Test functions are important to validate and compare the performance of optimization algorithms. There have been many test or benchmark functions reported in the literature; however, there is no standard list or set of benchmark functions. Ideally, test functions should have diverse properties so that can be truly useful to test new algorithms in an unbiased way. For this purpose, we have reviewed and compiled a rich set of 175 benchmark functions for unconstrained optimization problems with diverse properties in terms of modality, separability, and valley landscape. This is by far the most complete set of functions so far in the literature, and tt can be expected this complete set of functions can be used for validation of new optimization in the future.

Problems demanding globally optimal solutions are ubiquitous, yet many are intractable when they involve constrained functions having many local optima and interacting, mixed-type variables.The differential evolution (DE) algorithm is a practical approach to global numerical optimization which is easy to understand, simple to implement, reliable, and fast. Packed with illustrations, computer code, new insights, and practical advice, this volume explores DE in both principle and practice. It is a...

List of figures. List of tables. Preface. Part One: Global optimization: a brief review. 1.1. General problem statement and special model forms. 1.2. Solution approaches. Part Two: Partition strategies in global optimization: the continuous and the Lipschitzian case. 2.1. An introduction to partition algorithms. 2.2. Convergence properties of adaptive partition algorithms. 2.3. Partition algorithms on intervals. 2.4. Partition algorithms on multidimensional intervals. 2.5. Simplex partition stra...

Test functions are important to validate new optimization algorithms and to compare the performance of various algorithms. There are many test functions in the literature, but there is no standard list or set of test functions one has to follow. New optimization algorithms should be tested using at least a subset of functions with diverse properties so as to make sure whether or not the tested algorithm can solve certain type of optimization efficiently. Here we provide a selected list of test p...

The Repulsive Particle Swarm (RPS) method of global optimization is perhaps the simplest to understand and implement. Due to its simplicity, it can be easily modified to suit the purpose and therefore, it has better prospects as well. The method has been frequently used in the field of artificial intelligence. It is well founded on philosophical and methodological grounds (bounded rationality and efficacy of decentralized decision-making to reach the global best) also. The method of RPS has been...

#1Xin-She Yang(University of Cambridge)H-Index: 87

Modern optimisation algorithms are often metaheuristic, and they are very promising in solving NP-hard optimisation problems. In this paper, we show how to use the recently developed firefly algorithm to solve non-linear design problems. For the standard pressure vessel design optimisation, the optimal solution found by FA is far better than the best solution obtained previously in the literature. In addition, we also propose a few new test functions with either singularity or stochastic compone...

In the past decades, different kinds of metaheuristic optimization algorithms [1, 2] have been developed; Simulated Annealing (SA) [3, 4], Evolutionary Algorithms (EAs) [5–7], Differential Evolution (DE) [8, 9], Particle Swarm Optimization (PSO) [10, 11], Ant Colony Optimization (ACO) [12, 13], and Estimation of Distribution Algorithms (EDAs) [14, 15] are just a few of them. These algorithms have shown excellent search abilities but often lose their efficacy when applied to large and complex pro...

This study proposes a new PSOS-model based damage identification procedure using frequency domain data. The formulation of the objective function for the minimization problem is based on the Frequency Response Functions (FRFs) of the system. A novel strategy for the control of the Particle Swarm Optimization (PSO) parameters based on the Nelder-Mead algorithm (Simplex method) is presented; consequently, the convergence of the PSOS becomes independent of the heuristic constants and its stability ...

A collection of unconstrained optimization test functions is presented. The purpose of this collection is to give to the optimization community a large number of general test functions to be used in testing the unconstrained optimization algorithms and comparisons studies. For each function we give its algebraic expression and the standard initial point. Some of the test fnctions are from the CUTE collection established by Bongartz, Conn, Gould and Toint, (1995), others are from More, Garbow and...

Abstract null null An algorithm whose performance depends on the objective function being aligned with a privileged coordinate system is a poor choice in general because it is unlikely that the optimal orientation will be known in advance. In this paper, a property of meta-heuristic algorithms, named affine invariance, is introduced to verify whether the algorithm is depended on the privileged coordinate system or not. The concept of affine invariance is described in detail, and some classical a...

