Global Numerical Optimization Research Articles

Covariance and crossover matrix guided differential evolution for global numerical optimization.

Differential evolution (DE) is an efficient and robust evolutionary algorithm and has wide application in various science and engineering fields. DE is sensitive to the selection of mutation and crossover strategies and their associated control parameters. However, the structure and implementation of DEs are becoming more complex because of the diverse mutation and crossover strategies that use distinct parameter settings during the different stages of the evolution. A novel strategy is used in this study to improve the crossover and mutation operations. The crossover matrix, instead of a crossover operator and its control parameter CR, is proposed to implement the function of the crossover operation. Meanwhile, Gaussian distribution centers the best individuals found in each generation based on the proposed covariance matrix, which is generated between the best individual and several better individuals. Improved mutation operator based on the crossover matrix is randomly selected to generate the trial population. This operator is used to generate high-quality solutions to improve the capability of exploitation and enhance the preference of exploration. In addition, the memory population is randomly chosen from previous generation and used to control the search direction in the novel mutation strategy. Accordingly, the diversity of the population is improved. Thus, CCDE, which is a novel efficient and simple DE variant, is presented in this paper. CCDE has been tested on 30 benchmarks and 5 real-world optimization problems from the IEEE Congress on Evolutionary Computation (CEC) 2014 and CEC 2011, respectively. Experimental and statistical results demonstrate the effectiveness of CCDE for global numerical and engineering optimization. CCDE can solve the test benchmark functions and engineering problems more successfully than the other DE variants and algorithms from CEC 2014.

Fuzzy adaptive teaching–learning-based optimization for global numerical optimization

Teaching–learning-based optimization (TLBO) is one of the latest metaheuristic algorithms being used to solve global optimization problems over continuous search space. Researchers have proposed few variants of TLBO to improve the performance of the basic TLBO algorithm. This paper presents a new variant of TLBO called fuzzy adaptive teaching–learning-based optimization (FATLBO) for numerical global optimization. We propose three new modifications to the basic scheme of TLBO in order to improve its searching capability. These modifications consist, namely of a status monitor, fuzzy adaptive teaching–learning strategies, and a remedial operator. The performance of FATLBO is investigated on four experimental sets comprising complex benchmark functions in various dimensions and compared with well-known optimization methods. Based on the results, we conclude that FATLBO is able to deliver excellence and competitive performance for global optimization.

RETRACTED ARTICLE: An innovative natural-derived meta-heuristic optimization method

Nowadays, wide-ranging meta-heuristic optimization methods have grown in popularity because of varied natural events. They have mostly considered biological systems like colonials’ behavior. A novel meta-heuristic optimization method, called synthetic raindrop algorithm (SRA), is presented for global numerical optimization in this study. As it comes from its name, it derives from the natural phenomenon of rainfall. This algorithm utilizes five operators to depict the changing process of a raindrop, including raindrop generation, raindrop descent, raindrop collision, raindrop flowing and raindrop updating. Numerical experiments are performed on all the CEC2005 contest benchmark functions to evaluate this algorithm performance. The achieved results indicate that SRA is competitive with eight other avant-grade original intelligent optimization algorithms and their developed ones.

Chemical reaction optimization for solving shortest common supersequence problem

Shortest common supersequence (SCS) is a classical NP-hard problem, where a string to be constructed that is the supersequence of a given string set. The SCS problem has an enormous application of data compression, query optimization in the database and different bioinformatics activities. Due to NP-hardness, the exact algorithms fail to compute SCS for larger instances. Many heuristics and meta-heuristics approaches were proposed to solve this problem. In this paper, we propose a meta-heuristics approach based on chemical reaction optimization, CRO_SCS that is designed inspired by the nature of the chemical reactions. For different optimization problems like 0-1 knapsack, quadratic assignment, global numeric optimization problems CRO algorithm shows very good performance. We have redesigned the reaction operators and a new reform function to solve the SCS problem. The outcomes of the proposed CRO_SCS algorithm are compared with those of the enhanced beam search (IBS_SCS), deposition and reduction (DR), ant colony optimization (ACO) and artificial bee colony (ABC) algorithms. The length of supersequence, execution time and standard deviation of all related algorithms show that CRO_SCS gives better results on the average than all other algorithms.

