Evolution of Non-Deterministic Incremental Algorithms as a New Approach for Search in State Spaces

Let us call a non-deterministic incremental algorithm one that is able to construct any solution to a combinatorial problem by selecting incrementally an ordered sequence of choices that defines this solution, each choice being made non-deterministically. In that case, the state space can be represented as a tree, and a solution is a path from the root of that tree to a leaf. This paper describes how the simulated evolution of a population of such non-deterministic incremental algorithms offers a new approach for the exploration of a state space, compared to other techniques like Genetic Algorithms (GA), Evolutionary Strategies (ES) or Hill Climbing. In particular, the efficiency of this method, implemented as the Evolving Non-Determinism (END) model, is presented for the sorting network problem, a reference problem that has challenged computer science. Then, we shall show that the END model remedies some drawbacks of these optimization techniques and even outperforms them for this pro..