| Research on optimization problems is valuable both in science research and in engineering practice, and always attracts people's attention. Since the middle of last century, there has been great development in the study and application of the optimization theory and methods. Nowadays, with the advanced hardware and software, the optimal solution of a very large optimization problem can be effective. Generally speaking, the optimization problem is aiming at seeking the optimal solution with various algorithms in the feasible region, and different algorithm takes different measures to reach the optimum. However, considering the complexity of the practical problems, the imperfection of the information, and the unavoidable artificial negligence, it is quite difficult to formulate the practical problems completely. A model may do not have any feasible region because of the contradictory constraints or the violated constraints. Under this circumstance, no efficient algorithm will work. Consequently, the analysis of the feasible region of optimizations problems is becoming more and more important.Although some mathematical approaches have been developed to analyze the feasible solution region in recent years, most of them are based on the Linear Programming, also they could not be utilized directly in practice. In fact, only when combining the mathematical theory with the engineering practice can we solve the practical problems effectively. So, under the guideline of system engineering thoughts, this paper carried out analysis in feasible region of Mixed-Integer Linear Programming (MILP), on the basis of the refinery production scheduling optimization model which is in the form of 0-1 MILP.The feasible region analysis consists of two aspects. The first problem is seeking feasibility. We need to know whether or not a model has a feasible sregion, and decide the feasibility status of the model. The second problem is analyzing infeasibility. To find the crux of the problem that results in the infeasibility of the model, and take corresponding steps to modify it.Based on the two problems above, research has been done as follows:First, introduced the scheduling optimization model, and built an instance model accordingly. Meanwhile, analyzed the parameters, constraints and structure of the model, and concluded the scheduling rules, to prepare for the next step.Second, analyzed the feasibility of a model. In order to estimate whether a model has a feasible region, an approach of diagnosing the feasibility of a model was described. At the same time, proposed a rule-based branch and bound algorithm aiming at testing the feasibility of a 0-1MILP, which could reduce the searching field. One feasible solution could be gained if the model is feasible, which can be as the initial solution for the next optimization algorithms. And the results of the analysis were verified by instance.Third, analyzed the infeasibility of a model. By learning the previous work related with Irreducible Infeasible Subset (IIS), and making use of the scheduling model, gave a two-stage IIS method based on constraints grouping. Then, according to learning the general modification method, and considering the parameter limitation in a practical model, researched on the parameter limited modification. Finally, in order to analyze the 0-1MILP model, a diagnosing method based on the IIS method was given. Make use of the proposed method, the conflict that causes the infeasibility could be find and corresponding adjustments of the parameters could be taken to gain the feasible solution region. And the results of the analysis were verified by instance.The article ended with a summary of the full text, put forward the issues which need to be solved in the future. |
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