Optimal-Behavior-Based Dynamic Calibration of the Automotive Diesel Engine

This paper presents a novel automotive engine management system (EMS) calibration methodology for rapid dynamometer test-bed data collection and mapping I.C. engine controllers with significant dynamic and transient performance requirements. This paper applies the methodology to an industrial state of the art WAVE-RT 1 model of a 1.5 L Turbo EU6.1 Diesel engine acting as a virtual dynamometer based engine. The approach directly yields a feedforward controller in a nonlinear polynomial structure that can be either directly implemented in the EMS or converted into a dynamic or static lookup table format. The methodology is based on multistage black-box modeling and dynamic system optimization. The process can exploit the power of global constrained numerical optimization codes and use system identification techniques with dynamic design of experiments. The objective of the engine controller optimization is to improve the fuel economy while maintaining specified (legislated) limits on emissions and map smoothness for driveability. The key contribution is a novel approach to obtaining a feedforward dynamic calibration controller from the system identification of the computed optimal behavior. Model structure selection techniques are shown to be usefully employed to further improve the accuracy of the system identification and so enhance the control performance of the dynamic controllers. The results indicate that the dynamic calibration methodology leads to a considerably reduced requirement for testing time and an improvement of between 1.9% and 2.6% in fuel economy over extra urban driving cycle without violating the emission constraints compared with current steady-state model-based calibration methods. 1 Ricardo PLC.

Adaptive backtracking search optimization algorithm with pattern search for numerical optimization

The backtracking search optimization algorithm (BSA) is one of the most recently proposed population-based evolutionary algorithms for global optimization. Due to its memory ability and simple structure, BSA has powerful capability to find global optimal solutions. However, the algorithm is still insufficient in balancing the exploration and the exploitation. Therefore, an improved adaptive backtracking search optimization algorithm combined with modified Hooke-Jeeves pattern search is proposed for numerical global optimization. It has two main parts: the BSA is used for the exploration phase and the modified pattern search method completes the exploitation phase. In particular, a simple but effective strategy of adapting one of BSA's important control parameters is introduced. The proposed algorithm is compared with standard BSA, three state-of-the-art evolutionary algorithms and three superior algorithms in IEEE Congress on Evolutionary Computation 2014 (IEEE CEC2014) over six widely-used benchmarks and 22 real-parameter single objective numerical optimization benchmarks in IEEE CEC2014. The results of experiment and statistical analysis demonstrate the effectiveness and efficiency of the proposed algorithm.

A Multi-Stage Krill Herd Algorithm for Global Numerical Optimization

A multi-stage krill herd (MSKH) algorithm is presented to fully exploit the global and local search abilities of the standard krill herd (KH) optimization method. The proposed method involves exploration and exploitation stages. The exploration stage uses the basic KH algorithm to select a good candidate solution set. This phase is followed by fine-tuning a good candidate solution in the exploitation stage with a focused local mutation and crossover (LMC) operator in order to enhance the reliability of the method for solving global numerical optimization problems. Moreover, the elitism scheme is introduced into the MSKH method to guarantee the best solution. The performance of MSKH is verified using twenty-five standard and rotated and shifted benchmark problems. The results show the superiority of the proposed algorithm to the standard KH and other well-known optimization methods.

Differential evolution with guiding archive for global numerical optimization

Differential evolution (DE) is a simple, yet efficient, population-based global evolutionary algorithm. DE may suffer from stagnation. This study presents a DE framework with guiding archive (GAR-DE) to help DE escape from the situation of stagnation. The proposed framework constructs a guiding archive and executes stagnation detection at each iteration. Guiding archive is composed of a certain number of relatively high-quality solutions. These solutions are collected in terms of fitness as well as diversity. If a stagnated individual is detected, the proposed framework selects a solution from guiding archive to replace the base vector in mutation operator. In this way, more promising solutions are provided to guide the evolution and effectively help DE escape from the situation of stagnation. The proposed framework is applied to six original DE algorithms, as well as two advanced DE variants. Experimental results on 28 benchmark functions and 8 real-world application problems show that the proposed framework can enhance the performance of most DE algorithms studied.

Chaotic Teaching-Learning-Based Optimization with Lévy Flight for Global Numerical Optimization.

