A new class of test functions for global optimization

In this paper we propose a new class of test functions for unconstrained global optimization problems. The class depends on some parameters through which the difficulty of the test problems can be controlled. As a basis for future comparison, we propose a selected set of these functions, with increasing difficulty, and some computational experiments with two simple global optimization algorithms.

[1]  L. Darrell Whitley,et al.  Building Better Test Functions , 1995, ICGA.

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

[3]  H. Zimmermann Towards global optimization 2: L.C.W. DIXON and G.P. SZEGÖ (eds.) North-Holland, Amsterdam, 1978, viii + 364 pages, US $ 44.50, Dfl. 100,-. , 1979 .

[4]  Jorge J. Moré,et al.  Testing Unconstrained Optimization Software , 1981, TOMS.

[5]  C. Floudas Handbook of Test Problems in Local and Global Optimization , 1999 .

[6]  Bernardetta Addis,et al.  Local optima smoothing for global optimization , 2005, Optim. Methods Softw..

[7]  Fabio Schoen,et al.  A wide class of test functions for global optimization , 1993, J. Glob. Optim..

[8]  Graham R. Wood,et al.  Matching Stochastic Algorithms to Objective Function Landscapes , 2005, J. Glob. Optim..

[9]  C. A. FLOUDAS,et al.  Global Optimization: Local Minima and Transition Points , 2005, J. Glob. Optim..

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

[11]  Robert H. Leary,et al.  Global Optimization on Funneling Landscapes , 2000, J. Glob. Optim..

[12]  Marco Locatelli,et al.  On the Multilevel Structure of Global Optimization Problems , 2005, Comput. Optim. Appl..

[13]  Hans-Paul Schwefel,et al.  Numerical Optimization of Computer Models , 1982 .

[14]  Sven Leyffer,et al.  A Trust-Region Algorithm for Global Optimization , 2006, Comput. Optim. Appl..

[15]  János D. Pintér,et al.  Global Optimization: Software, Test Problems, and Applications , 2002 .

[16]  Panos M. Pardalos Generation of large-scale quadratic programs for use as global optimization test problems , 1987, TOMS.

[17]  Tamás Vinkó,et al.  A comparison of complete global optimization solvers , 2005, Math. Program..

[18]  J. Doye Physical Perspectives on the Global Optimization of Atomic Clusters , 2000, cond-mat/0007338.

[19]  J. Doye,et al.  Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms , 1997, cond-mat/9803344.

[20]  Klaus Schittkowski,et al.  Test examples for nonlinear programming codes , 1980 .

[21]  Rudolf Mathar,et al.  A class of test functions for global optimization , 1994, J. Glob. Optim..

[22]  Klaus Schittkowski,et al.  More test examples for nonlinear programming codes , 1981 .

[23]  S. K. Mishra,et al.  Nonconvex Optimization and Its Applications , 2008 .

[24]  Fabio Schoen,et al.  Global Optimization of Morse Clusters by Potential Energy Transformations , 2004, INFORMS J. Comput..

[25]  L. F. Escudero Book reviewMore test examples for nonlinear programming codes: Klaus SCHITTKOWSKI Volume 282 in: Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, 1987, iv + 261 pages, DM49.00 , 1988 .

[26]  Yaroslav D. Sergeyev,et al.  Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization , 2003, TOMS.

[27]  Aimo A. Törn,et al.  Global Optimization , 1999, Science.

[28]  J. B. Rosen,et al.  Construction of large-scale global minimum concave quadratic test problems , 1986 .

[29]  Nelson Maculan,et al.  A Function to Test Methods Applied to Global Minimization of Potential Energy of Molecules , 2004, Numerical Algorithms.