Modality of Particle Swarm Optimization to Improve Decision Making Process of Analytical Hierarchy Processing

Author Name(s): Prof. Suraj Bandichode, Prof. Bhumesh Masram, Prof. Sofia Pillai, Prof. Umesh Sakhare, Mr. Mayur Wankhade
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AHP has been widely used in various real world applications. Numerous decision making process involves the use of pair-wise comparison matrix of AHP, and consistency ration is the most key issue related with AHP. In this research work, Particle Swarm Optimization algorithm is employed to reduce the consistency ratio of decision making process Analytical Hierarchy Process (AHP). The aim of proposed method is to reduce the CR. Consistency evaluation of AHP have been studied in literature since from 70’s. The reported methods are quite complicated and difficult. Many methods could not maintain the original judgment provided by domain expert. We have presented a very simple and yet effective method to minimize of consistency ratio (almost zero) which will also preserves the domain expert’s opinion. The robustness of proposed method is presented by applying it to real world case study. The experimentation shows that the proposed method is efficient and accurate to satisfy the consistency requirements of AHP.


Various MCDM – Multi Criteria Decision Making techniques have been suggested and implemented in literature over pass three decades and for the adoption of weights most of these techniques used pair-wise comparison matrix which is reported (Saaty 2003). MCDM is a finite alternative selection problem based on given attributes. The significance of attributes in the decision making process was first incorporated by Saaty in Analytical Hierarchy Processing (AHP) to resolve the factors like quantitative and qualitative for decision makers. Analytical hierarchy processing has been applied widely on various cases studies and numerous applications. Pair wise comparison matrix in AHP is generally expressed on 1 to 9 scale by the decision makers, this decision making process is based on makers expertise and experience. Inconsistency in judgment and hence in pair-wise comparison matrix of AHP is most important issue to address. Consistency is also difficult to achieve when large numbers of attributes were considered. Even consistency can be raised due to limitations of experience and expertise. Revising the pair-wise comparison matrix and also to preserve the expertise judgment is challenging task and many existing approaches are very complicated and difficult to achieve it. Consistency Ratio (CR) is computed as CI/RI where CR is Consistency Index and RI is Random Index. Saaty Suggested that, CR < 0.1 is acceptable for the decision making process but practically it is very complicated process to achieve the CR while preserving judgment. There are two mechanisms by which inconsistent pair wise matrices can be made consistent: (1) The domain expert or decision maker can modify or reassess the matrix, however this approach is very time consuming. (2) To get the optimal matrix values by either statistical approach or by optimization. This approach has taken attention of many researchers to modify the inconsistent pair-wise comparison matrix


In this research work, a simple and efficient mechanism is proposed based on particle swarm optimization to tune the parameters of pair-wise comparison matrix of AHP. In this research work, PSO has been applied to reduce the consistency ration of Analytical hierarchy processing and robustness of proposed method is presented with case study. The other intelligent algorithm also might be used to solve this problem.

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