3.4. Avoiding Premature ConvergenceMost of the global optimization methods suffer from premature convergence. One of the most used approaches to tackle this problem is to introduce diversity to the velocity sellckchem or the position of a particle. As mutation operators are to the genetic algorithm, so is introduction of diversity to PSO algorithms. The focus of this paper is to introduce the diversity by employing scout particles. The details of how the proposed DPSO algorithm circumvents premature convergence are described in Section 4.Garc��a-Villoria and Pastor [27] introduce the concept of diversity into the velocity updating function. The proposed dynamic diversity PSO (PSO-c3dyn) dynamically changes the diversity coefficients of all particles through iterations.

The more heterogeneity of the population will be, the less diversity will be introduced to the velocity updating function, and vice versa. Blackwell and Bentley [28] incorporate diversity into the population by preventing the homogeneous particles from clustering tightly to each other in the search space. They provide collision-avoiding swarms that reduce the attraction of the swarm center and increase the coverage of a swarm in the search space. Silva et al. [16] attempt to apply the diversity to both the velocity and the population by a predator particle and several scout particles. A predator particle is intended to balance the exploitation and exploration of the swarm, while scout particles are designed to implement different exploration strategies. The closer the predator particle will be to the best particle, the higher probability of perturbation will be.

4. DPSO with Scout ParticlesThis section details how to tackle the materials acquisition problem by discrete particle swarm optimization with scout particles. The representation of a particle and the initialization method for the studied problem are described in Section Brefeldin_A 4.1. Then, Section 4.2 elaborates on the details of preventing premature convergence by deploying scout particles. Section 4.3 redefines a constraints handling mechanism for solving the constrained optimization problem.4.1. Representation and InitializationThe solution of materials acquisition problem with n materials and m departments obtained by particle s at iteration t can be represented by an n �� m binary matrix, proposed by Wu et al. [29], as shown in (15). Each entry of the matrix (Pst)ij indicates whether material i is acquired by department j or not. Note that each entry of the matrix (Pst)ij corresponds to the decision variable (xij) that was mentioned in Section 2.1:Pst=[Ps(11)t?Ps(1m)t???Ps(n1)t?Ps(nm)t].