When trial individual dominates target individual, the trial vector (otherwise the target vector) remains to the next generation. This mechanism is different from the selection operation of the HDE, where all the target and trial individuals are kept to be chosen according ARQ197 mw to the front rank and crowding distance. So, DE is not suitable for solving this MSJRD.Figure 3Nondominated solutions of the final population obtained by DE.6. Conclusions and Future ResearchIn this study, a new multiobjective JRD model with stochastic demand is proposed which takes into account the service level while making the replenishment and delivery decisions. Then, two approaches to solve this complex optimization problem are designed using an improved HDE. The main contributions are as follows.

Considering the difficulty to estimate the shortage cost in reality, the shortage quantity is utilized as another standard to evaluate the rationality of decisions besides the total cost. To our best knowledge, this is the first time to propose a practical multiobjective stochastic JRD model. The MOEA is adopted to solve the proposed multiobjective JRD model. The results of the numerical example and Pareto solution analysis show the feasibility of the MOEA to handle the proposed MSJRD. It enriches the application field of the MOEA.The comparison of two approaches for the MSJRD verifies that LP and MOEA are suitable for solving this MSJRD problem. Furthermore, results show that the proposed HDE is more effective than DE and GA whatever LP or MOEA method is used.

This illustrates that DE is likely to combine with other algorithms so as to provide a more effective way to solve complex problems.The future research on the multiobjective JRD problem should consider more realistic assumptions such as uncertain costs, freight consolidation, and budget constraint.AcknowledgmentsThis research is partially supported by the National Natural Science Foundation of China (70801030; 71101060; 71131004; 71371080) and Humanities and Social Sciences Foundation of the Chinese Ministry of Education (no. 11YJC630275).

AbbreviationsDi: Annual demand rate of item iS: Major ordering costsi: Minor ordering cost of item ihi: Annual inventory holding cost of item iT: Basic cycle time (decision variable)ki: Multiplier of T (decision Drug_discovery variable)Ti: Cycle time of item i (decision variable)Ri: Maximum inventory level of item i during replenishment intervalzi: Safety stock factor of item i (decision variable)L: Lead time of items��i: Standard deviation of item iM: Least common multiple of ki��i: Stock-out cost per unit for item ic: Distribution cost per unit distanceFp: Stopover cost at supplier pd(j): Shortest path needed for distribution in jth basic cycle.
The molecular structure of the complex with atom numbering scheme is shown in Figure 1. The crystal data and structure refinement are presented in Table 1, and selected bond lengths and angles are given in Table 2.