Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2018 Jan 11;8(1):453.
doi: 10.1038/s41598-017-18940-4.

On the efficiency of nature-inspired metaheuristics in expensive global optimization with limited budget

Ya D Sergeyev  1   2 , D E Kvasov  3   4 , M S Mukhametzhanov  3   4
Affiliations

On the efficiency of nature-inspired metaheuristics in expensive global optimization with limited budget

Ya D Sergeyev et al. Sci Rep. .

Abstract

Global optimization problems where evaluation of the objective function is an expensive operation arise frequently in engineering, decision making, optimal control, etc. There exist two huge but almost completely disjoint communities (they have different journals, different conferences, different test functions, etc.) solving these problems: a broad community of practitioners using stochastic nature-inspired metaheuristics and people from academia studying deterministic mathematical programming methods. In order to bridge the gap between these communities we propose a visual technique for a systematic comparison of global optimization algorithms having different nature. Results of more than 800,000 runs on 800 randomly generated tests show that both stochastic nature-inspired metaheuristics and deterministic global optimization methods are competitive and surpass one another in dependence on the available budget of function evaluations.

PubMed Disclaimer

Conflict of interest statement

The authors declare that they have no competing interests.

Figures

Figure 1
Figure 1
Construction of operational characteristics for deterministic methods and of the operational zone for metaheuristic Firefly Algorithm (FA) built on the hard 5-dimensional class of 100 GKLS test functions. (a) Operational characteristics for methods DIRECT, DIRECT-L, and ADC. After executing 34,000 trials DIRECT-L has solved 31 problem, DIRECT 42 problems, and ADC 65 problems; after performing 94,000 trials DIRECT-L has solved 46 problems, DIRECT 58 problems, and ADC all 100 problems. (b) The operational zone built using 10,000 runs performed by FA (100 runs for each of the 100 problems). The upper and the lower boundaries of the zone are shown as dark blue curves.
Figure 2
Figure 2
Operational characteristics built on two 5-dimensional classes of 100 GKLS test functions for deterministic methods DIRECT, DIRECT-L, and ADC and operational zones for stochastic metaheuristics Firefly Algorithm (FA), Genetic Algorithm (GA) and Artificial Bee Colony (ABC). (a) Operational characteristics for deterministic methods and the operational zone for FA for the simple 5-dimensional class. (b) The same as (a) for the hard class. (c) Operational characteristics for deterministic methods and the operational zone for GA for the simple 5-dimensional class. (d) The same as (c) for the hard class. (e) Operational characteristics for deterministic methods and the operational zone for ABC for the simple 5-dimensional class. (f) The same as (e) for the hard class.
Figure 3
Figure 3
Aggregated operational zones for stochastic metaheuristics Firefly Algorithm (FA), Genetic Algorithm (GA), and Artificial Bee Colony (ABC) and operational characteristics for deterministic methods DIRECT, DIRECT-L, and ADC built on two 5-dimensional classes of 100 GKLS test functions. (a) Operational characteristics for deterministic methods and the aggregated operational zone for FA for the simple 5-dimensional class. (b) The same as (a) for the hard class. (c) Operational characteristics for deterministic methods and the aggregated operational zone for GA for the simple 5-dimensional class. (d) The same as (c) for the hard class. (e) Operational characteristics for deterministic methods and the aggregated operational zone for ABC for the simple 5-dimensional class. (f) The same as (e) for the hard class.
See this image and copyright information in PMC

References

    1. Horst, R. & Pardalos, P. M. (eds) Handbook of Global Optimization, vol. 1 (Kluwer Academic Publishers, Dordrecht, 1995).
    1. Pintér JD. Global Optimization in Action (Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications) Dordrecht: Kluwer Academic Publishers; 1996.
    1. Sergeyev YD, Kvasov DE. Deterministic Global Optimization: An Introduction to the Diagonal Approach. New York: Springer; 2017.
    1. Price K, Storn RM, Lampinen JA. Differential Evolution: A Practical Approach to Global Optimization. Natural Computing Series. New York: Springer; 2005.
    1. Sergeyev YD, Strongin RG, Lera D. Introduction to Global Optimization Exploiting Space-Filling Curves. New York: Springer; 2013.

Publication types

LinkOut - more resources