Multiupdate mode quantum evolutionary algorithm and its applications to combination and permutation problems

Based on the concept and principles of quantum computing, this paper proposes a new evolutionary algorithm called multiupdate mode quantum evolutionary algorithm (MMQEA). MMQEA, like the other classic evolutionary algorithms, is also characterized by the representation of the individual evaluation function and the population dynamics; however, instead of binary, numeric, or symbolic representation, MMQEA uses two interactional q-bit strings as an individual. Update modes are introduced as a variational operation that evolves the individuals to make a better solution. The proposed individual structure and update modes are inspired by quantum entanglement. Update modes perform as reproducing the states of a pair of q-bit strings of individual simultaneously. For guiding the individual evolution to maintain the population diversity and avoid prematurity, each q-bit string of individual provides its evolutionary history information to another. To demonstrate its effectiveness and applicability, the proposed algorithm was tested on two famous combinatorial optimization problems, namely, the knapsack problem and flow shop problem. The results show that MMQEA performs very well compared to quantum evolutionary algorithm (QEA) and the conventional genetic algorithm.