An adaptive population multi-objective quantum-inspired evolutionary algorithm for multi-objective 0/1 knapsack problems

The multi-objective quantum-inspired evolutionary algorithm (MQEA) is a relatively recent technique for solving multi-objective optimization problems (MOPs). In the MQEA, quantum bit (Q-bit) individuals are classified into several groups, with each group assigned one objective solution (one of the non-dominated solutions found so far) as the reference sign string. For a fixed population size, the number of Q-bit individuals assigned to each objective solution decreases with increasing number of found non-dominated solutions. As a result, more or fewer Q-bit individuals assigned to each objective solution may lead a confused order of local and global search. To mitigate this issue, an adaptive population MQEA (APMQEA) is proposed in this work. In the APMQEA, the number of Q-bit individuals assigned to each objective solution is fixed, and the population size is adaptively changed according to the number of found non-dominated solutions. Experimental results for the multi-objective 0/1 knapsack problem show that the APMQEA finds solutions close to the Pareto-optimal front and maintains a good spread of the non-dominated set.