Numerical Function Optimization Problems Research Articles

Towards a Decision Support System for Optimizing the Location of Warehouses in a Supply Chain by Using the Bee Colony Algorithm

One of the goals that a company sets is the customer's satisfaction, which is a priority item. This clearly shows that the concerns of companies are focused on the customer and how this later could be served quickly. This work addresses the problem of optimization of the location of the distribution centers of a final product to customers, in a given region. The problem addressed in this paper is the location of the position (emplacement) to build a new distribution center (warehouses), taking into account the constraint of the distance between a distribution center and the various points of sale, and the constraint of the cost of land to build a distribution center. The optimization method used for this problem is the artificial bee colony algorithm (ABC), which was initially applied to numerical function optimization problems, inspired from the behavioral model bees during foraging.

An improved differential harmony search algorithm for function optimization problems

To overcome the drawbacks of the harmony search (HS) algorithm and further enhance its effectiveness and efficiency, an improved differential HS (IDHS) is proposed to solve numerical function optimization problems. The proposed IDHS has a novel improvisation scheme that integrates DE/best/1/bin and DE/rand/1/bin from the differential evolution (DE) algorithm to enhance its local search and exploration capabilities and a new pitch adjustment rule that benefits from the best solution in the harmony memory to increase its convergence speed. With dynamically adjusted parameters, the proposed IDHS can balance exploitation and exploration throughout the search process. The numerical results of an experiment with classic testing functions and those of a comparative experiment show that IDHS outperforms eight algorithms in the HS family and three widely used population-based algorithms in different families, including DE, particle swarm optimization, and improved fruit fly optimization algorithm. IDHS demonstrates fast convergence and an especially good capability to handle difficult high-dimensional optimization problems.

A new metaheuristic algorithm: car tracking optimization algorithm

Over the last decade, several metaheuristic algorithms have emerged to solve numerical function optimization problems. Since the performance of these algorithms presents a suboptimal behavior, a large number of studies have been carried out to find new and better algorithms. Therefore, this paper proposes a new metaheuristic algorithm, namely the car tracking optimization algorithm; it is inspired by observing the programming methods of other metaheuristic algorithms. And the proposed algorithm has been tested over 55 benchmark functions, and the results have been compared with firefly algorithm (FA), cuckoo searching algorithm (CS), and vortex search algorithm (VS). The results indicate that the performance of the proposed algorithm surpasses FA, CS, and VS algorithm.

An improved krill herd algorithm with global exploration capability for solving numerical function optimization problems and its application to data clustering

Krill herd algorithm is a stochastic nature-inspired algorithm for solving optimization problems. The performance of krill herd algorithm is degraded by poor exploitation capability. In this study, we propose an improved krill herd algorithm (IKH) by making the krill the global search capability. The enhancement comprises of adding global search operator for exploration around the defined search region and thus the krill individuals move towards the global best solution. The elitism strategy is also applied to maintain the best krill during the krill update steps. The proposed method is tested on a set of twenty six well-known benchmark functions and is compared with thirteen popular optimization algorithms, including original KH algorithm. The experimental results show that the proposed method produced very accurate results than KH and other compared algorithms and is more robust. In addition, the proposed method has high convergence rate. The high performance of the proposed algorithm is then employed for data clustering problems and is tested using six real datasets available from UCI machine learning laboratory. The experimental results thus show that the proposed algorithm is well suited for solving even data clustering problems.

Enhanced shuffled frog-leaping algorithm for solving numerical function optimization problems

The shuffled frog-leaping algorithm (SFLA) is a relatively new meta-heuristic optimization algorithm that can be applied to a wide range of problems. After analyzing the weakness of traditional SFLA, this paper presents an enhanced shuffled frog-leaping algorithm (MS-SFLA) for solving numerical function optimization problems. As the first extension, a new population initialization scheme based on chaotic opposition-based learning is employed to speed up the global convergence. In addition, to maintain efficiently the balance between exploration and exploitation, an adaptive nonlinear inertia weight is introduced into the SFLA algorithm. Further, a perturbation operator strategy based on Gaussian mutation is designed for local evolutionary, so as to help the best frog to jump out of any possible local optima and/or to refine its accuracy. In order to illustrate the efficiency of the proposed method (MS-SFLA), 23 well-known numerical function optimization problems and 25 benchmark functions of CEC2005 are selected as testing functions. The experimental results show that the enhanced SFLA has a faster convergence speed and better search ability than other relevant methods for almost all functions.

