3.1. The Detail Techniques of ACSA (1) Affinity Measure. Affinity of the algorithm is the objective of model, the smaller the better. In order to extend the search space, the algorithm accepts solutions which fail to satisfy the constraints. However, penalty coefficient will be added to the affinity measure. (2) The Design of Antibody. The selleck product length of antibody equals the amount of shippers in I. The antibody codes are in J, and the amount should not exceed the maximum number p. To better understand the design of antibody, a simple example consisting of seven
shippers and four candidate freight transport centers is proposed. p equals three (see Figure 1). Candidate center 3 is not included in the antibody, which means candidate center 3 is not chosen as a transport center. Figure 1 The design of antibody for the optimization model. (3) Mutation Operation. The mutation operation is shown in Figure 2. p equals four. If the amount of chosen candidate centers reaches maximum, randomly choose a code e. Change both e and the codes whose values are the same as e (see Figure 2(a)). Else randomly choose a code e and change its value (see Figure 2(b)). Figure 2 The mutation operation of model M-I. 3.2. Cloud Model (1) Cloud Model. CM is used to transform the qualitative data into quantitative data. A Cloud Drop is a realization of the
qualitative concept; the distribution of Cloud Drops is called Cloud. Three numerical characteristics are used to describe the Cloud; those are expected value Ex, entropy En, and hyper entropy He. The typical CMs are Normal Cloud, Trapezoid Cloud, and Triangle Cloud. If distribution function of Cloud follows the normal distribution, the CM is called Normal Cloud. Three Normal Clouds with different characteristics are shown in Figure 3. Compared the three Clouds, it can be found that the bigger the characteristics are, the more divergent
the Cloud will be. Figure 3 Three examples of the Normal Cloud. The characteristics of Normal Cloud can be got by the following operations: Ex=f¯,En=f¯−fminc1,He=Enc2, (12) where c1 and c2 are control coefficients. f¯ is the average value of affinities in the group. fi is affinity of the antibody. fmin is the minimum affinity of the antibody. (2) Cloud Generator. Cloud Generator (CG) is the algorithm of CM. The inputs of the generator are the three numerical characteristics. The outputs are Cloud Drops. CG can realize the mapping from qualitative AV-951 data to quantitative data. There are many CGs such as Forward Cloud Generator, Backward Cloud Generator, X Condition Cloud Generator, and Y Condition Cloud Generator. The Forward Cloud Generator is used to generate Cloud Drops based on the samples which are in set (Ex, En, and He). The Cloud Drops can be got by the following formulas: En′=NORMEn,He2,Qcloud=e−fi−Ex2/2En′2. (13) Q cloud is a Cloud Drop which means the uncertainty degree of the inputs, Qcloud ∈ (0,1). 4. Progress of the Algorithm C-ACSA combines the advantages of CM and ACSA.