algorithms for clustering. We�find that representations of clustering based around centroids and medoids produce more desirable clustering solutions and Pareto fronts. We also �find that mutation operators that greatly disrupt the clustering solutions lead to better exploration of the Pareto front whereas mutation operators that modify the clustering solutions in a more moderate way lead to higher quality clustering solutions. We then perform more specific investigations into the performance of mutation operators focussing on operators that promote clustering solution quality, exploration of the Pareto front and a hybrid combination. We use a number of techniques to assess the performance of the mutation operators as the algorithms execute. We confirm that a disruptive mutation operator leads to better exploration of the Pareto front and mutation operators that modify the clustering solutions lead to the discovery of higher quality clustering solutions. We find that our implementation of a hybrid mutation operator does not lead to a good improvement with respect to the other mutation operators but does show promise for future work

An improved MOEA/D algorithm for multi-objective multicast routing with network coding

Network coding enables higher network throughput, more balanced traffic, and securer data transmission. However, complicated mathematical operations incur when packets are combined at intermediate nodes, which, if not operated properly, lead to very high network resource consumption and unacceptable delay. Therefore, it is of vital importance to minimize various network resources and end-to-end delays while exploiting promising benefits of network coding. Multicast has been used in increasingly more applications, such as video conferencing and remote education. In this paper the multicast routing problem with network coding is formulated as a multi-objective optimization problem (MOP), where the total coding cost, the total link cost and the end-to-end delay are minimized simultaneously. We adapt the multi-objective evolutionary algorithm based on decomposition (MOEA/D) for this MOP by hybridizing it with a population-based incremental learning technique which makes use of the global and historical information collected to provide additional guidance to the evolutionary search. Three new schemes are devised to facilitate the performance improvement, including a probability-based initialization scheme, a problem-specific population updating rule, and a hybridized reproduction operator. Experimental results clearly demonstrate that the proposed algorithm outperforms a number of state-of-the-art MOEAs regarding the solution quality and computational time