COMPASS_SEARCH The Compass Search Optimization Algorithm

COMPASS_SEARCH is a FORTRAN77 library which seeks the minimizer of a scalar function of several variables using compass search, a direct search algorithm that does not use derivatives.

The algorithm, which goes back to Fermi and Metropolis, is easy to describe. The algorithm begins with a starting point X, and a step size DELTA.

For each dimension I, the algorithm considers perturbing X(I) by adding or subtracting DELTA.

If a perturbation is found which decreases the function, this becomes the new X. Otherwise DELTA is halved.

The iteration halts when DELTA reaches a minimal value.

The algorithm is not guaranteed to find a global minimum. It can, for instance, easily be attracted to a local minimum. Moreover, the algorithm can diverge if, for instance, the function decreases as the argument goes to infinity.

Languages:

COMPASS_SEARCH is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

ASA047, a FORTRAN77 library which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

ENTRUST, a MATLAB program which minimizes a scalar function of several variables using trust-region methods.

NELDER_MEAD, a MATLAB program which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

PRAXIS, a FORTRAN77 library which implements the principal axis method of Richard Brent for minimization of a function without the use of derivatives.

TEST_OPT, a FORTRAN90 library which defines test problems requiring the minimization of a scalar function of several variables.

TEST_OPT_CON, a FORTRAN90 library which defines test problems for the minimization of a scalar function of several variables, with the search constrained to lie within a specified hyper-rectangle.

TOMS178, a FORTRAN77 library which optimizes a scalar functional of multiple variables using the Hooke-Jeeves method.

John Burkardt

Reference:

1. Evelyn Beale,
On an Iterative Method for Finding a Local Minimum of a Function of More than One Variable,
Technical Report 25,
Statistical Techniques Research Group,
Princeton University, 1958.
2. Richard Brent,
Algorithms for Minimization without Derivatives,
Dover, 2002,
ISBN: 0-486-41998-3,
LC: QA402.5.B74.
3. Charles Broyden,
A class of methods for solving nonlinear simultaneous equations,
Mathematics of Computation,
Volume 19, 1965, pages 577-593.
4. David Himmelblau,
Applied Nonlinear Programming,
McGraw Hill, 1972,
ISBN13: 978-0070289215,
LC: T57.8.H55.
5. Tamara Kolda, Robert Michael Lewis, Virginia Torczon,
Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods,
SIAM Review,
Volume 45, Number 3, 2003, pages 385-482.
6. Ken McKinnon,
Convergence of the Nelder-Mead simplex method to a nonstationary point,
SIAM Journal on Optimization,
Volume 9, Number 1, 1998, pages 148-158.
7. Zbigniew Michalewicz,
Genetic Algorithms + Data Structures = Evolution Programs,
Third Edition,
Springer, 1996,
ISBN: 3-540-60676-9,
LC: QA76.618.M53.
8. Jorge More, Burton Garbow, Kenneth Hillstrom,
Testing unconstrained optimization software,
ACM Transactions on Mathematical Software,
Volume 7, Number 1, March 1981, pages 17-41.
9. Michael Powell,
An Iterative Method for Finding Stationary Values of a Function of Several Variables,
Computer Journal,
Volume 5, 1962, pages 147-151.
10. Howard Rosenbrock,
An Automatic Method for Finding the Greatest or Least Value of a Function,
Computer Journal,
Volume 3, 1960, pages 175-184.

List of Routines:

• COMPASS_SEARCH carries out a direct search minimization algorithm.
• R8VEC_PRINT prints an R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN77 source codes.

Last revised on 17 January 2012.