Quantum-inspired firefly algorithm with particle swarm optimization for discrete optimization problems

The firefly algorithm is a recent meta-heuristic inspired from nature. It is based on swarm intelligence of fireflies and generally used for solving continuous optimization problems. This paper proposes a new algorithm called Quantum-inspired Firefly Algorithm with Particle Swarm Optimization (QIFAPSO) that among other things, adapts the firefly approach to solve discrete optimization problems. The proposed algorithm uses the basic concepts of quantum computing such as superposition states of Q-bit and quantum measure to ensure a better control of the solutions diversity. Moreover, we use a discrete representation for fireflies and we propose a variant of the well-known Hamming distance to compute the attractiveness between them. Finally, we combine two strategies that cooperate in exploring the search space: the first one is the move of less bright fireflies towards the brighter ones and the second strategy is the PSO movement in which a firefly moves by taking into account its best position as well as the best position of its neighborhood. Of course, these two strategies of fireflies' movement are adapted to the quantum representation used in the algorithm for potential solutions. In order to validate our idea and show the efficiency of the proposed algorithm, we have used the multidimensional knapsack problem which is known as an NP-Complete problem and we have conducted various tests of our algorithm on different instances of this problem. The experimental results of our algorithm are competitive and in most cases are better than that of existing methods.