A distributed agent-based approach for simulation-based optimization

Structural design and optimization in engineering are increasingly addressing non-standard optimization problems (NSPs). These problems are characterized by a complex topology of the optimization space with respect to nonlinearity, multimodality, discontinuity, etc. By that, NSP can only be solved by means of computer simulations. In addition, the corresponding numerical approaches applied often tend to be noisy. Typical examples for NSP occur in robust optimization, where the solution has to be robust with respect to implementation errors, production tolerances or uncertain environmental conditions. However, a generally applicable strategy for solving such problem categories always equally efficiently is not yet available. To improve the situation, a distributed agent-based optimization approach for solving NSPs is introduced in this paper. The elaborated approach consists of a network of cooperating but also competing strategy agents that wrap various strategies, especially optimization methods (e.g. SQP, DE, ES, PSO, etc.) using different search characteristics. In particular, the strategy agents contain an expert system modeling their specific behavior in an optimization environment by means of rules and facts on a highly abstract level. Further, different common interaction patterns have been defined to describe the structure of a strategy network and its interactions. For managing the complexity of NSPs using multi-agent systems (MASs) efficiently, a simulation and experimentation platform has been developed. Serving as a computational steering tool, it applies MAS technology and accesses a network of various optimization strategies. As a consequence, an elegant interactive steering, a customized modeling and a powerful visualization of structural optimization processes are established. To demonstrate the far reaching applicability of the proposed approach, numerical examples are discussed, including nonlinear function and robust optimization problems. The results of the numerical experiments illustrate the potential of the agent-based strategy network approach for collaborative solving, where observed synergy effects lead to an effective and efficient solution finding.

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

[2]  Z. Geem Music-Inspired Harmony Search Algorithm: Theory and Applications , 2009 .

[3]  El-Ghazali Talbi,et al.  On Parallel Evolutionary Algorithms on the Computational Grid , 2006, Parallel Evolutionary Computations.

[4]  Eleonora Riva Sanseverino,et al.  An Evolutionary Parallel Tabu Search approach for distribution systems reinforcement planning , 2002, Adv. Eng. Informatics.

[5]  M. Clerc,et al.  Particle Swarm Optimization , 2006 .

[6]  Christian Jacob,et al.  Illustrating Evolutionary Computation with Mathematica , 2001 .

[7]  Kathryn A. Dowsland,et al.  Simulated Annealing , 1989, Encyclopedia of GIS.

[8]  Dimitris Bertsimas,et al.  Robust Optimization for Unconstrained Simulation-Based Problems , 2010, Oper. Res..

[9]  Ruhul A. Sarker,et al.  AMA: a new approach for solving constrained real-valued optimization problems , 2009, Soft Comput..

[10]  Agostino Poggi,et al.  Developing Multi-agent Systems with JADE , 2007, ATAL.

[11]  Jiming Liu,et al.  Multiagent Optimization System for Solving the Traveling Salesman Problem (TSP) , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[12]  Michael Affenzeller,et al.  MODELLING OF AN AGENT-BASED SCHEDULE OPTIMISATION SYSTEM , 2004 .

[13]  John W. Chinneck Discovering the Characteristics of Mathematical Programs via Sampling , 2002, Optim. Methods Softw..

[14]  Antonio J. Nebro,et al.  jMetal: A Java framework for multi-objective optimization , 2011, Adv. Eng. Softw..

[15]  Distributed Solution of Simulation-Based Optimization Problems on Networks of Workstation , 2000, Computación y Sistemas.

[16]  Dimitris Bertsimas,et al.  Robust optimization with simulated annealing , 2010, J. Glob. Optim..

[17]  Zong Woo Geem,et al.  Music-Inspired Harmony Search Algorithm , 2009 .

[18]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[19]  Ian F. C. Smith,et al.  A direct stochastic algorithm for global search , 2003, Appl. Math. Comput..

[20]  E. Salajegheh,et al.  Optimum design of trusses with discrete sizing and shape variables , 1993 .

[21]  El-Ghazali Talbi,et al.  COSEARCH: A Parallel Cooperative Metaheuristic , 2006, J. Math. Model. Algorithms.

[22]  Michel Gendreau,et al.  Handbook of Metaheuristics , 2010 .

