Algorithm For Global Optimization Problems Research Articles

Orthogonal based Differential Evolution for Absolute Value Equation

This paper presents an improved differential evolution (DE) based on orthogonal crossover to solve complex absolute value equation problems. Absolute value equation problems are NP-hard multimodal problems. Differential evolution (DE) is one of fast and robust, accurate evolutionary algorithms for global optimization problems and solution of absolute value equation problems. In this paper, orthogonal based differential evolution, which is proposed through incorporation differential evolution with orthogonal crossover, is excogitated to solve three absolute value equation problems. Several experiments are conducted on absolute value equation problems, the solution accuracy, convergence rate and robustness of ODE are compared with other state-ofthe-art orthogonal based algorithms. The comparison results show that ODE is a fast, effective, efficient and robust algorithm for solving absolute value equation problems.

Dynamic group-based differential evolution using a self-adaptive strategy for global optimization problems

This paper describes a dynamic group-based differential evolution (GDE) algorithm for global optimization problems. The GDE algorithm provides a generalized evolution process based on two mutation operations to enhance search capability. Initially, all individuals in the population are grouped into a superior group and an inferior group based on their fitness values. The two groups perform different mutation operations. The local mutation model is applied to individuals with better fitness values, i.e., in the superior group, to search for better solutions near the current best position. The global mutation model is applied to the inferior group, which is composed of individuals with lower fitness values, to search for potential solutions. Subsequently, the GDE algorithm employs crossover and selection operations to produce offspring for the next generation. In this paper, an adaptive tuning strategy based on the well-known 1/5th rule is used to dynamically reassign the group size. It is thus helpful to trade off between the exploration ability and the exploitation ability. To validate the performance of the GDE algorithm, 13 numerical benchmark functions are tested. The simulation results indicate that the approach is effective and efficient.

Hybrid harmony search and artificial bee colony algorithm for global optimization problems

Harmony search (HS) is one of the newest and the easiest to code music inspired heuristics for optimization problems. In order to enhance the accuracy and convergence rate of harmony search, a hybrid harmony search is proposed by incorporating the artificial bee colony algorithm (ABC). The artificial bee colony algorithm is a new swarm intelligence technique inspired by intelligent foraging behavior of honey bees. The ABC and its variants are used to improve harmony memory (HM). To compare and analyze the performance of our proposed hybrid algorithms, a number of experiments are carried out on a set of well-known benchmark global optimization problems. The effects of the parameters about the hybrid algorithms are discussed by a uniform design experiment. Numerical results show that the proposed algorithms can find better solutions when compared to HS and other heuristic algorithms and are powerful search algorithms for various global optimization problems.

Artificial Tribe Algorithm and Its Performance Analysis

In this paper, a novel intelligent optimization algorithm - Artificial Tribe Algorithm (A T A) is presented based on the analyses of the principle and unif orm framework of the Bionic Intelligent Optimization Algorithm s (BIOA). ATA simulate s the existent skills of the natural tribes, and actualizes the optimization purpose through the propagation and migration behaviors of the tribes. The main factors which influence the performance of ATA have been discussed. ATA is used for unconstrained and constrained functions optimization and the results produced by ATA, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Artificial Fish-Swarm Algorithm (AFSA) have been compared. The results show that ATA is a powerful algorithm for global optimization problems.

Stratified Sampling Differential Evolution Algorithm for Global Optimization Problem

Differential Evolution (DE) is one kind of evolution algorithm, which based on difference of individuals. DE has exhibited good performance on optimization problem. However, when a local optimal solution is reached with classical Differential Evolution, all individuals in the population gather around it, and escaping from these local optima becomes difficult. To avoid premature convergence of DE, we present in this paper a novel variant of DE algorithm, called SSDE, which uses the stratified sampling method to replace the random sampling method. The proposed SSDE algorithm is compared with some variant DE. The numerical results show that our approach is robust, competitive and fast.

Stratified Sampling Differential Evolution Algorithm for Global Optimization Problem

Differential Evolution (DE) is one kind of evolution algorithm, which based on difference of individuals. DE has exhibited good performance on optimization problem. However, when a local optimal solution is reached with classical Differential Evolution, all individuals in the population gather around it, and escaping from these local optima becomes difficult. To avoid premature convergence of DE, we present in this paper a novel variant of DE algorithm, called SSDE, which uses the stratified sampling method to replace the random sampling method. The proposed SSDE algorithm is compared with some variant DE. The numerical results show that our approach is robust, competitive and fast.

An Optimization Algorithm Based on Binary Difference and Gravitational Evolution

Abstract Universal gravitation is a natural phenomenon. Inspired by Newton's universal gravitation model and based on binary differences strategy, we propose an algorithm for global optimization problems, which is called the binary difference gravitational evolution (BDGE) algorithm. BDGE is a population-based algorithm, and the population is composed of particles. Each particle is treated as a virtual object with two attributes of position and quality. Some of the best objects in the population compose the reference-group and the rest objects compose the floating-group. The BDGE algorithm could find the global optimum solutions through two critical operations: the self-update of reference-group and the interactive-update process between the reference-group and floating-group utilizing the gravitational evolution method. The parameters of BDGE are set by a trial-and-error process and the BDGE is proved that it can converge to the global optimal solution with probability 1. Benchmark functions are used to ...

