A novel three-phase trajectory informed search methodology for global optimization

A new deterministic method for solving a global optimization problem is proposed. The proposed method consists of three phases. The first phase is a typical local search to compute a local minimum. The second phase employs a discrete sup-local search to locate a so-called sup-local minimum taking the lowest objective value among the neighboring local minima. The third phase is an attractor-based global search to locate a new point of next descent with a lower objective value. The simulation results through well-known global optimization problems are shown to demonstrate the efficiency of the proposed method.

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

[2]  M. Bartholomew-Biggs,et al.  Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations , 1989 .

[3]  S. Vavasis Nonlinear optimization: complexity issues , 1991 .

[4]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

[5]  Roberto Battiti,et al.  The continuous reactive tabu search: Blending combinatorial optimization and stochastic search for global optimization , 1996, Ann. Oper. Res..

[6]  Stefano Fanelli,et al.  Matrix algebras in Quasi-Newton methods for unconstrained minimization , 2003, Numerische Mathematik.

[7]  A. V. Levy,et al.  The Tunneling Algorithm for the Global Minimization of Functions , 1985 .

[8]  Terrence J. Sejnowski,et al.  Analysis of hidden units in a layered network trained to classify sonar targets , 1988, Neural Networks.

[9]  Mehiddin Al-Baali Improved Hessian approximations for the limited memory BFGS method , 2004, Numerical Algorithms.

[10]  Ronald R. Willis,et al.  New Computer Methods for Global Optimization , 1990 .

[11]  Panos M. Pardalos,et al.  Recent Advances in Global Optimization , 1991 .

[12]  Leon O. Chua,et al.  Nonlinear programming without computation , 1984 .

[13]  Bedri C. Cetin,et al.  Terminal repeller unconstrained subenergy tunneling (trust) for fast global optimization , 1993 .

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

[15]  C. T. Kelley,et al.  Detection and Remediation of Stagnation in the Nelder--Mead Algorithm Using a Sufficient Decrease Condition , 1999, SIAM J. Optim..

[16]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[17]  A. Ruszczynski,et al.  Nonlinear Optimization , 2006 .

[18]  T. Fox Nonlinear optimization with linear constraints using a projection method , 1982 .

[19]  Jacob Barhen,et al.  TRUST: A deterministic algorithm for global optimization , 1997 .

[20]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[21]  David J. Evans,et al.  The Annealing Evolution Algorithm as Function Optimizer , 1995, Parallel Comput..

[22]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[23]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .

[24]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[25]  Yong Yao,et al.  Dynamic tunneling algorithm for global optimization , 1989, IEEE Trans. Syst. Man Cybern..

[26]  D Cvijovicacute,et al.  Taboo search: an approach to the multiple minima problem. , 1995, Science.

[27]  Leon O. Chua,et al.  Global optimization: a naive approach , 1990 .

[28]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[29]  M. Fukushima,et al.  Minimizing multimodal functions by simplex coding genetic algorithm , 2003 .

[30]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[31]  P. Siarry,et al.  A genetic algorithm with real-value coding to optimize multimodal continuous functions , 2001 .

[32]  Jaewook Lee Dynamic gradient approaches to compute the closest unstable equilibrium point for stability region estimate and their computational limitations , 2003, IEEE Trans. Autom. Control..

[33]  Arnold Neumaier,et al.  Global Optimization by Multilevel Coordinate Search , 1999, J. Glob. Optim..

[34]  Hubertus Th. Jongen,et al.  Nonlinear optimization in IRN , 1987 .