Recently, MOEA/D (multi-objective evolutionary algorithm based on decomposition) has achieved great success in the field of evolutionary multi-objective optimization and has attracted a lot of attention. It decomposes a multi-objective optimization problem (MOP) into a set of scalar subproblems using uniformly distributed aggregation weight vectors and provides an excellent general algorithmic framework of evolutionary multi-objective optimization. Generally, the uniformity of weight vectors in MOEA/D can ensure the diversity of the Pareto optimal solutions, however, it cannot work as well when the target MOP has a complex Pareto front (PF; i.e., discontinuous PF or PF with sharp peak or low tail). To remedy this, we propose an improved MOEA/D with adaptive weight vector adjustment (MOEA/D-AWA). According to the analysis of the geometric relationship between the weight vectors and the optimal solutions under the Chebyshev decomposition scheme, a new weight vector initialization method and an adaptive weight vector adjustment strategy are introduced in MOEA/D-AWA. The weights are adjusted periodically so that the weights of subproblems can be redistributed adaptively to obtain better uniformity of solutions. Meanwhile, computing efforts devoted to subproblems with duplicate optimal solution can be saved. Moreover, an external elite population is introduced to help adding new subproblems into real sparse regions rather than pseudo sparse regions of the complex PF, that is, discontinuous regions of the PF. MOEA/D-AWA has been compared with four state of the art MOEAs, namely the original MOEA/D, Adaptive-MOEA/D, [Formula: see text]-MOEA/D, and NSGA-II on 10 widely used test problems, two newly constructed complex problems, and two many-objective problems. Experimental results indicate that MOEA/D-AWA outperforms the benchmark algorithms in terms of the IGD metric, particularly when the PF of the MOP is complex.

In this paper, multiagent systems and genetic algorithms are integrated to form a new algorithm, multiagent genetic algorithm (MAGA), for solving the global numerical optimization problem. An agent in MAGA represents a candidate solution to the optimization problem in hand. All agents live in a latticelike environment, with each agent fixed on a lattice-point. In order to increase energies, they compete or cooperate with their neighbors, and they can also use knowledge. Making use of these agent-agent interactions, MAGA realizes the purpose of minimizing the objective function value. Theoretical analyzes show that MAGA converges to the global optimum. In the first part of the experiments, ten benchmark functions are used to test the performance of MAGA, and the scalability of MAGA along the problem dimension is studied with great care. The results show that MAGA achieves a good performance when the dimensions are increased from 20-10,000. Moreover, even when the dimensions are increased to as high as 10,000, MAGA still can find high quality solutions at a low computational cost. Therefore, MAGA has good scalability and is a competent algorithm for solving high dimensional optimization problems. To the best of our knowledge, no researchers have ever optimized the functions with 10,000 dimensions by means of evolution. In the second part of the experiments, MAGA is applied to a practical case, the approximation of linear systems, with a satisfactory result.

Automatic classification of fruits via computer vision is still a complicated task due to the various properties of numerous types of fruits. We propose a novel classification method based on a multi-class kernel support vector machine (kSVM) with the desirable goal of accurate and fast classification of fruits. First, fruit images were acquired by a digital camera, and then the background of each image was removed by a split-and-merge algorithm; Second, the color histogram, texture and shape features of each fruit image were extracted to compose a feature space; Third, principal component analysis (PCA) was used to reduce the dimensions of feature space; Finally, three kinds of multi-class SVMs were constructed, i.e., Winner-Takes-All SVM, Max-Wins-Voting SVM, and Directed Acyclic Graph SVM. Meanwhile, three kinds of kernels were chosen, i.e., linear kernel, Homogeneous Polynomial kernel, and Gaussian Radial Basis kernel; finally, the SVMs were trained using 5-fold stratified cross validation with the reduced feature vectors as input. The experimental results demonstrated that the Max-Wins-Voting SVM with Gaussian Radial Basis kernel achieves the best classification accuracy of 88.2%. For computation time, the Directed Acyclic Graph SVMs performs swiftest.

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Community structure is one of the most important properties in networks, and community detection has received an enormous amount of attention in recent years. Modularity is by far the most used and best known quality function for measuring the quality of a partition of a network, and many community detection algorithms are developed to optimize it. However, there is a resolution limit problem in modularity optimization methods. In this study, a memetic algorithm, named Meme-Net, is proposed to optimize another quality function, modularity density, which includes a tunable parameter that allows one to explore the network at different resolutions. Our proposed algorithm is a synergy of a genetic algorithm with a hill-climbing strategy as the local search procedure. Experiments on computer-generated and real-world networks show the effectiveness and the multiresolution ability of the proposed method.

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