Recently, teaching-learning-based optimization (TLBO), as one of the emerging nature-inspired heuristic algorithms, has attracted increasing attention. In order to enhance its convergence rate and prevent it from getting stuck in local optima, a novel metaheuristic has been developed in this paper, where particular characteristics of the chaos mechanism and Lévy flight are introduced to the basic framework of TLBO. The new algorithm is tested on several large-scale nonlinear benchmark functions with different characteristics and compared with other methods. Experimental results show that the proposed algorithm outperforms other algorithms and achieves a satisfactory improvement over TLBO.

A novel animal migration algorithm for global numerical optimization

Animal migration optimization (AMO) searches optimization solutions by migration process and updating process. In this paper, a novel migration process has been proposed to improve the exploration and exploitation ability of the animal migration optimization. Twenty-three typical benchmark test functions are applied to verify the effects of these improvements. The results show that the improved algorithm has faster convergence speed and higher convergence precision than the original animal migration optimization and other some intelligent optimization algorithms such as particle swarm optimization (PSO), cuckoo search (CS), firefly algorithm (FA), bat-inspired algorithm (BA) and artificial bee colony (ABC).

Modeling and Optimizing Tensile Strength and Yield Point on a Steel Bar Using an Artificial Neural Network With Taguchi Particle Swarm Optimizer

A Taguchi particle swarm optimization (TPSO) with a three-layer feedforward artificial neural network (ANN) is used to model and optimize the chemical composition of a steel bar. The novel contribution of a TPSO is the use of a Taguchi method mechanism to exploit better solutions in the search space through iterations, the use of the conventional non-linear PSO to increase convergence speed, and the use of random movement for particle diversity. The exploration and exploitation capability of the TPSO were confirmed by performance comparisons with other PSO-based algorithms in solving high-dimensional global numerical optimization problems. Experiments in this paper showed that the TPSO provides higher computational efficiency and higher robustness when solving problems involving seven non-linear benchmark functions, including three unimodal functions, one multimodal functions, two rotated functions, and one shifted functions. The results for the computational experiments show that the TPSO outperforms other PSO-based algorithms reported in the literature. Finally, the results obtained by a TPSO-based ANN model of the chemical composition of the steel bar were consistent with the actual data. That is, the proposed TPSO with three-layer feedforward ANN can be used in practical applications.

A novel hybrid Cultural Algorithms framework with trajectory-based search for global numerical optimization

In recent years, Cultural Algorithms (CAs) have attracted substantial research interest. When applied to highly multimodal and high dimensional problems, Cultural Algorithms suffer from fast convergence followed by stagnation. This research proposes a novel hybridization between Cultural Algorithms and a modified multiple trajectory search (MTS). In this hybridization, a modified version of Cultural Algorithms is applied to generate solutions using three knowledge sources namely situational knowledge, normative knowledge, and topographic knowledge. From these solutions, several are selected to be used by the modified multi-trajectory search. All solutions generated by both component algorithms are used to update the three knowledge sources in the belief space of Cultural Algorithms. In addition, an adaptive quality function is used to control the number of function evaluations assigned to each component algorithm according to their success rates in the recent past iterations. The function evaluations assigned to Cultural Algorithms are also divided among the three knowledge sources according to their success rates in recent generations of the search. Moreover, the quality function is used to tune the number of offspring these component algorithms are allowed to contribute during the search. The proposed hybridization between Cultural Algorithms and the modified trajectory-based search is employed to solve a test suite of 25 large-scale benchmark functions. The paper also investigates the application of the new algorithm to a set of real-life problems. Comparative studies show that the proposed algorithm can have superior performance on more complex higher dimensional multimodal optimization problems when compared with several other hybrid and single population optimizers.

