Quantum-Inspired Differential Evolution with Particle Swarm Optimization for Knapsack Problem

This paper presents a new hybrid algorithm called QDEPSO (Quantum inspired Differential Evolution with Particle Swarm Optimization) which combines differential evolution (DE), particle swarm optimization method (PSO) and quantum-inspired evolutionary algorithm (QEA) in order to solve the 0-1 optimization problems. In the initialization phase, the QDEPSO uses the concepts of quantum computing as the superposition state of qubits as well as the quantum measurement to represent and generate the diversity of the initial solutions. The second phase is an alternation between the DE operations (mutation, crossover and selection) and the adaptation of update formula of the velocity and the position of PSO algorithm. The effect of this step is to determine the rotation quantum angle to explore search space of solutions. To evaluate the performance of the proposed algorithm, we use the knapsack 0-1 problem as a class of combinatorial optimization NP-hard problems. The obtained results for 0-1 knapsack problem have proven the superior performance of QDEPSO compared to Quantum-inspired Evolutionary algorithm (QEA), Adaptive Quantum-inspired Differential Evolution Algorithm (AQDE), Quantum Swarm Evolutionary algorithm (QSE) and Quantum Inspired Harmony Search Algorithm (QIHSA).