Visualizing and Exploring the Dynamics of Optimization via Circular Swap Mutations in Constraint-Based Problem Spaces

This paper presents an investigation into utilizing circular swap mutations and partial brute forcing in guiding a stochastic search toward an optimal solution. The findings have potential implications for computational intelligence approaches in massive search spaces with known constraints. The efficacy of the method is examined using Sudoku puzzles ranging from 17 to 37 clues. The study graphically depicts the magnitude of the problem space, thus revealing the spatial proximity of states and the nature in which intertwined constraints affect the scope for locating a solution. These insights potentially assist in comprehending the problem space when designing solutions for vast, multidimensional problems. Constraint-aware circular swap mutations can serve as a successful strategy in the design of computational intelligence algorithms that need to be made capable of escaping local optima under temporal constraints. Future directions for research are also suggested. These include mathematically examining paths to optimal solutions and reverse-generating fitness landscapes.