Iterative ordinal optimization and its applications

Ordinal optimization (OO) is a method of speeding up the process of stochastic optimization via parametric simulation. However, OO still has limitations as it stands. One drawback is the fact that the search space for many problems can be huge due to combinatorial explosion. In this paper, we introduce the concept and procedure of iterative ordinal optimization to overcome this limitation. The key idea is to narrow or restrict the search to favor “good” subsets of the search space through limited sampling. It is in the spirit of traditional hill climbing except instead of moving from point to point in the search space, we move from one subset or search representation to another. As an illustration of the methodology, we study the famous unsolved Witsenhausen problem (1968). We find a solution that is 50% better than the best known solution