In this paper, we propose a novel metaheuristic optimization technique named Chess Piece Movements Optimization (CPMO) algorithm, which draws inspiration from two classical chess-based mathematical problems: the Knight’s Tour and the N-Queens problem. By modeling the Knight’s Tour, CPMO uses L-shaped “knight” jumps for broad global exploration, and by referencing the N-Queens problem, it employs “queen” moves for focused local exploitation. Fuzzy set theory is integrated to handle uncertainties in parameter tuning and solution selection, providing a smooth, adaptive transition between exploration and exploitation. To evaluate performance, CPMO is benchmarked against Particle Swarm Optimization, Bat Algorithm, and a standard Genetic Algorithm on eight standard test functions. Experimental results demonstrate CPMO’s competitive edge in convergence speed and solution quality, highlighting its potential as a versatile and efficient optimization tool.