Cultural Algorithm with Shared Memory Tackles Classic Knight's Tour Chess Problem
A developer applied a Cultural Algorithm to solve the Knight's Tour, a classic problem requiring a chess knight to visit every square on an 8×8 board exactly once. Unlike standard genetic algorithms that evolve solutions purely through random selection and reproduction, the Cultural Algorithm adds a shared 'Belief Space' that stores collective knowledge across generations. This Belief Space is divided into three components: situational knowledge that copies moves from top-performing paths, normative knowledge that tracks which squares tend to appear at each path position in strong solutions, and historical knowledge that identifies recurring three-move sequences in successful tours. Each knowledge type probabilistically nudges new candidate solutions rather than forcing them, maintaining a balance between random exploration and guided exploitation. The experiment demonstrated that encoding structured, accumulated memory into an evolutionary algorithm can improve solution quality on combinatorial problems like the Knight's Tour.