#1Jorge M. Cruz-Duarte(Tec: Monterrey Institute of Technology and Higher Education)H-Index: 3

#2Ivan Amaya(Tec: Monterrey Institute of Technology and Higher Education)H-Index: 1

Last. Yong Shi(CAS: Chinese Academy of Sciences)H-Index: 55

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Abstract null null Literature is prolific with metaheuristics for solving continuous optimisation problems. But, in practice, it is difficult to choose one appropriately for several reasons. First and foremost, ‘new’ metaheuristics are being proposed at an alarmingly fast rate, rendering impossible to know them all. Moreover, it is necessary to determine a good enough set of parameters for the selected approach. Hence, this work proposes a strategy based on a hyper-heuristic model powered by Sim...

Abstract null null null This paper introduces a new null evolutionary algorithm null with the support of an actual quantum processor, a computing device which uses phenomena from quantum mechanics to enable a considerable speed-up in computation. In particular, the proposed approach uses null null quantum superposition null null null and null entanglement null to implement quantum evolutionary concepts such as quantum chromosome, entangled crossover, rotation mutation, and quantum elitism, to ef...

Last. Jong Wan Hu(Incheon National University)H-Index: 17

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Abstract null null Process optimization using metaheuristic algorithms is rapidly gaining interest from engineering practitioners and researchers. This study uses the cuckoo search algorithm (CSA) to find the optimum parameters of a novel smart damper under seismic excitations. For this purpose, seismic responses of four-story and nine-story building configurations under seven pairs of ground motions have been considered. The smart damper is a shear polyurethane friction (SPF) passive control de...

Last. A. E. Eiben(VU: VU University Amsterdam)H-Index: 56

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Abstract The challenge of robotic reproduction {making of new robots by recombiningtwo existing ones{ has been recently cracked and physically evolving robot systems have come within reach. Here we address the next big hurdle: producing an adequate brain for a newborn robot. In particular, we address the task of targeted locomotion which is arguably a fundamental skill in any practical implementation. We introduce a controller architecture and a generic learning method to allow a modular robot w...

Parameter selection during the construction of surrogates is often conducted by minimizing the Mean Squared Cross-Validation Error (MSE-CV). Surrogates constructed using MSE are poorly optimized us...

#1Dhrubajyoti Gupta(NIT DGP: National Institute of Technology, Durgapur)H-Index: 2

#2Ananda Rabi Dhar(NIT DGP: National Institute of Technology, Durgapur)

Last. Shibendu Shekhar Roy(NIT DGP: National Institute of Technology, Durgapur)H-Index: 13

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Firefly algorithm is one of the most promising population-based meta-heuristic algorithms. It has been successfully applied in many optimization problems. Several modifications have been proposed to the original algorithm to boost the performance in terms of accuracy and speed of convergence. This work proposes a partition cum unification based genetic firefly algorithm to explore the benefits of both the algorithms in a novel way. With this, the initial population is partitioned into two compar...

Last. Wei-Feng Tao(NPU: Northwestern Polytechnical University)

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Abstract A new dimension-reduction method (DRM), called’subset active subspace method (SASM)’, is proposed to compute small failure probabilities encountered in high-dimensional reliability analysis of engineering systems. The basic idea is to introduce a recursive procedure to improve the efficiency, accuracy and applicability of the conventional active subspace method (ASM). For the reliability problems with a rare event, SASM firstly transfers the original high-dimensional reliability problem...

Abstract The sine cosine algorithm (SCA) is a recently proposed swarm intelligence optimization based on sine and cosine mathematical functions. It has a novel principle to process global optimization, but when solving large-scale global optimization problems, the performance of this algorithm is greatly reduced. To tackle this problem, a dynamic sine cosine algorithm (DSCA) is proposed. DSCA includes a nonlinear random convergence parameter to update equation, dynamically balancing the explorat...