Iterative Optimizers

9Balance and Perceived Difficulty

To study the relationships between balance profiles and the perceived difficulty of a problem for a given optimizer, we simplify as much as possible:

• – by considering constant profiles of different values h, denoted as ;
• – by defining pair-based optimizers (Explo2 algorithm, profile), which we shall denote here by Explo2();
• – by starting from the smallest possible initial population (2, with Explo2).

9.1. Constant profile-based experiments

Let us revisit our little Alpine problem in dimension 2 and execute Explo2() a hundred times for values of h increasing from 0.2 to 1.5 and a budget of 200 evaluations for each run. Figure 9.1 shows with an example (h = 0.4) how the optimizer quickly “catches” the desired profile.

Figure 9.1. A constant profile and the actual profile generated by Explo2

The CDFs obtained (actually, a magnified view of the results smaller than 0.04) are shown in Figure 9.2. With such a bare example, it can clearly be observed that it is more beneficial to do more explorations than exploitations. The profile of value 1 (perfect ...