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About 7,410 papers for “Test functions for optimization”

On test functions for evolutionary multi-objective optimization

Tatsuya Okabe, Yaochu Jin, Markus Olhofer et al. · Surrey Research Insight Open Access (The University of Surrey) · 2004

In order to evaluate the relative performance of optimization algorithms benchmark problems are frequently used. In the case of multi-objective optimization (MOO), we will show in this paper that most known benchmark problems belong to a constrained class of functions with piecewise linear Pareto fronts in the parameter space. We present a straightforward way to define benchmark problems with an arbitrary Pareto front both in the fitness and parameter spaces. Furthermore, we introduce a difficulty measure based on the mapping of probability density functions from parameter to fitness space. Finally, we evaluate two MOO algorithms for new benchmark problems. © Springer-Verlag 2004.

Cited by 0

Composite Test Functions for Benchmarking Nonlinear Optimization Software

János D. Pintér · Mathematics · 2025

Nonlinear optimization (NLO) is widely applicable to model and solve decision problems arising in engineering, economic, financial, and scientific studies. Due to the general scope of NLO, optimization model difficulty varies substantially, requiring the utilization of robust, efficient, and flexible solver software. In order to develop constructive guidelines regarding suitable software choices, broad, representative, and reproducible classes of test problems are needed. In this article, we propose flexible and expandable classes of composite test functions, based on earlier introduced or brand-new test problems with known solutions. In our illustrative tests, we use the high-level computing system Mathematica as a model development platform, with some of its readily available NLO solver options. The suggested general approach can be easily adapted to develop benchmarking studies using other modeling environments, test model collections, and solver options.

Cited by 0Open access

Novel composition test functions algorithm for numerical optimization

Peng Fu-ming · 2011

Since coming out, novel composition test functions have received wide attention from evolutionary computation researchers and have now become the target functions for numerical optimization algorithms. However, its numerical optimization can be transformed into numerical optimization of one-dimensional functions, which significantly reduces optimization level of difficulty. A novel composition test functions algorithm for numerical optimization is proposed, which quotes a muti-population coevolutionary algorithm for numerical optimization and uses it to optimize the one-dimensional functions. The experiments proved the algorithm for numerical optimization of novel composition test functions converges to the global optimal solutions.

Cited by 2

Runge Kutta Optimization for Fixed Size Multimodal Test Functions

Fatih CANTAŞ, Serdar Özyön, Celal Yaşar · International Scientific and Vocational Studies Journal · 2022

In this study, it is aimed to increase the success of the Runge Kutta (RUN) algorithm, which is used in the solution of many optimization problems in the literature, on fixed-size test functions by changing the parameter values. Optimization can be defined as making a system most efficient at the least possible cost under certain constraints. For this process, many optimization algorithms have been designed in the literature and used to obtain the best solutions for certain problems. The most important parts in solving these problems are modeling the problem correctly, determining the parameters and constraints of the problem, and finally choosing a suitable meta-heuristic algorithm for the solution of the objective function. Not every algorithm is suitable for every problem structure. Therefore, in this study, the suitability of the RUN algorithm for the solution of fixed-size functions will be evaluated. Theoretically, Runge-Kutta methods used in numerical analysis are an important type of the family of closed and open iterative methods for solution approximations of ordinary differential equations. The RUN algorithm is also designed with inspiration from these methods. In order to evaluate the performance of the RUN algorithm on fixed-size functions in the study, 10 fixed-size multimodal test functions (Shekel's Foxholes, Kowalik, Six-Hump Camel-Back, Branin, Goldstein-Price, Hartman3, Hartman6, Shekel5, Shekel7, Shekel10) have been found in the literature before was selected. Solutions for each of the selected functions are obtained by changing the parameter values of the RUN algorithm. The obtained solution values were evaluated by comparing the solutions obtained with Slime Mold Algorithm (SMA) and Hunger Games Search (HGS) algorithms.

Cited by 4Open access

COMBINING GREY WOLF OPTIMIZATION AND WHALE OPTIMIZATION ALGORITHM FOR BENCHMARK TEST FUNCTIONS

Mustafa Serter Uzer, Onur İnan · Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi · 2023

Many optimization problems have been successfully addressed using metaheuristic approaches. These approaches are frequently able to choose the best answer fast and effectively. Recently, the use of swarm-based optimization algorithms, a kind of metaheuristic approach, has become more common. In this study, a hybrid swarm-based optimization method called WOAGWO is proposed by combining the Whale Optimization Algorithm (WOA) and Grey Wolf Optimization (GWO). This method aims to realize a more effective hybrid algorithm by using the positive aspects of the two algorithms. 23 benchmark test functions were utilized to assess the WOAGWO. By running the proposed approach 30 times, the mean fitness and standard deviation values were computed. These results were compared to WOA, GWO, Ant Lion Optimization algorithm (ALO), Particle Swarm Optimization (PSO), and Improved ALO (IALO) in the literature. The WOAGWO algorithm, when compared to these algorithms in the literature, produced the optimal results in 5 of 7 unimodal benchmark functions, 4 of 6 multimodal benchmark functions, and 9 of 10 fixed-dimension multimodal benchmark functions. Therefore, the suggested approach generally outperforms the findings in the literature. The proposed WOAGWO seems to be promising and it has a wide range of uses.

Cited by 0Open access

Analytic Test Functions for Generalizable Evaluation of Convex Optimization Techniques

Thomas Lux, Tyler H. Chang · 2020

Convex optimization algorithms such as gradient descent, quasi-Newton methods, and their variants are designed to find the global minimum of strongly convex functions. When these algorithms are applied to the minimization of non-convex functions they offer no robust theoretical guarantees. Despite the lack of guarantees, many methods still find good solutions in practice and are widely used in academia and industry to solve non-convex problems. In this paper, a set of analytic test functions and transformations are presented that can be used to quantify the expected performance of optimization algorithms on difficult (non-convex) optimization problems. The test functions and transformations in this set are used to compare and evaluate the convergence rates of stochastic gradient descent, L-BFGS, AdaGrad, and Adam.

Cited by 0

MVF - Multivariate Test Functions Library in C for Unconstrained Global Optimization

Ernesto Padernal Adorio, Revised January · 2005

Mvf.c is a library of multidimensional functions written in C for unconstrained global optimization or with simple box constraints. This article describes the functions currently in the library, the supporting random number functions and instructions in creating Python bindings using the SWIG interface generator. Updated March 5, 2004.

Cited by 110

GENERATION OF COMPLEX NONLINEAR BENCHMARK FUNCTIONS FOR OPTIMIZATION USING FUZZY SETS AND CLASSICAL TEST FUNCTIONS

Juan David Velásquez Henao, Juan David Velásquez Henao · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2011

In this paper we present a novel methodology to generate complex functions using twodimensional fuzzy sets as weights for combining classical benchmark functions These new functions have different characteristics from original ones but the minimum borders and geometry characteristics of the functions are still known Three different combinations of two functions Rosenbrock and Bukins F4 are used to exemplify the method and its potential to generate specific test functions to study and improve optimization methods

Cited by 0Open access