Chunguo Wu

A Pheromone-Rate-Based Analysis on the Convergence Time of ACO Algorithm

Ant colony optimization (ACO) has widely been applied to solve combinatorial optimization problems in recent years. There are few studies, however, on its convergence time, which reflects how many iteration times ACO algorithms spend in converging to the optimal solution. Based on the absorbing Markov chain model, we analyze the ACO convergence time in this paper. First, we present a general result for the estimation of convergence time to reveal the relationship between convergence time and pheromone rate. This general result is then extended to a two-step analysis of the convergence time, which includes the following: 1) the iteration time that the pheromone rate spends on reaching the objective value and 2) the convergence time that is calculated with the objective pheromone rate in expectation. Furthermore, four brief ACO algorithms are investigated by using the proposed theoretical results as case studies. Finally, the conclusions of the case studies that the pheromone rate and its deviation determine the expected convergence time are numerically verified with the experiment results of four one-ant ACO algorithms and four ten-ant ACO algorithms.

Hybrid chromosome genetic algorithm for generalized traveling salesman problems

Generalized Traveling Salesman Problem (GTSP) is one of the challenging combinatorial optimization problems in a lot of applications. In general, GTSP is more complex than Traveling Salesman Problem (TSP). In this paper, a novel hybrid chromosome genetic algorithm (HCGA), in which the hybrid binary and integer codes are adopted, is proposed as an improvement of generalized chromosome genetic algorithm (GCGA). In order to examine the effectiveness of HCGA, 16 benchmark problems are simulated. The experimental results show that HCGA can perform better than GCGA does in solving GTSP.

An Efficient Genetic Algorithm for Optimization Problems with Time-Consuming Fitness Evaluation

In classical genetic algorithm, fitness evaluations are often very expensive or highly time-consuming, especially for some engineering optimization problems. We present an efficient genetic algorithm (GA) by combining clustering methods with an empirical fitness estimating formula. The new individuals are clustered at first, and then only the cluster representatives are really evaluated by its original time-consuming fitness computing processes, and other individuals undergo high efficient fitness evaluating processes by using the empirical fitness estimating formula. To further improve the accuracy of fitness estimations, we present a schema discovery strategy by extracting the common encoding characters from both high-fitness individual group and low-fitness individual group, and then adjust the estimated fitness for each individual based on the matching with the discovered schema. Experiments show that the schema discovery strategy contributes remarkably to the accuracy of fitness estimation. Numerical experiments of some well-known benchmark problems and a practical engineering problem demonstrate that the proposed method could improve the efficiency by over 30% in terms of the times of real fitness evaluations at the similar optimization accuracy of classical genetic algorithm.

Adaptive and iterative least squares support vector regression based on quadratic Renyi entropy

An adaptive and iterative LSSVR algorithm based on quadratic Renyi entropy is presented in this paper. LS-SVM loses the sparseness of support vector which is one of the important advantages of conventional SVM. The proposed algorithm overcomes this drawback. The quadratic Renyi entropy is the evaluating criterion for working set selection, and the size of working set is determined at the process of iteration adaptively. The regression parameters are calculated by incremental learning and the calculation of inversing a large scale matrix is avoided. So the running speed is improved. This algorithm reserves well the sparseness of support vector and improves the learning speed.

Globally-optimal prediction-based adaptive mutation particle swarm optimization

Particle swarm optimizations (PSOs) are drawing extensive attention from both research and engineering fields due to their simplicity and powerful global search ability. However, there are two issues needing to be improved: one is that the classical PSO converges slowly; the other is that classical PSO tends to result in premature convergence, especially for multi-modal problems. This paper attempts to address these two issues. Firstly, to improve the convergent efficiency, this paper proposes an asymptotic predicting model of the globally-optimal solution, which is used to predict the global optimum based on extracting the features reflecting the evolutionary trend. The predicted global optimum is then taken as the third exemplar, in a way similar to the individual historical best solution and the swarm historical best solution in guiding the evolutionary process of other particles. To reduce the probability that the population is trapped into a local optimum due to the premature phenomenon, this paper proposes an adaptive mutation strategy, which is used to help the trapped particles to escape away from the local optimum by using the extended non-uniform mutation operator. Finally, we combine the two entities to develop a globally-optimal prediction-based adaptive mutation particle swarm optimization (GPAM-PSO). In numerical experimental parts, we compare the proposed GPAM-PSO with 11 existing PSO variants by using 22 benchmark problems of 30-dimensions and 100-dimensions, respectively. Numerical experiments demonstrate that the proposed GPAM-PSO could improve the accuracy and efficiency remarkably, which means that the combination of the globally-optimal prediction-based search and the adaptive mutation strategy could accelerate the convergence and reduce premature phenomenon effectively. Generally speaking, GPAM-PSO performs most efficiently and robustly. Moreover, the performance on an engineering problem demonstrates the practical application of the proposed GPAM-PSO algorithm.

