hik is transport demand of shipper i in scenario k. dij is distance between shipper i and railway freight transport centerj. Cj is fixed cost to construct a PA-824 clinical trial center at candidate center j. I is set of shippers, i ∈ I.
J is set of candidate centers, j ∈ J. (b) Objective Function of Robust Optimization Model. To set up robust optimization model, expected optimization model should be set at first. Define δ(k) as the probability of scenario k, which means the realization probability of the scenario. K is set of scenarios. Expected value of optimization model is as follows: E(z)=μ1c∑k∈K ∑i∈I ∑j∈Jhikdijxijkδk+μ2∑k∈K ∑j∈JCjyjkδk. (2) The robust optimization model further measures the deviation between expected and actual objective values. If actual objective value zk is worse than
the expected value E(z), scenario k will influence the optimized result. So only the zk which is worse than E(z) is considered in the deviation Δ: Δ=∑k∈Kmax0,zk−Ezδk. (3) Objective function of robust optimization model can be presented as follows: Z=Ez+κΔ, (4) where κ is weight of the deviation value in the objective. (3) Constraints (a) Each shipper must be assigned to one freight transport center in scenario k: ∑j∈Jxijk=1 ∀i∈I, k∈K. (5) (b) Candidate center j cannot serve any shipper, if j is not chosen as a freight transport center: xijk≤yjk ∀i∈I, j∈J, k∈K. (6) (c) The total number of chosen freight transport center should be constrained: ∑j∈Jyjk≤p ∀k∈K, (7) where p is maximum number of chosen freight transport center, which is preestablished. (d) The sum of distance which is greater than coverage distance DC at a freight transport center should not exceed ε. Both DC and ε are prespecified: ∑i∈Ilijxijk≤ε ∀j∈J, k∈K. (8) The coefficient lij is defined as follows: lij=dijdij>DC0otherwise. (9) (f) The transport demand serviced by freight transport center j cannot exceed its capacity Capj: ∑i∈Ihikxijk≤Capj ∀j∈J, k∈K. (10) (4) The Robust Optimization Mathematical Model. The robust optimization model of freight transport center
location problem can be stated as follows: (M-I) Min Z=μ1c∑k∈K ∑i∈I ∑j∈Jhikdijxijδk+μ2∑k∈K ∑j∈JCjyjkδk+κ∑k∈Kmax0,zk−E(z)δ(k)s.t. formulas (5)–(8),(10)xijk∈0,1 ∀i∈I, j∈J, k∈Kyjk∈0,1 ∀j∈J, k∈K. Carfilzomib (11) 3. Solution Algorithm ACSA [15–17] has clone, mutation, and selection operations. It is shown to be an evolutionary strategy which has high convergence rate and diversified antibodies. CM is proposed by Li and Du , which is used to convert the qualitative data into quantitative data. It is widely applied in many fields such as evolutionary algorithm, intelligent control, and fuzzy evaluation. CM has the character of randomness and stable tendentiousness. It can be used to control the direction of search and improve the convergence rate, according to the affinity of the antibody. The ACSA is combined with CM into a new heuristics, called C-ACSA method.