Can deterministic chaos improve differential evolution for the linear ordering problem?

Linear ordering problem is a popular NP-hard combinatorial optimization problem attractive for its complexity, rich library of test data, and variety of real world applications. It has been solved by a number of heuristic as well as metaheuristic methods in the past. The implementation of nature-inspired metaheuristic optimization and search methods usually depends on streams of integer and floating point numbers generated in course of their execution. The pseudo-random numbers are utilized for an in-silico emulation of probability-driven natural processes such as arbitrary modification of genetic information (mutation, crossover), partner selection, and survival of the fittest (selection, migration) and environmental effects (small random changes in particle motion direction and velocity). Deterministic chaos is a well known mathematical concept that can be used to generate sequences of seemingly random real numbers within selected interval in a predictable and well controllable way. In the past, it has been used as a basis for various pseudo-random number generators with interesting properties. Recently, it has been shown that it can be successfully used as a source of stochasticity for nature-inspired algorithms solving a continuous optimization problem. In this work we compare effectiveness of the differential evolution with different pseudo-random number generators and chaotic systems as sources of stochasticity when solving the linear ordering problem.

[1]  Neal R. Wagner.  The Logistic Lattice in Random Number Generation , 2001 .

[2]  Thomas Stützle,et al.  Search Space Analysis of the Linear Ordering Problem , 2003, EvoWorkshops.

[3]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[4]  Lawrence V. Snyder,et al.  A random-key genetic algorithm for the generalized traveling salesman problem , 2006, Eur. J. Oper. Res..

[5]  Emilio Corchado,et al.  Soft computing models to identify typical meteorological days , 2011, Log. J. IGPL.

[6]  Wen-Wei Lin,et al.  Randomness Enhancement Using Digitalized Modified Logistic Map , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[7]  Gerhard Reinelt,et al.  A benchmark library and a comparison of heuristic methods for the linear ordering problem , 2012, Comput. Optim. Appl..

[8]  Ponnuthurai N. Suganthan,et al.  Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization , 2011, Inf. Sci..

[9]  Ville Tirronen,et al.  Study on the Effects of Pseudorandom Generation Quality on the Performance of Differential Evolution , 2011, ICANNGA.

[10]  Emilio Corchado,et al.  A soft computing method for detecting lifetime building thermal insulation failures , 2010, Integr. Comput. Aided Eng..

[11]  Rainer Storn,et al.  Differential evolution design of an IIR-filter , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[12]  Camelia-Mihaela Pintea,et al.  Solving the linear ordering problem using ant models , 2009, GECCO '09.

[13]  Miguel A. Vega-Rodríguez,et al.  Sensitiveness of Evolutionary Algorithms to the Random Number Generator , 2011, ICANNGA.

[14]  M. Luescher,et al.  A Portable High-quality Random Number Generator for Lattice Field Theory Simulations , 1993 .

[15]  Zbigniew Kotulski,et al.  Pseudorandom Number Generators Based on Chaotic Dynamical Systems , 2001, Open Syst. Inf. Dyn..

[16]  Václav Snásel,et al.  Differential Evolution and Genetic Algorithms for the Linear Ordering Problem , 2009, KES.

[17]  R. Povinelli,et al.  Analyzing Logistic Map Pseudorandom Number Generators for Periodicity Induced by Finite Precision Floating-Point Representation , 2012 .

[18]  Václav Snásel,et al.  Differential evolution for the linear ordering problem implemented on CUDA , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[19]  Fred W. Glover,et al.  An Experimental Evaluation of a Scatter Search for the Linear Ordering Problem , 2001, J. Glob. Optim..

[20]  Jan Platos,et al.  Genetic algorithms for the linear ordering problem , 2009 .

[21]  Ivan Zelinka,et al.  Randomness and Chaos in Genetic Algorithms and Differential Evolution , 2013, 2013 5th International Conference on Intelligent Networking and Collaborative Systems.

[22]  Lu Wang,et al.  Self-adapting Differential Evolution Algorithm with Chaos Random for Global Numerical Optimization , 2010, ISICA.

[23]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[24]  J. Mitchell,et al.  Solving Linear Ordering Problems with a Combined Interior Point/Simplex Cutting Plane Algorithm , 2000 .

[25]  Václav Snášel,et al.  Evolving feasible linear ordering problem solutions , 2008, CSTST.

[26]  T. Stützle,et al.  The Linear Ordering Problem: Instances, Search Space Analysis and Algorithms , 2004 .

[27]  M. Andrecut,et al.  Logistic Map as a Random Number Generator , 1998 .

[28]  Nithin Nagaraj,et al.  The B-Exponential Map: A Generalization of the Logistic Map, and Its Applications In Generating Pseudo-random Numbers , 2006, ArXiv.

[29]  V. Snášel,et al.  Modeling Permutations for Genetic Algorithms , 2009, 2009 International Conference of Soft Computing and Pattern Recognition.

[30]  Ajith Abraham.  Editorial - Hybrid Soft Computing and Applications , 2009, Int. J. Comput. Intell. Appl..

[31]  Andrew Lim,et al.  Designing A Hybrid Genetic Algorithm for the Linear Ordering Problem , 2003, GECCO.