An Orthogonal Evolutionary Algorithm With Learning Automata for Multiobjective Optimization

A Novel Enhanced Nonnegative Matrix Factorization Method for Face Recognition

Nonnegative matrix factorization (NMF), distinguished from the approaches for holistic feature representation, is able to acquire meaningful basis images for parts-based representation. However, NMF does not utilize the data-label information and usually achieves undesirable performance in classification. To address the above-mentioned problem of NMF, this paper proposes a new enhanced NMF (ENMF) method for facial image representation and recognition. We seek to learn powerfully discriminative feature by a label-based regularizer which describes the relationship between the data. It is desired that minimizing the regularizer makes the data from the same class have high similarity and the data from different classes have low similarity. This good property will contribute to improving the performance of NMF. Therefore, we propose an objective function of ENMF by incorporating the label-based regularizer into the loss function. Subsequently, we find the stationary point of the constructed auxiliary function by means of Cardano’s formula and derive the update rules of our ENMF algorithm. The convergence of the proposed ENMF is both theoretically sound and empirically validated. Finally, the proposed ENMF method is successfully applied to face recognition. Four publicly available face datasets, namely AR, Caltech 101, Yale, and CMU PIE, are chosen for evaluations. Compared with the state-of-the-art NMF-based algorithms, the experimental results illustrate that the proposed ENMF algorithm achieves superior performance.

Domain Learning Particle Swarm Optimization with a hybrid mutation strategy

When traditional particle swarm optimization algorithms deal with highly complex, ultra-high-dimensional problems, traditional particle learning strategies can only provide little help. In this paper, a particle swarm optimization algorithm with a hybrid variation domain dimension learning strategy is proposed, which uses the domain dimension average of the current particle dimension to generate guiding particles. At the same time, an improved inertia weight is also used, which effectively avoids the algorithm from easily falling into local optimum. To verify the strong competitiveness of the algorithm, the algorithm is tested on nineteen benchmark functions and compared with several well-known particle swarm algorithms. The experimental results show that the algorithm proposed in this paper has a significant effect on unimodal functions, and has a better effect on multimodal functions. Guided particles, improved inertia weight and mutation strategy can effectively balance local search and global search, and can better converge to the global optimal solution.

An Improved Evolutionary Algorithm Based on a Multi-Search Strategy and an External Population Strategy for Many-Objective Optimization

Balancing the convergence and diversity of many-objective evolutionary algorithms is difficult and challenging. In this work, a multi-search strategy based on decomposition is proposed to generate good offspring and improve convergence, and an external population strategy is used to maintain the diversity of the obtained solutions. The multi-search strategy allows the selection of sparse and convergent nondominated solutions to carry out the exploration and exploitation steps. Experiments are conducted on 15 benchmark functions from the CEC 2018 with 5, 10, and 15 objectives. The results indicate that the proposed algorithm can obtain a set of solutions with better diversity and convergence than the five efficient state-of-the-art algorithms, i.e. NSGAIII, MOEA/D, MOEA/DD, KnEA, and RVEA.

An Efficient Particle Swarm Optimization with Multidimensional Mean Learning

Particle swarm optimization (PSO) algorithm is a stochastic and population-based optimization algorithm. Its traditional learning strategy is implemented by updating the best position using the particle’s own historical best experience and its neighborhood’s best experience to find the optimal solution of the problem. However, the learning strategy is ineffective when dealing with highly complex problems. In this paper, a particle swarm optimization algorithm based on a multidimensional mean learning strategy is proposed. In this algorithm, an opposition-based learning strategy is utilized to initialize the population to enhance the exploitation capability. Furthermore, the historical best positions of all the particles are reconstructed in a vertical crossover manner that is based on the mean information of multiple optimal dimensions to generate the guiding particles. Additionally, an improved inertia weight is used to further guide all the particle movements to balance the capability of the proposed algorithm for global exploration and local exploitation. The proposed algorithm is tested on 12 benchmark functions and is compared with some well-known PSO algorithms. The experimental results show that the proposed algorithm obtains more competitive optimal solution compared with other PSO algorithms when solving high-dimensional complex problems.

Optimal Scale of Urbanization with Scarce Water Resources: A Case Study in an Arid and Semi-Arid Area of China

A complex interwoven relationship exists between water resources and urbanization, which is of much interest in international water science research. To study the urban development in large cities facing water deficiency problems, it is important to identify rational thresholds of urbanization to achieve optimal utilization of limited water resources, and to promote sustainable economic and population growth and social development. A multi-objective optimization model is proposed to search for the optimal scale of urbanization of large cities with limited water resources. To solve a large-dimensional multi-objective optimization problem, the non-dominated sorting genetic algorithm (NSGA-II) is improved to the OENSGA-II based on the orthogonal generation method and the E-optimality method and applied to a typical arid city, Xi’an of China, which underwent rapid urbanization in recent years. For Xi’an, a statistically significant positive correlation is found between urbanization rate (Ur) and gross domestic product (GDP), domestic water, tertiary industry water, and ecological water. However, Ur is negatively correlated with the primary industry water. If the current urbanization trend continues, the water resources available are far from sufficient to support the future city of Xi’an. In this work, it was found that, by implementing restrictive water resources management and water saving measures, the economic threshold of Xi’an could be raised to 1890.3 and 2403.3 billion yuan, while the population threshold could be raised to 11.0 and 13.9 million, and Ur to 79.9% and 85.9% in 2020 and 2030, respectively. The corresponding maximum urban area to be constructed based on the projected population will be 964.81 and 1197.6 km2 in those years. It will be prudent for Xi’an to practice strict water resource management, and to allocate its water resources among various water sectors effectively and equitably to avoid major water shortage problems in the future.