[23]  Gerhart I. Schuëller,et al.  Computational methods in optimization considering uncertainties – An overview , 2008 .

[24]  Hans A. Eschenauer,et al.  SAPOP: an optimization procedure for multicriteria structural design , 1993 .

[25]  H. P Nii,et al.  Blackboard Systems , 1986 .

[26]  Hans-Paul Schwefel,et al.  Evolution and Optimum Seeking: The Sixth Generation , 1993 .

[27]  Shengdun Zhao,et al.  A flexible tolerance genetic algorithm for optimal problems with nonlinear equality constraints , 2009, Adv. Eng. Informatics.

[28]  M. Baitsch,et al.  An Object-Oriented Approach to High Order Finite Element Analysis of Three-Dimensional Continua , 2006 .

[29]  Jiming Liu,et al.  Graph coloring by multiagent fusion search , 2009, J. Comb. Optim..

[30]  Michael Wooldridge,et al.  Introduction to multiagent systems , 2001 .

[31]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

[32]  Tad Hogg,et al.  Better Than The Best: The Power of Cooperation , 1993 .

[33]  Teodor Gabriel Crainic,et al.  A first multilevel cooperative algorithm for capacitated multicommodity network design , 2006, Comput. Oper. Res..

[34]  Ramesh Sharda,et al.  Metaheuristic Optimization via Memory and Evolution , 2005 .

[35]  Christopher G. Lasater,et al.  Design Patterns , 2008, Wiley Encyclopedia of Computer Science and Engineering.

[36]  Günter Rudolph,et al.  Parallel Approaches for Multiobjective Optimization , 2008, Multiobjective Optimization.

[37]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[38]  Godfrey C. Onwubolu,et al.  New optimization techniques in engineering , 2004, Studies in Fuzziness and Soft Computing.

[39]  Thomas Stützle,et al.  Iterated local search for the quadratic assignment problem , 2006, Eur. J. Oper. Res..

[40]  Christian Igel,et al.  A computational efficient covariance matrix update and a (1+1)-CMA for evolution strategies , 2006, GECCO.

[41]  E. Hinton,et al.  Reliable structural optimization with error estimation, adaptivity and robust sensitivity analysis , 1997 .

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

[43]  Teodor Gabriel Crainic,et al.  Explicit and Emergent Cooperation Schemes for Search Algorithms , 2008, LION.

[44]  Bernhard Sendhoff,et al.  Robust Optimization - A Comprehensive Survey , 2007 .

[45]  Jorge Nocedal,et al.  Knitro: An Integrated Package for Nonlinear Optimization , 2006 .

[46]  Andrea Roli,et al.  MAGMA: a multiagent architecture for metaheuristics , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[47]  P. Pardalos,et al.  Handbook of global optimization , 1995 .

[48]  Burkhardt Funk,et al.  A Blackboard Architecture for Workflows , 2007, CAiSE Forum.

[49]  Bahram Alidaee,et al.  Metaheuristic Optimization via Memory and Evolution: Tabu Search and Scatter Search (Operations Research/Computer Science Interfaces Series) , 2005 .

[50]  Dietrich Hartmann,et al.  Object Oriented Finite Element Analysis for Structural Optimization using p-Elements , 2004 .

[51]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[52]  Rong-Song He,et al.  A hybrid real-parameter genetic algorithm for function optimization , 2006, Adv. Eng. Informatics.

[53]  Asuman E. Ozdaglar,et al.  Distributed Subgradient Methods for Multi-Agent Optimization , 2009, IEEE Transactions on Automatic Control.

[54]  Paul Davidsson,et al.  Combining Agent-Based Approaches and Classical Optimization Techniques , 2005, EUMAS.

[55]  Robert H. Leary,et al.  Global Optima of Lennard-Jones Clusters , 1997, J. Glob. Optim..

[56]  Akbar A. Javadi,et al.  A hybrid intelligent genetic algorithm , 2005, Adv. Eng. Informatics.

[57]  Kang Tai,et al.  Probability Collectives: A multi-agent approach for solving combinatorial optimization problems , 2010, Appl. Soft Comput..

[58]  Manfred Grauer,et al.  Decomposition and parallelization strategies for solving large‐scale MDO problems , 2007 .

[59]  M. Roma,et al.  Large-Scale Nonlinear Optimization , 2006 .