IBM ILOG Solver User's Manual > Evolutionary Algorithms > Modeling and Solving a Basic EA Problem

Modeling and Solving a Basic EA Problem

In this lesson, you will use the Solver IIM Evolutionary Algorithm (EA) Framework to solve the "one max" problem, a basic binary digit (bit) optimization problem. In this problem, you try to find the solution that maximizes the number of times the digit 1 appears within a given set of 0-1 variables.

To understand how this problem works, consider an initial population of 4 solutions, each a string of 6 bits:

001101

010111

101000

110010

You use evolutionary algorithm techniques to create new generations until one of these generations contains the desired solution:

111111

In the example that follows, your initial population is 50 randomly generated solutions, each of which is 50 bits long. You use tournament selection, mutation, and replacement of parents by offspring to search for the solution that maximizes the objective function. The objective function is the number of times the digit 1 appears. The optimal solution is one where the digit 1 appears 50 times.

While this is not a difficult optimization problem, this example allows you to become familiar with the evolutionary algorithm concepts without too many modeling concerns. The solving process is split into two steps:

Create an initial population using random generation.
Write a basic generation loop:

Create the reproduction goal, which uses tournament selection to choose which parents will reproduce and then uses the mutation operator reproduce.
Create the replacement goal. In this example, the parent population will be entirely replaced by the offspring population.
For each generation, solve the problem using the generation goal (which combines the reproduction and replacement goals) and display the generation statistics. Break the loop when the solution that equals the optimum value (the problem size) is found or a certain number of generations is reached.

The first step in this procedure is discussed in the section "Creating an initial solution pool". The second step is discussed in the section "Writing a simple generation loop".

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