Optimization with dynamic functions

ABSTRACT

Many optimization methods are iterative in nature and require users to specify constraints and objectives. The normal way to handle this type of problem would be to create a loop with an execute statement inside the body of the loop. The loop is necessary because of the iterative nature of the algorithm and the execute statement is necessary because the objective function is user-defined."Execute" can be costly inside a loop. While there are existing ways to remove "execute" from the loop, they are awkward. However, dynamic functions can be built ahead of time and called inside the loop. Defined operators allow an arbitrary optimization function to be passed to the looping function.The method of simulated annealing can deal with large-scale optimization problems without getting trapped in local minima. Constraints can be treated as objectives with a high penalty for violations. Hence we can eliminate constraints and deal only with objectives. A series of objectives is combined into a single objective function. Since the objectives are defined by the user, a dynamic function is created. The goal is to reduce the result of the dynamic function to zero (negative values are not permitted). The function is called iteratively until a specific tolerance is reached.This paper will use an example from the mortgage industry to demonstrate the use of dynamic functions in iterative optimization methods.

REFERENCES

• 1: William H. Press , Brian P. Flannery , Saul A. Teukolsky , William T. Vetterling, Numerical recipes: the art of scientific computing, Cambridge University Press, New York, NY, 1986
• 2: ROSS, PHILIP J (1988), Taguchi Techniques for Quality Engineerinb McGraw Hill.
• 3: FREUND, JOHN E. (1992), Modem Elementary Statmics, 8th Ed., Prentice Hall
• 4: HILI.rF.R and LtEBERMANN, (1986) Introduction w Operations Research ,Chapter 15, McGraw Hill.
• 5: BOENDER and ROMEIJN (1995), "Stochastic Methods", Handbook of Global Optimization, Klower Academic Publishers.

INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES

Additional Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES

General Terms:
Design, Languages