Dilation Functions in Global Optimization

Complex tasks in Computer Science can be reformulated as optimization problems, in which the global optimum of a given function must be identified. Such problems are typically noisy, multi-modal, non-convex and non-separable, and they require the application of population-based global search metaheuristics to effectively explore the search space. In this work, we address the issue of manipulating the search space of these complex optimization problems to the aim of improving the exploration and exploitation capabilities of metaheuristics. In particular, we show that the implicit assumption in global optimization problems, i.e., that candidate solutions are represented by vectors of values whose meaning has a straightforward interpretation, is not always adequate and that the semantics of parameters can be modified by re-mapping their values in the search space by means of user-defined Dilation Functions. Dilation Functions are general purpose transformations that can be applied to any metaheuristics and optimization problem to "compress" or "dilate" some regions of the search space, allowing to improve the quality of the initial population and the exploitation of promising areas, especially in the case of Swarm Intelligence algorithms. The advantages given by the application of Dilation Functions have been observed by running experiments with Fuzzy Self-Tuning Particle Swarm Optimization and Covariance Matrix Adaptation Evolution Strategies, for the optimization of the Ackley benchmark function and for the parameter estimation of a "synthetic" model of a biochemical system.

[1]  Giancarlo Mauri,et al.  A memetic hybrid method for the Molecular Distance Geometry Problem with incomplete information , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[2]  Giancarlo Mauri,et al.  Multimodal medical image registration using Particle Swarm Optimization: A review , 2016, 2016 IEEE Symposium Series on Computational Intelligence (SSCI).

[3]  Carlos A. Coello Coello,et al.  Handling constraints using multiobjective optimization concepts , 2004 .

[4]  Andreas Zell,et al.  Modeling metabolic networks in C . glutamicum : a comparison of rate laws in combination with various parameter optimization strategies , 2009 .

[5]  Giancarlo Mauri,et al.  Computational Intelligence for Parameter Estimation of Biochemical Systems , 2018, 2018 IEEE Congress on Evolutionary Computation (CEC).

[6]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[7]  Jing Wang,et al.  Space transformation search: a new evolutionary technique , 2009, GEC '09.

[8]  Carmen G. Moles,et al.  Parameter estimation in biochemical pathways: a comparison of global optimization methods. , 2003, Genome research.

[9]  Carlos A. Coello Coello,et al.  Constraint-handling in nature-inspired numerical optimization: Past, present and future , 2011, Swarm Evol. Comput..

[10]  Daniel A. Ashlock,et al.  Evolvable warps for data normalization , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[11]  Giancarlo Mauri,et al.  Fuzzy Self-Tuning PSO: A settings-free algorithm for global optimization , 2017, Swarm Evol. Comput..

[12]  Michael N. Vrahatis,et al.  Recent approaches to global optimization problems through Particle Swarm Optimization , 2002, Natural Computing.

[13]  H. Kitano Systems Biology: A Brief Overview , 2002, Science.

[14]  D. Ackley A connectionist machine for genetic hillclimbing , 1987 .

[15]  Nikolaus Hansen,et al.  The CMA Evolution Strategy: A Comparing Review , 2006, Towards a New Evolutionary Computation.

[16]  Marco S. Nobile,et al.  The impact of particles initialization in PSO: Parameter estimation as a case in point , 2015, 2015 IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB).

[17]  Sheridan K. Houghten,et al.  Restarting and recentering genetic algorithm variations for DNA fragment assembly: The necessity of a multi-strategy approach , 2016, Biosyst..

[18]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[19]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[20]  Chunming FU,et al.  Improved Differential Evolution with Shrinking Space Technique for Constrained Optimization , 2017 .

[21]  Giancarlo Mauri,et al.  Estimating reaction constants in stochastic biological systems with a multi-swarm PSO running on GPUs , 2012, GECCO '12.

[22]  Daniela Besozzi,et al.  Reaction-Based Models of Biochemical Networks , 2016, CiE.

[23]  Jianhong Zhou,et al.  A novel quantum-behaved particle swarm optimization with random selection for large scale optimization , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

[24]  Roman Senkerik,et al.  Towards Human Cell Simulation , 2019, High-Performance Modelling and Simulation for Big Data Applications.

[25]  Giancarlo Mauri,et al.  A GPU-Based Multi-swarm PSO Method for Parameter Estimation in Stochastic Biological Systems Exploiting Discrete-Time Target Series , 2012, EvoBIO.

[26]  Marco S. Nobile,et al.  Computational Strategies for a System-Level Understanding of Metabolism , 2014, Metabolites.

[27]  Václav Snásel,et al.  Metaheuristic design of feedforward neural networks: A review of two decades of research , 2017, Eng. Appl. Artif. Intell..

[28]  Giancarlo Mauri,et al.  GPU-powered model analysis with PySB/cupSODA , 2017, Bioinform..

[29]  S. Bhat,et al.  Modeling and analysis of mass-action kinetics , 2009, IEEE Control Systems.

[30]  Fei He,et al.  Sensitivity analysis and robust experimental design of a signal transduction pathway system , 2008 .

[31]  Yuren Zhou,et al.  Accelerating adaptive trade‐off model using shrinking space technique for constrained evolutionary optimization , 2009 .

[32]  Giancarlo Mauri,et al.  GPU-accelerated simulations of mass-action kinetics models with cupSODA , 2014, The Journal of Supercomputing.

[33]  Marco S. Nobile,et al.  Reboot strategies in particle swarm optimization and their impact on parameter estimation of biochemical systems , 2017, 2017 IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB).