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Futuristic Greedy Algorithm on some NP-complete Problems

Bakht Hemmat, Ali | 2021

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  1. Type of Document: Ph.D. Dissertation
  2. Language: English
  3. Document No: 54256 (52)
  4. University: Sharif University of Technology, International Campus, Kish Island
  5. Department: Science and Engineering
  6. Advisor(s): Izadi, Mohammad
  7. Abstract:
  8. Many problems in the field of 0-1 integer programming are NP-Complete. Execution time for exact solving these problems is very high due to many constraints and decision variables. Hence, scientists use Fast algorithms, for example, the Greedy algorithms, in the approximated solution of these problems.A classic greedy approach may not search the whole solution space for better choices. However, other methods with a greedy approach, such as meta heuristic and hyper heuristic, in addition to local search, consider the more search space. These methods search randomly, so it does not provide a good guarantee for finding the proper solutions. Finding suitable solutions in this category of algorithms depends on tuning the parameters and distributing the selections in solution space and other factors. Hence, we presented a new greedy method that this method could find proper greedy selection in each greedy step.We evaluated the proposed method in three topics with three independent types of 0-1 integer programming problems. In the first research, we investigated decreasing the execution time of reducers by revising clustering. These tests were performed in the Hadoop structure. Our research results indicate that the proposed approach improves the execution time about 3.9% less than the fastest algorithm in our experiments. The Futuristic greedy could improve execution time by load balancing in reducers. In the second research, the proposed approach could improve clustering precision to detect communities. We implemented it with the map-reduce technique in the Hadoop structure. Experimental results in datasets illustrate that the average of the rand index of clusters accomplished by 99.32 % in the proposed method. Besides, these results confirm that there is a reduction in execution time by the proposed algorithm. In the third research, we solve a fully dynamic bin packing problem for virtual machine allocation in the cloud environment. The goal of problem-solving is to reduce the number of allocated hosts (bins) and virtual machines (items) migration rates for reducing energy consumption. This study demonstrates a greedy futuristic approach for fully dynamic bin packaging with an average asymptotic approximation ratio of 1.231, better than other existing algorithms. The proposed algorithm illustrates an asymptotic approximation ratio of (t/ (t-1)) OPT, where the value of t depends on the distribution of the arrived and departed items. Also, OPT is the number of bins by an optimal solution. Finally, in experiments of datasets using a maximum utilization of 80% of each bin, the average migration rate is 0.338. This method could reduce the cost of maintaining and purchasing hosts. Also, this method could diminish the migration rate of virtual machines. As a result, migration decreasing improves the energy consumption cost in the cloud environment.The main points of this research include the following points: fist point, at each step of the proposed method, many other candidates may be removed from the solution space by selecting one greedy candidate. Among the deleted candidates, the appropriate future selections may also be removed. By deleting these appropriate selections, the final solution of the greedy method will most likely not be an optimal solution. The proposed approach of this thesis tries to select proper local choices as much as possible. Problems can be solved using this proposed approach to calculate the approximated impact of each local selection on future selections.Second point, the proposed approach estimates properly trading off between different greedy indexes. This proper estimation is determined depending on choices in the solution space and other factors. Also, the solution recovered from this proposed approach can be considered a primary solution for meta heuristic and hyper heuristic methods because these primary solutions are close to an optimal solution. Therefore, meta heuristic and hyper heuristic methods can be accomplished better solutions in NP-Complete problems by developing these primary solutions
  9. Keywords:
  10. Metaheuristic Method ; NP-Complete ; Futuristic Greedy Algorithm ; Hyperheuristic Algorithm

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