Teaching-learning-based optimization with a fuzzy grouping learning strategy for global numerical optimization

The Teaching-Learning-Based Optimization (TLBO) algorithm is a novel heuristic method that is inspired by the philosophy of teaching and learning in a class. In the Teacher Phase of the original TLBO algorithm, all learners are combined in one group and learn only from the teacher, which quickly leads to declining population diversity. Utilizing fuzzy K-means clustering to objectively divide all learners into smaller-sized groups more closely conforms to the modern idea of intra-class grouping for teaching and learning. Furthermore, fuzzy K-means clustering can objectively divide learners as nearly as possible according to their interests and abilities, which helps each learner to grow to his or her fullest extent. This paper presents a novel version of TLBO, TLBO with a Fuzzy Grouping Learning Strategy (FGTLBO), in which fuzzy K-means clustering is used to create K centers, each of which acts as the mean of its corresponding group. Performance and accuracy of the FGTLBO algorithm are examined on CEC2005 standard benchmark functions, and these results are compared with various other versions of TLBO. The experimental results verify that the FGTLBO algorithm is very competitive in terms of solution quality and convergence rate.

Aerodynamic Shape Optimization via Global Extremum Seeking

Optimization of aerodynamic shapes using computational fluid dynamics (CFD) approaches has been successfully demonstrated over a number of years; however, the typical optimization approaches employed utilize gradient algorithms that guarantee only the local optimality of the solution. While numerous global optimization techniques exist, they are usually too time consuming in practice. In this brief, a modified global optimization algorithm (DIRECT-L) is introduced and is utilized in the context of sampled-data global extremum seeking. The theoretical framework and conditions under which the convergence to the steady state of the CFD solver can be interpreted as plant dynamics are stated. This method alleviates the computational burden by reducing sampling and requiring only partial convergence of the CFD solver for each iteration of the optimization design process. The approach is demonstrated on a simple example involving drag minimization on a 2-D aerofoil.

The performance comparison of a new version of artificial raindrop algorithm on global numerical optimization

Very recently, a new metaheuristic called artificial raindrop algorithm (ARA) was proposed. This search algorithm inspired from the phenomenon of natural rainfall, including the generation of raindrop, the descent of raindrop, the collision of raindrop, the flowing of raindrop and the updating of vapor. However, the original ARA only focused on the changing process of a raindrop. In this paper, we present an extension of ARA (ARAE) to more raindrops without any major conceptual change to its structure. In the proposed ARAE, all vapors are dynamically divided into several small-sized groups according to the relative distance of vapors in each generation. Each vapor has an associated weight proportion to the fitness value. The raindrop in the corresponding group is then generated based on weighted mean of the current vapors positions. But beyond that, some operators of ARA are further modified to enhance its exploration/exploitation capabilities. In order to thoroughly evaluate the performance of ARAE, a comprehensive comparative study has been carried on the CEC2005 contest benchmark functions. The obtained results indicate that ARAE has overall better performance than ARA, and is very competitive with respect to other twenty-four state-of-the-art original intelligent optimization algorithms and twenty-four improved metaheuristic algorithms. Finally, the proposed ARAE is also applied to artificial neural networks and the promising results on the nonlinear function approximation show the applicability of ARAE for problem solving.

Adaptive differential evolution algorithm with novel mutation strategies in multiple sub-populations

Differential evolution (DE) algorithm has been shown to be a very effective and efficient approach for solving global numerical optimization problems, which attracts a great attention of scientific researchers. Generally, most of DE algorithms only evolve one population by using certain kind of DE operators. However, as observed in nature, the working efficiency can be improved by using the concept of work specialization, in which the entire group should be divided into several sub-groups that are responsible for different tasks according to their capabilities. Inspired by this phenomenon, a novel adaptive multiple sub-populations based DE algorithm is designed in this paper, named MPADE, in which the parent population is split into three sub-populations based on the fitness values and then three novel DE strategies are respectively performed to take on the responsibility for either exploitation or exploration. Furthermore, a simple yet effective adaptive approach is designed for parameter adjustment in the three DE strategies and a replacement strategy is put forward to fully exploit the useful information from the trial vectors and target vectors, which enhance the optimization performance. In order to validate the effectiveness of MPADE, it is tested on 55 benchmark functions and 15 real world problems. When compared with other DE variants, MPADE performs better in most of benchmark problems and real-world problems. Moreover, the impacts of the MPADE components and their parameter sensitivity are also analyzed experimentally.

