Solving NP-hard number matrix games with Wisdom of Artificial Crowds

J. Redding, University of Louisville
J. Schreiver, University of Louisville
C. Shrum, University of Louisville
A. Lauf, University of Louisville
R. Yampolskiy, University of Louisville


Solving puzzles based on number-sum or ordered matrices is an NP-hard problem that requires considerable computational effort. Prime examples of these are the games Sudoku and Kakuro. Kakuro relies on number sequences that must sum to a number indicator shown on the puzzle. Sudoku requires that numbers be listed in an implicit sequence in blocks and rows. Both puzzles require exclusivity of the numbers listed in each row and logical grouping. As a result, solving these puzzles requires an iterative approach. We show that Genetic Algorithms (GA) can be augmented with postprocessing by a Wisdom of Artificial Crowds (WoAC) to constrain the solution space after a number of generations. Using the WoAC method, compared to using GA alone, we can reduce the time to a successful solution by a factor of 50% for easy and medium-difficulty puzzles. Our work has broader applications in the fields of multi-agent theory and collective decision making, as the WoAC method allows for crowd-based improvements to well-known genetic algorithm methods.