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Operations Research Models and Methods
Computation Section
Subunit Optimize
 - Random Generation

The Random option creates a fixed number of solutions whose components are determined by random selection. This feature might be useful when exhaustive enumeration and Fibonacci search require too many observations.

To illustrate we use the two dimensional forecasting example used earlier. We are searching for the optimum values of the parameters alpha and beta that are determined by the integer variables m1 and m2.

alpha = 2/(m1 + 1), beta = 2/(m2 + 1)

As before, we choose Add Form from the menu to construct the combinatorial form. After the form is constructed we link the model variables to the combinatorial variables and the combinatorial objective to the model objective. When all is ready we choose Search from the menu.

When the Random option is selected, the Random Solutions field is enabled. We choose to generate 100 solutions and display the best 20 feasible solutions. Each solution is generated independently. First the value of x1 is randomly selected with each integer in its range having equal likelihood. The value of x2 is then randomly selected from its range. If there are more variables, the process continues until all variables have values. If the Feasible State cell is TRUE, the solution is feasible. The Objective Value is computed via the worksheet formulas for each feasible solution and compared to those previously generated. The results for the example are below.


The example above shows the results after 100 observations. Based on exhaustive enumeration, we know the optimum solution is (9,20). The best provided by this random search gave (9, 19). Certainly random search does not guarantee an optimum result.

The example had no conditions on feasibility except the variable ranges, so all solutions generated were feasible. For problems with constraints limiting feasibility, there is no guarantee that the random process will generate feasible solutions.

It is possible to combine random search with an improvement process to reach better results. We describe this on a later page.

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Operations Research Models and Methods
by Paul A. Jensen
Copyright 2004 - All rights reserved