A Parallel Algorithm for Global Optimization Problems in a Distribuited Computing Environment

The problem of finding a global minimum of a real function on a set S Rn occurs in many real world problems. Since its computational complexity is exponential, its solution can be a very expensive computational task. In this paper, we introduce a parallel algorithm that exploits the latest computers in the market equipped with more than one processor, and used in clusters of computers. The algorithm belongs to the improvement of local minima algorithm family, and carries on local minimum searches iteratively but trying not to find an already found local optimizer. Numerical experiments have been carried out on two computers equipped with four and six processors; fourteen configurations of the computing resources have been investigated. To evaluate the algorithm performances the speedup and the efficiency are reported for each configuration.

Improving particle swarm optimization performance with local search for high-dimensional function optimization

Particle swarm optimization (PSO) is one recently proposed population-based stochastic optimization technique, and gradient-based descent methods are efficient local optimization techniques that are often used as a necessary ingredient of hybrid algorithms for global optimization problems (GOPs). By examining the properties of the two methods, a two-stage hybrid algorithm for global optimization is proposed. In the present algorithm, the gradient descent technique is used to find a local minimum of the objective function efficiently, and a PSO method with latent parallel search capability is employed to help the algorithm to escape from the previously converged local minima to a better point which is then used as a starting point for the gradient methods to restart a new local search. The above search procedure is applied repeatedly until a global minimum is found (when a global minimum is known in advance) or the maximum number of function evaluations is reached. In addition, a repulsion technique and partially initializing population method are incorporated in the new algorithm to increase its global jumping ability. Simulation results on 15 test problems including five large-scale ones with dimensions up to 1000 demonstrate that the proposed method is more stable and efficient than several other existing methods.

Parent-centric differential evolution algorithm for global optimization problems

Differential evolution (DE) is a population based evolutionary search algorithm widely used for solving optimization problems. In the present article we investigate the application of parent-centric approach on the performance of classical DE, without tampering with the basic structure of DE. The parent-centric approach is embedded in the mutation phase of DE. We propose two versions of (DE) called differential evolution with parent-centric crossover (DEPCX) and differential evolution with probabilistic parent-centric crossover (ProDEPCX) in order to improve the performance of classical DE. The proposed algorithms are validated on a test bed of ten benchmark functions and the numerical results are compared with basic DE and a modified version called trigonometric differential evolution (TDE). Empirical analysis of numerical results on the benchmark problems show that the performance of proposed versions is either at par or better in comparison to TDE and basic DE in terms of convergence rate and quality of fitness function value.

Hybrid artificial fish swarm algorithm for global optimization problems

Based on the Powell algorithm and Adaptive Artificial Fish Swarm Algorithm (AAFSA), a hybrid artificial fish swarm algorithm (AAFSA-Powell) for global optimization problems was presented by inserting Powell algorithm into AAFSA. As a local search operator, Powell algorithm has strong local search ability, whereas artificial fish swarm algorithm has global convergence. Therefore, the hybrid algorithm is capable of improving the global search ability of the algorithm, as well as reducing the computational burden. The numerical experimental results show that the algorithm can converge quickly with high adjustment.

A Robust Archived Differential Evolution Algorithm for Global Optimization Problems

A robust archived differential evolution algorithm is put forward by means of embedding a flexibility processing operator and an efficiency processing operator based on original DE and ADE. A special constraint-handling mechanism based on dynamic penalty functions and fitness calculation of individuals is adopted in the proposed method to deal with various constraints effectively, which is further extended by means of a flexibility processing operator so as to make it suitable for different type problems, including those with or without constraint(s) and those with continuous, discrete or mixed discrete-continuous variables. Furthermore, an archive of solutions is maintained during the evolutionary process so as to keep the useful information of previous solutions and local optima for the estimation of new solutions. Based on the archive of solutions, an iterative control operator and an efficiency processing operator are designed in the algorithm. The former guides the evolutionary process towards a promising search space, avoiding unnecessary and worthless search. The latter improves the local searching efficiency and the final searching quality. Experimental results based on a suite of six well-known optimization problems reveal that the proposed algorithm is robust, effective, efficient and suitable for different type global optimization problems.

To be fair or efficient or a bit of both

Introducing a new concept of ( α , β ) -fairness, which allows for a bounded fairness compromise, so that a source is allocated a rate neither less than 0 ⩽ α ⩽ 1 , nor more than β ⩾ 1 , times its fair share, this paper provides a framework to optimize efficiency (utilization, throughput or revenue) subject to fairness constraints in a general telecommunications network for an arbitrary fairness criterion and cost functions. We formulate a non-linear program (NLP) that finds the optimal bandwidth allocation by maximizing efficiency subject to ( α , β ) -fairness constraints. This leads to what we call an efficiency–fairness function, which shows the benefit in efficiency as a function of the extent to which fairness is compromised. To solve the NLP we use two algorithms. The first is a well-known branch-and-bound-based algorithm called Lipschitz Global Optimization and the second is a recently developed algorithm called Algorithm for Global Optimization Problems (AGOP). We demonstrate the applicability of the framework to a range of examples from sharing a single link to efficiency fairness issues associated with serving customers in remote communities.

Parallel Computing in Optimization.

Parallel Computing in Optimization.