Global Particle Swarm Optimization for High Dimension Numerical Functions Analysis

The Particle Swarm Optimization (PSO) Algorithm is a popular optimization method that is widely used in various applications, due to its simplicity and capability in obtaining optimal results. However, ordinary PSOs may be trapped in the local optimal point, especially in high dimensional problems. To overcome this problem, an efficient Global Particle Swarm Optimization (GPSO) algorithm is proposed in this paper, based on a new updated strategy of the particle position. This is done through sharing information of particle position between the dimensions (variables) at any iteration. The strategy can enhance the exploration capability of the GPSO algorithm to determine the optimum global solution and avoid traps at the local optimum. The proposed GPSO algorithm is validated on a 12-benchmark mathematical function and compared with three different types of PSO techniques. The performance of this algorithm is measured based on the solutions’ quality, convergence characteristics, and their robustness after 50 trials. The simulation results showed that the new updated strategy in GPSO assists in realizing a better optimum solution with the smallest standard deviation value compared to other techniques. It can be concluded that the proposed GPSO method is a superior technique for solving high dimensional numerical function optimization problems.

Improved artificial bee colony algorithm with mutual learning

The recently invented artificial bee colony (ABC) algorithm is an optimization algorithm based on swarm intelligence that has been used to solve many kinds of numerical function optimization problems. It performs well in most cases, however, there still exists an insufficiency in the ABC algorithm that ignores the fitness of related pairs of individuals in the mechanism of finding a neighboring food source. This paper presents an improved ABC algorithm with mutual learning (MutualABC) that adjusts the produced candidate food source with the higher fitness between two individuals selected by a mutual learning factor. The performance of the improved MutualABC algorithm is tested on a set of benchmark functions and compared with the basic ABC algorithm and some classical versions of improved ABC algorithms. The experimental results show that the MutualABC algorithm with appropriate parameters outperforms other ABC algorithms in most experiments.

A hybrid algorithm for optimizing multi-modal functions

A new genetic algorithm is presented based on the musical performance. The novelty of this algorithm is that a new genetic algorithm, mimicking the musical process of searching for a perfect state of harmony, which increases the robustness of it greatly and gives a new meaning of it in the meantime, has been developed. Combining the advantages of the new genetic algorithm, simplex algorithm and tabu search, a hybrid algorithm is proposed. In order to verify the effectiveness of the hybrid algorithm, it is applied to solving some typical numerical function optimization problems which are poorly solved by traditional genetic algorithms. The experimental results show that the hybrid algorithm is fast and reliable.

유전자 알고리즘의 성능향상을 위한 비례-적분-미분 평가방법

본 논문에서는 유전자 알고리즘의 성능향상을 위한 비례-적분-미분 평가방법을 제안한다. 비례-적분-미분 평가방법에서는 평가함수에 의하여 계산된 적합도와 더불어 각 개체의 부모 적합도, 초기세대로부터 이전세대까지의 최소, 최대 적합도를 이용하여 평가함으로서 유전자 알고리즘의 성능저하를 가져오는 조숙수렴 (premature convergence) 확률을 줄여주어 결과적으로 유전자 알고리즘의 성능을 향상시키게 된다. 비례-적분-미분 평가방법의 성능을 보이기 위하여 유전자 알고리즘 성능 검증에 많이 사용되어온 대표적인 함수 최적화 문제들을 적용하여 실험해본 결과 제안한 방법이 유전자 알고리즘의 성능을 크게 향상 시킬 수 있음을 확인하였다. 제안한 평가방법은 다른 형태의 유전자 알고리즘의 성능향상을 위해서도 쉽게 적용될수 있다. This paper proposes a proportional-integral-derivative (PID) evaluation method for enhancing performance of genetic algorithms. In PID evaluation, the fitness of individuals is evaluated by not only the fitness derived from an evaluation function, but also the parents fitness of each individual and the minimum and maximum fitness from initial generation to previous generation. This evaluation decreases the probability that the genetic algorithms fall into a premature convergence phenomenon and results in enhancing the performance of genetic algorithms. We experimented our evaluation method with typical numerical function optimization problems. It was found from extensive experiments that out evaluation method can increase the performance of genetic algorithms greatly. This evaluation method can be easily applied to the other types of genetic algorithms for improving their performance.