A sensitivity analysis method aimed at enhancing the metaheuristics for continuous optimization

An efficient covering of the search space is an important issue when dealing with metaheuristics. Sensitivity analysis methods aim at evaluating the influence of each variable of a problem on a model (i.e. objective function) response. Such methods provide knowledge on the function behavior and would be suitable for guiding metaheuristics. To evaluate correctly the dimensions influences, usual sensitivity analysis methods need a lot of evaluations of the objective function or are constrained with an experimental design. In this paper, we propose a new method, with a low computational cost, which can be used into metaheuristics to improve their search process. This method is based on two global sensitivity analysis methods: the linear correlation coefficient technique and Morris’ method. We propose to transform the global study of a non linear model into a local study of quasi-linear sub-parts of the model, in order to evaluate the global influence of each input variable on the model. This sensitivity analysis method will use evaluations of the objective function done by the metaheuristic to compute a weight of each variable. Then, the metaheuristic will generate new solutions choosing dimensions to offset, according to these weights. The tests done on usual benchmark functions of sensitivity analysis and continuous optimization (CEC 2013) reveal two issues. Firstly, our sensitivity analysis method provides good results, it correctly ranks each dimension’s influence. Secondly, integrating a sensitivity analysis method into a metaheuristic (here, Differential Evolution and ABC with modification rate) improves its results.

[1]  Bruno Sudret,et al.  Global sensitivity analysis using polynomial chaos expansions , 2008, Reliab. Eng. Syst. Saf..

[2]  Dervis Karaboga,et al.  A comprehensive survey: artificial bee colony (ABC) algorithm and applications , 2012, Artificial Intelligence Review.

[3]  Thomas Bartz-Beielstein,et al.  Experimental research in evolutionary computation , 2007, GECCO '07.

[4]  Carlo Meloni,et al.  Uncertainty Management in Simulation-Optimization of Complex Systems : Algorithms and Applications , 2015 .

[5]  Theresa Dawn Robinson,et al.  Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping , 2008 .

[6]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[7]  Huaguang Zhang,et al.  Neural-Network-Based Constrained Optimal Control Scheme for Discrete-Time Switched Nonlinear System Using Dual Heuristic Programming , 2014, IEEE Transactions on Automation Science and Engineering.

[8]  Kin Keung Lai,et al.  A Novel Support Vector Machine Metamodel for Business Risk Identification , 2006, PRICAI.

[9]  Roger D. Braddock,et al.  The New Morris Method: an efficient second-order screening method , 2002, Reliab. Eng. Syst. Saf..

[10]  Dervis Karaboga,et al.  AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION , 2005 .

[11]  Patrick Siarry,et al.  A Continuous Genetic Algorithm Designed for the Global Optimization of Multimodal Functions , 2000, J. Heuristics.

[12]  Kin Keung Lai,et al.  A novel support vector machine metamodel for business risk identification , 2006 .

[13]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[14]  D. Simon,et al.  12-1-2008 Biogeography-Based Optimization , 2019 .

[15]  Andrea Saltelli,et al.  An effective screening design for sensitivity analysis of large models , 2007, Environ. Model. Softw..

[16]  Ponnuthurai N. Suganthan,et al.  Recent advances in differential evolution - An updated survey , 2016, Swarm Evol. Comput..

[17]  S. Grunwald,et al.  A global sensitivity analysis tool for the parameters of multivariable catchment models , 2006 .

[18]  A. Jourdan,et al.  Optimal Latin hypercube designs for the Kullback–Leibler criterion , 2010 .

[19]  Dervis Karaboga,et al.  A modified Artificial Bee Colony algorithm for real-parameter optimization , 2012, Inf. Sci..

[20]  B. Iooss,et al.  A Review on Global Sensitivity Analysis Methods , 2014, 1404.2405.

[21]  Huaguang Zhang,et al.  A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Astrid Jourdan,et al.  Global sensitivity analysis using complex linear models , 2011, Statistics and Computing.

[23]  Zhengdong Lu,et al.  Fast neural network surrogates for very high dimensional physics-based models in computational oceanography , 2007, Neural Networks.

[24]  Zita Vale,et al.  Enhanced Multi-Objective Energy Optimization by a Signaling Method , 2016 .

[25]  Rajesh Kumar,et al.  A review on particle swarm optimization algorithms and their applications to data clustering , 2011, Artificial Intelligence Review.

[26]  M. Ramu,et al.  Surrogate Based Analysis and Optimization of Roof Slab of Future Fast Breeder Reactor , 2009 .

[27]  KumarRajesh,et al.  A review on particle swarm optimization algorithms and their applications to data clustering , 2011 .

[28]  Andrea Saltelli,et al.  Sensitivity Analysis for Importance Assessment , 2002, Risk analysis : an official publication of the Society for Risk Analysis.

[29]  Angel A. Juan,et al.  A review of simheuristics: Extending metaheuristics to deal with stochastic combinatorial optimization problems , 2015 .

[30]  Olivier Roustant,et al.  Calculations of Sobol indices for the Gaussian process metamodel , 2008, Reliab. Eng. Syst. Saf..

[31]  S. Tarantola,et al.  Reduced‐complexity modeling of braided rivers: Assessing model performance by sensitivity analysis, calibration, and validation , 2013 .

[32]  Patrick Siarry,et al.  Tabu Search applied to global optimization , 2000, Eur. J. Oper. Res..

[33]  Patrick Siarry,et al.  A sensitivity analysis method for driving the Artificial Bee Colony algorithm's search process , 2016, Appl. Soft Comput..

[34]  R. Srinivasan,et al.  A global sensitivity analysis tool for the parameters of multi-variable catchment models , 2006 .

[35]  Johann Dréo,et al.  Hybrid Continuous Interacting Ant Colony aimed at Enhanced Global Optimization , 2007, Algorithmic Oper. Res..

[36]  Guoqiang Li,et al.  Development and investigation of efficient artificial bee colony algorithm for numerical function optimization , 2012, Appl. Soft Comput..