The Non-Walking Triangle Optimization Representation: Enabling Monte Carlo Tree Search-like Methods for Real Parameter Optimization Problems

Real parameter estimation is typically performed by an algorithm that operates directly on vectors of real parameters. This study presents an extension of a representation for real parameter optimization that is discrete and based on the iterated partition of simplices, known as the Walking Triangle Representation (WTR), and pairs it with Monte Carlo Tree Search (MCTS)-like algorithms. The number of moves allowed to the WTR is reduced to only its centering move, where a vertex of the simplex is replaced by its center of mass. This representation converts a real parameter optimization to a discrete form, which can then be paired with MCTS-like algorithms. The tree structure of MCTS allows one to keep track of and exploit information from previous attempts (tree extensions) when choosing the next set of moves to try. Six real parameter optimization problems were used to test the algorithm. Four parameters in the algorithm were studied, including: minimum gene length, maximum gene length, number of tree extensions, and probability of exploration (chance). The algorithm regularly performed consistently well, even with a low number of fitness evaluations (typical number of fitness evaluations is up to 3750 per run). This paper focuses on the ability of the Non-Walking Triangle Representation to convert real parameter optimization problems into discrete representations. This concept is demonstrated through the evaluation of the Non-Walking Triangle Monte Carlo Tree Search (MCNon-Walk) algorithm's ability to find optima in a variety of real parameter optimization problems, using differential evolution as a baseline for comparison.