# Suppose the coupled task set has n kind of way for tearing; combi

Suppose the coupled task set has n kind of way for tearing; combining with formula (2), formula selleck chemicals (1) can be transformed

into min⁡⁡TT=min⁡⁡T1,T2,…,Tn. (3) Formula (3) is time aggregative model based on task transmission and interaction. As can be seen from this model the shortest task transmission and interaction represent an optimal task execution sequence. According to this task sequence, the whole design duration of coupled set will come to the shortest one. Moreover, the measurement of aggregative time is to calculate the execution time Ti of all the tasks. The measurement of task transmission and interaction is described as follows: tr=SF×t, (4) where tr is practical transmission time. SF can be calculated by the following formula, where m is the number of impact influences, Vi is the value of Fi, and ei is the weight of Fi: SF=∑i=1mei×Vi. (5) According to the analysis, the model can be built based on the following assumptions . All tasks are done in every stage. Rework performed is a function

of the work done in the previous iteration stage. The work transformation parameters in the matrix do not vary with time. We take formula (5) mentioned above as the first objective function which is used to measure the quality loss of decoupling process. The other objective function, development cost, is adopted by using cumulative sum of the whole iteration process. In addition, the constraint condition of the model can be expressed as follows: Ωj = ∑i=1naij < 1(i, j ∈ Ak), which makes the entries either in every row or in every column sum to less than one. Based on these analyses, the hybrid model set up in this paper is described as follows:  Object 1:  tr=SF×t, (6)  Object 2:lim⁡T→∞⁡∑t=0TΛt=I−Λ−1, (7)  Satisfy Ωj=∑i=1naij<1 i,j∈Ak, (8) where formulas (6) and (7) are objective functions, where the first one represents quality loss and the other development cost. The symbol Ak in constraint condition (8) denotes small coupled sets

after tearing approach and aij is an element in Ak. This constraint condition is used to assure that the decomposed small coupled set Ak can converge. 4. Artificial Bee Colony Algorithm for Finding a Near-Optimal Solution The hybrid model set up in the above section is difficult in finding out the optimal solution by conventional methods such as branch and bound method and Lagrangian relaxation method. Due to its simplicity and high-performance searching ability, heuristic algorithm has been widely used in Entinostat NP-hard problems. As a new swarm intelligence algorithm, artificial bee colony algorithm (ABC) has strong local and global searching abilities and has been applied to all kinds of engineering optimization problems. In this section, the ABC algorithm is used to solve this coupled problem. 4.1. Artificial Bee Colony Algorithm The ABC algorithm is one of the most recently introduced optimization algorithms inspired by intelligent foraging behavior of a honey bee swarm.