A literature survey of benchmark functions for global optimisation problems

Jamil, Mohsin; Yang, Xin-She

doi:10.1504/ijmmno.2013.055204

Cited by 819 publications

(487 citation statements)

References 64 publications

Supporting

Mentioning

474

Contrasting

Unclassified

Order By: Relevance

“…C is the searching step size vector shown in (14), C2 is a random element of C chosen according to the percentage repetition of C elements as shown in (15). µ and  are two random numbers ∈ [0,1].…”

Section: Grass Roots Algorithm Mathematical Modelmentioning

confidence: 99%

Grass Fibrous Root Optimization Algorithm

Akkar¹,

Mahdi²

2017

IJISA

View full text Add to dashboard Cite

Abstract-This paper proposes a novel meta-heuristic optimization algorithm inspired by general grass plants fibrous root system, asexual reproduction, and plant development. Grasses search for water and minerals randomly by developing its location, length, primary root, regenerated secondary roots, and small branches of roots called hair roots. The proposed algorithm explore the bounded solution domain globally and locally. Globally using the best grasses survived by the last iteration, and the root system of the best grass obtained so far by the iteration process and locally uses the primary roots, regenerated secondary roots and hair roots of the best global grass. Each grass represents a global candidate solution, while regenerated secondary roots stand for the locally obtained solution. Secondary generated hair roots are equal to the problem dimensions. The performance of the proposed algorithm is tested using seven standard benchmark test functions, comparing it with other metaheuristic well-known and recently proposed algorithms.

show abstract

Section: Grass Roots Algorithm Mathematical Modelmentioning

confidence: 99%

Grass Fibrous Root Optimization Algorithm

Akkar¹,

Mahdi²

2017

IJISA

View full text Add to dashboard Cite

show abstract

“…The most significant collections of global optimization benchmark problems can be found in [18,86,87]. Each benchmark problem has its individual characteristic, such as whether it is a multimodal, a unimodal or a random shape function as illustrated in Figure 1.…”

Section: Benchmark Function and Experiments Materialsmentioning

confidence: 99%

A Comparative Study on Recently-Introduced Nature-Based Global Optimization Methods in Complex Mechanical System Design

2017

View full text Add to dashboard Cite

Advanced global optimization algorithms have been continuously introduced and improved to solve various complex design optimization problems for which the objective and constraint functions can only be evaluated through computation intensive numerical analyses or simulations with a large number of design variables. The often implicit, multimodal, and ill-shaped objective and constraint functions in high-dimensional and "black-box" forms demand the search to be carried out using low number of function evaluations with high search efficiency and good robustness. This work investigates the performance of six recently introduced, nature-inspired global optimization methods: Artificial Bee Colony (ABC), Firefly Algorithm (FFA), Cuckoo Search (CS), Bat Algorithm (BA), Flower Pollination Algorithm (FPA) and Grey Wolf Optimizer (GWO). These approaches are compared in terms of search efficiency and robustness in solving a set of representative benchmark problems in smooth-unimodal, non-smooth unimodal, smooth multimodal, and non-smooth multimodal function forms. In addition, four classic engineering optimization examples and a real-life complex mechanical system design optimization problem, floating offshore wind turbines design optimization, are used as additional test cases representing computationally-expensive black-box global optimization problems. Results from this comparative study show that the ability of these global optimization methods to obtain a good solution diminishes as the dimension of the problem, or number of design variables increases. Although none of these methods is universally capable, the study finds that GWO and ABC are more efficient on average than the other four in obtaining high quality solutions efficiently and consistently, solving 86% and 80% of the tested benchmark problems, respectively. The research contributes to future improvements of global optimization methods.

show abstract

“…W procesie testowania poprawności pracy algorytmów wykorzystano 13 funkcji [16], których charakterystykę przedstawiono w tabeli 2.…”

Section: Funkcje Testoweunclassified

“…Dla każdego z nich określono współczynnik sukcesu, średnie oraz standardowe odchylenie. Na rysunku 5 przedstawiono funkcję Easom [16] oraz Salomon [16], w których algorytmy osiągnęły najniższy współczynnik sukcesu (SR).…”

Section: Tabela 2 Zestawienie Funkcji Testującychunclassified