Genetic Quantum Algorithm for Solving Knapsack Problem with MATLAB Implementation

This article presents a MATLAB implementation of a genetic quantum algorithm designed to solve the classic knapsack optimization problem. The knapsack problem represents a fundamental optimization challenge where items must be selected to maximize total value without exceeding a given weight capacity. The genetic quantum algorithm combines evolutionary computation principles with quantum-inspired mechanisms to achieve superior performance in solving complex optimization problems. The implementation features quantum-inspired chromosome encoding using qubit representation, where each gene exists in a superposition of states, and employs quantum rotation gates for chromosome updating. The algorithm utilizes quantum measurement for state collapse to binary solutions, followed by genetic operations including tournament selection, single-point crossover with adaptive probabilities, and bit-flip mutation. Fitness evaluation incorporates penalty functions for constraint handling when weight limits are exceeded. We provide detailed explanations of the quantum population initialization, quantum observation process, and the integration of quantum interference for solution enhancement. The complete MATLAB source code is included, enabling readers to easily understand, execute, and modify the algorithm for their specific needs. By studying this implementation, users can gain practical insights into applying genetic quantum algorithms to solve similar combinatorial optimization challenges in various domains.