P-MEMPSODE: Parallel and irregular memetic global optimization

A parallel memetic global optimization algorithm suitable for shared memory multicore systems is proposed and analyzed. The considered algorithm combines two well-known and widely used population-based stochastic algorithms, namely Particle Swarm Optimization and Differential Evolution, with two efficient and parallelizable local search procedures. The sequential version of the algorithm was first introduced as MEMPSODE (MEMetic Particle Swarm Optimization and Differential Evolution) and published in the CPC program library. We exploit the inherent and highly irregular parallelism of the memetic global optimization algorithm by means of a dynamic and multilevel approach based on the OpenMP tasking model. In our case, tasks correspond to local optimization procedures or simple function evaluations. Parallelization occurs at each iteration step of the memetic algorithm without affecting its searching efficiency. The proposed implementation, for the same random seed, reaches the same solution irrespectively of being executed sequentially or in parallel. Extensive experimental evaluation has been performed in order to illustrate the speedup achieved on a shared-memory multicore server. Program summaryProgram title: p-MEMPSODECatalogue identifier: AEXJ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEXJ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 9950No. of bytes in distributed program, including test data, etc.: 141503Distribution format: tar.gzProgramming language: ANSI C.Computer: Workstation.Operating system: Developed under the Linux operating system using the GNU compilers v.4.4.3 (or higher). Uses the OpenMP API and runtime system.RAM: The code uses O(n×N) internal storage, n being the dimension of the problem and N the maximum population size. The required memory is dynamically allocated.Word size: 64Classification: 4.9.Nature of problem: Numerical global optimization of real valued functions is an indispensable methodology for solving a multitude of problems in science and engineering. Many problems exhibit a number of local and/or global minimizers, expensive function evaluations or require real-time response. In addition, discontinuities of the objective function, non-smooth and deceitful landscapes constitute challenging obstacles for most optimization algorithms.Solution method: We implement a memetic global optimization algorithm that combines stochastic, population-based methods with deterministic local search procedures. More specifically, the Unified Particle Swarm Optimization and the Differential Evolution algorithms are harnessed with the derivative-free Torczon’s Multi-Directional Search and the gradient-based BFGS method. The produced hybrid algorithms possess inherent parallelism that is exploited efficiently by means of the OpenMP tasking model. Given the same random seed, the proposed implementation reaches the same solution irrespective of being executed sequentially or in parallel.Restrictions: The current version of the software uses only double precision arithmetic. An OpenMP-enabled (version 3.0 or higher) compiler is required.Unusual features: The software requires bound constraints on the optimization variables.Running time: The running time depends on the complexity of the objective function (and its derivatives if used) as well as on the number of available cores. Extensive experimental results demonstrate that the speedup closely approximates ideal values.

An improved differential evolution algorithm with triangular mutation for global numerical optimization

This paper presents an Improved Differential Evolution (IDE) algorithm for solving global numerical optimization problems over continuous space. The proposed algorithm introduces a new triangular mutation rule based on the convex combination vector of the triplet defined by the three randomly chosen vectors and the difference vector between the best and the worst individuals among the three randomly selected vectors. The mutation rule is combined with the basic mutation strategy through a non-linear decreasing probability rule. Furthermore, a restart mechanism is also proposed to avoid premature convergence. IDE is tested on a well-known set of unconstrained problems and shows its superiority to state-of-the-art differential evolution variants.

A hybrid bird mating optimizer algorithm with teaching-learning-based optimization for global numerical optimization

Bird Mating Optimizer (BMO) is a novel meta-heuristic optimization algorithm inspired by intelligent mating behavior of birds. However, it is still insufficient in convergence of speed and quality of solution. To overcome these drawbacks, this paper proposes a hybrid algorithm (TLBMO), which is established by combining the advantages of Teaching-learning-based optimization (TLBO) and Bird Mating Optimizer (BMO). The performance of TLBMO is evaluated on 23 benchmark functions, and compared with seven state-of-the-art approaches, namely BMO, TLBO, Artificial Bee Bolony (ABC), Particle Swarm Optimization (PSO), Fast Evolution Programming (FEP), Differential Evolution (DE), Group Search Optimization (GSO). Experimental results indicate that the proposed method performs better than other existing algorithms for global numerical optimization.

A hybrid bird mating optimizer algorithm with teaching-learning-based optimization for global numerical optimization

A hybrid bird mating optimizer algorithm with teaching-learning-based optimization for global numerical optimization