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عنوان فارسی مقاله:
بهینه سازی مگاپن برای مساله برنامه ریزی فلاوشاپ بدون انتظار با استفاده از مفاهیم کارآمد
عنوان انگلیسی مقاله:
Optimization of makespan for no-wait flowshop scheduling problems using efficient matheuristics
سال انتشار : 2016
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بخشی از مقاله انگلیسی:
3. Proposed matheuristics
The proposed matheuristics consist of three phases. In the first phase, two versions of the MNEH constructive heuristics are used to obtain the initial seed sequences for solving the Fm j nwtj Cmax problem. Then, in the second phase, the Fm j nwtj Cmax problem is converted into an ATSP, and the LHK algorithm is then applied to improve upon the initial solution and obtain a near-optimal solution. Finally, in the third phase, the near-optimal solution obtained by the LHK algorithm is set as the UB of the corresponding BIP mathematical model of the transformed ATSP; the BIP model is solved using the Gurobi optimizer, a state-of-the-art mathematical programming solver, in order to obtain the optimal solution. Since two constructive heuristics are used to generate the initial seed sequence in the first phase, two versions of the matheuristic exist, which are Matheuristic1 and Matheuristic2. The three phases are described in detail below. Phase I. : Using MNEH constructive heuristics to obtain initial seed sequences The procedures for implementing the two versions of the MNEH constructive heuristics, which can rapidly generate an initial seed sequence for solving the Fm j nwtj Cmax problem, are described as follows. Step 1: Generate a job list π ¼ ðπ1; :::; πnÞ with respect to an indicator value. In this work, two versions of constructive heuristics, MNEH1 and MNEH2, are used to generate π. MNEH1 serves to sort n jobs in a non-increasing order of their total processing times to yield a job list π. MNEH2 uses the nearest neighbor (NN) algorithm [42] to yield a job list π. The procedure for executing the NN algorithm is as follows. Step 1.1: Start from a dummy job as the current vertex. Step 1.2: Find the shortest edge that connects the current vertex to an unvisited vertex V. Step 1.3: Set the current vertex to V and mark V as visited. Step 1.4: If all of the vertices in the domain are visited, then terminate; otherwise, go back to Step 1.2.
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