Hierarchical Solving Method for Large Scale TSP Problems

This paper presents a hierarchical algorithm for solving large-scale traveling salesman problem (TSP), the algorithm first uses clustering algorithms to large-scale TSP problem into a number of small-scale collections of cities, and then put this TSP problem as a generalized traveling salesman problem (GTSP), convert solving large-scale TSP problem into solving GTSP and several small-scale TSP problems. Then all the sub-problems will be solved by ant colony algorithm and At last all the solutions of each sub-problem will be merged into the solution of the large-scale TSP problem by solution of GTSP. Experimental part we uses the traditional ant colony algorithm and new algorithm for solving large-scale TSP problem, numerical simulation results show that the proposed algorithm for large-scale TSP problem has a good effect, compared with the traditional ant colony algorithm, the solving efficiency has been significantly improved.

Global prediction-based adaptive mutation particle swarm optimization

Particle swarm optimization (PSO) algorithm has attracted great attention as a stochastic optimizing method due to its simplicity and power strength in optimization fields. However, two issues are still to be improved, especially, for complex multimodal problems. One is the premature convergence for multimodal problems. The other is the low efficiency for complex problems. To address these two issues, firstly, a strategy based on the global optimum prediction is proposed. A predicting model is established on the low-dimensional feature space with the principle component analysis technique, which has the ability to predict the global optimal position by the feature reflecting the evolution tendency of the current swarm. Then the predicted position is used as a guideline exemplar of the evolution process together with pbest and gbest. Secondly, a strategy, called adaptive mutation, is proposed, which can evaluate the crowding level of the aggregating particle swarm by using the distribution topology of each dimension, and hence, can get the possible location of local optimums and escape from the valleys with the generalized non-uniform mutation operator subsequently. The performance of the proposed global prediction-based adaptive mutation particle swarm optimization (GPAM-PSO) is tested on 8 well-known benchmark problems, compared with 9 existing PSO in terms of both accuracy and efficiency. The experimental results demonstrate that GPAM-PSO outperforms all reference PSO algorithms on both the solution quality and convergence speed.

Boost particle swarm optimization with fitness estimation

It is well known that the classical particle swarm optimization (PSO) is time-consuming when used to solve complex fitness optimization problems. In this study, we perform in-depth research on fitness estimation based on the distance between particles and affinity propagation clustering. In addition, support vector regression is employed as a surrogate model for estimating fitness values instead of using the objective function. The particle swarm optimization algorithm based on affinity propagation clustering, the efficient particle swarm optimization algorithm, and the particle swarm optimization algorithm based on support vector regression machine are then proposed. The experimental results show that the new algorithms significantly reduce the computational counts of the objective function. Compared with the classical PSO, the optimization results exhibit no loss of accuracy or stability.

A Novel Method for Analysing the Population Dynamic Behavior of Particle Swarm Optimization

Most of the existing population behavior studies are about the analysis of the population dynamic behavior of genetic algorithm, while there is little analysis of the population dynamic behavior of particle swarm optimization (PSO). Therefore, there is an urgent need for a new method to characterize the population dynamic behavior of PSO in the search process. In this paper, we propose some metrics based on relative entropy, principal component analysis and correlation coefficient, to characterize the population dynamic behavior of PSO, named KL measure (KLM) and principal correlation coefficient (PCC). KLM and PCC are used to describe the divergence and correlation between the differences of objective functions and particle positions. Using these proposed metrics KLM and PCC, we can effectively divide the search process of the population into three stages: random search stage, fine search stage and convergence stage. Experimental results, with classical optimization problems and different running parameters, show that the proposed metrics KLM and PCC can capture the dynamic alteration of population behavior even when the population is in a relatively convergent state, hence, which can characterize the whole search process of the population in much fine granularity.

Mutual conversion of regression and classification based on least squares support vector machines

Classification and regression are most interesting problems in the fields of pattern recognition. The regression problem can be changed into binary classification problem and least squares support vector machine can be used to solve the classification problem. The optimal hyperplane is the regression function. In this paper, a one-step method is presented to deal with the multi-category problem. The proposed method converts the problem of classification into the function regression problem and is applied to solve the converted problem by least squares support vector machines. The novel method classifies the samples in all categories simultaneously only by solving a set of linear equations. Demonstrations of numerical experiments are performed and good performances are obtained. Simulation results show that the regression and classification can be converted each other based on least squares support vector machines.