To determine which constraint should be satisfied first, the sum of the lower bounds blog post on the numbers of materials in all languages ��l=1rLLl and in all categories ��k=1qCLk are computed. The one with less sum will be satisfied first by randomly selecting the material that belongs to language l or category k.Algorithm 2Initialization procedure of DPSO.4.2. Constraints HandlingIn the literature, repair operators and penalty functions are widely used approaches to handling constrained optimization problems. However, due to the computationally heavy load of repair operators, we focus on solely penalty functions. For each particle, the fitness value is evaluated by (16), where O(xij) is the objective value of the studied problem given in (1), and H(xij) is a penalty factor defined in (17).

A feasible solution reflects its objective value as the fitness value, while an infeasible solution receives an objective value and a penalized value by (17). It can be seen from (17) that each term is associated with constrains (3), (6), (7), (8), and (9), as mentioned in Section 2.2. For instance, if a solution reports that the expense of any department j exceeds the budget Bj, addressed in constraints (3), then a positive penalty value can be subtracted from the fitness value to reflect the infeasibility. One hasF(xij)=O(xij)?H(xij),(16)H(xij)=��j=1mmax0,��i=1nxijeij?BjBj+��l=1rmax��i=1nyiail?LLl+��l=1rmax+��k=1qmax0,��i=1nyibik?UCk+��k=1qmaxCUk?��i=1nyibik.(17)4.3.

Scout ParticlesPremature convergence is a challenging problem faced by PSO algorithms throughout the optimization process. To avoid premature convergence in the DPSO algorithm for the Drug_discovery studied problem, this paper employs scout particles to enhance the exploration. The concept is to send out scout particles to explore the search space and collect more extensive information of optimal solutions for other particles. If a scout particle finds a solution that is quite different from the best solution and the expected fitness value is better, the scout particle will share the information with some particles by affecting their velocities.The DPSO procedure with scout particles is depicted in Figure 1. Firstly, in order to generate a feasible swarm, the particles are generated by the initialization procedure as mentioned in Section 4.1. Secondly, when the swarm has not yet converged, the regular particle s (Pst) flies through the search space by the following steps: fitness evaluation, velocity calculation, and position updating.