In particle swarm optimization, the inertia weight is an important parameter for controlling its search capability. There have been intensive studies of the inertia weight in continuous optimization, but little attention has been paid to the binary case. This study comprehensively investigates the effect of the inertia weight on the performance of binary particle swarm optimization, from both theoretical and empirical perspectives. A mathematical model is proposed to analyze the behavior of binary particle swarm optimization, based on which several lemmas and theorems on the effect of the inertia weight are derived. Our research findings suggest that in the binary case, a smaller inertia weight enhances the exploration capability while a larger inertia weight encourages exploitation. Consequently, this paper proposes a new adaptive inertia weight scheme for binary particle swarm optimization. This scheme allows the search process to start first with exploration and gradually move towards exploitation by linearly increasing the inertia weight. The experimental results on 0/1 knapsack problems show that the binary particle swarm optimization with the new increasing inertia weight scheme performs significantly better than that with the conventional decreasing and constant inertia weight schemes. This study verifies the efficacy of increasing inertia weight in binary particle swarm optimization
