An assessment of the individual judgments and AHP-produced priority vectors for involved decision-makers indicates that the individual consistencies of decision makers may vary significantly, thus making the final group decision less reliable. In this paper, an approach is proposed as to how to combine decision makers' local priority vectors in AHP synthesis and reduce so-called group inconsistency. Instead of aggregating individual judgments (AIJ), or aggregating individually derived final priorities (AIP), we propose to perform an AHP synthesis of the best local priority vectors taken from the most consistent decision makers. The approach and related algorithm we label as MGPS after the key terms 'multicriteria group prioritization synthesis.' The concept is analogous to the one proposed by Srdjevic [1] for individual AHP applications where the best local priority vectors are selected based on the consistency performance of several of the most popular prioritization methods. Here, decision makers are combined instead of prioritization methods, and group context is fully implemented. After completing an evaluation of the decision makers inconsistencies in each node of the hierarchy, the selected best local priority vectors are synthesized in a standard manner, and the final solution is declared to be an AHP-group decision. Two numerical examples indicate that the developed approach and algorithm generate the final priorities of alternatives with the lowest overall inconsistency (in the multicriteria sense).

Synthesis of individual best local priority vectors in AHP-group decision making

https://www.research.manchester.ac.uk/portal/files/61784256/Abel_et_al._Inconsistency_Reduction_in_decision_making_via_MOO.pdf

Inconsistency reduction in decision making via multi-objective optimisation

A systematic work has been presented for condition assessment of suspension bridges in this study. Initially, a four-layer index system is built up. Subsequently, 45 experts are invited to determine the index weights by processing the experts’ opinions using the Group Decision-Making (GDM). The assigned weights seem more reasonable (especially weights of the tower and auxiliary facility) when compared with those in the existing China’s code. Next, assessment algorithms, the Local Variable Weight Model (LVWM) and Normal Cloud Model (NCM), are established based on the characteristics of the bridge condition assessment. The LVWM adjusts weight properly to make assessment results in line with the actual situation under extreme cases. The NCM describes not only the fuzziness but also the randomness in the assessment process. Finally, a case study is illustrated to verify the effectiveness of the methodology. For sake of highlighting the advantages of the LVWM, two more models are subjected to the case study, which are the Constant Weight Model (CWM) and Traditional Variable Weight Model (TVWM). Consequently, the assessment result of the LVWM is more in keeping with the actual situation than those of the CWM or TVWM.

Condition Assessment of Suspension Bridges Using Local Variable Weight and Normal Cloud Model

Optimizing the weights of Artificial Neural Networks (ANNs) is a great important of a complex task in the research of machine learning due to dependence of its performance to the success of learning process and the training method. This paper reviews the implementation of meta-heuristic algorithms in ANNs’ weight optimization by studying their advantages and disadvantages giving consideration to some meta-heuristic members such as Genetic algorithim, Particle Swarm Optimization and recently introduced meta-heuristic algorithm called Harmony Search Algorithm (HSA). Also, the application of local search based algorithms to optimize the ANNs weights and their benefits as well as their limitations are briefly elaborated. Finally, a comparison between local search methods and global optimization methods is carried out to speculate the trends in the progresses of ANNs’ weight optimization in the current resrearch.

Artificial Neural Network Weight Optimization: A Review

The quality of decision using the analytic hierarchy process (AHP) depends upon the consistency of the pairwise comparison matrices (PCM) in the AHP hierarchy. While several studies describe methods to improve consistency, the related issue of retaining authenticity of the judgements has received far less attention. In this paper, a multi-objective genetic algorithm is presented for the purpose of reducing the inconsistency of a PCM while ensuring a high degree of authenticity with respect to the original input. A number of Pareto-optimal solutions are generated as a result of the optimization. Heuristics for choosing one of these PCMs based on a trade-off between consistency and authenticity is also presented. To demonstrate the effectiveness of the proposed method two inconsistent PCMs are selected for rectification. Rectified PCMs from the proposed method as well as from other established methods are compared. It is seen that the proposed method results in consistency that compares favorably with existing methods while retaining a greater degree of authenticity. Though the proposed method is slow and computationally intensive, we believe that this is a cost worth incurring in the interest of reliability and authenticity of judgements.

Using genetic algorithm to improve consistency and retain authenticity in the analytic hierarchy process

Analytic hierarchy process is very extensive in decision-making of many objects and widely used in many fields as a classical multi attribute decision-making approach. But its judgment matrix is constructed only by decision-maker subjective judgment. Judgment matrix consistency is the core problem in the AHP. In this paper, a nonlinear programming model is proposed for improving the consistency of the judgment matrix. Then a genetic algorithm is designed to solve the nonlinear programming model to determine matrix consistency adjustments. The improved analytic hierarchy process is more objective, more logical and more compact.

Consistency Modification of Judgment Matrix Based on Genetic Algorithm in Analytic Hierarchy Process

BP algorithm can be applied in comprehensive evaluation. A hybrid neural network based on the combination of GA and BP algorithms is proposed. The algorithm made fully use of GA's global searching to improve the learning ability of BP neural network. Then, the method is used in comprehensive evaluation, which the genetic algorithm can improve the weights of the neural network and enhance the training precision of the neural network. The experimental results show that the method is valid and feasible.

Qiongxin Liu

Papers

Consistency Modification of Judgment Matrix Based on Genetic Algorithm in Analytic Hierarchy Process

A BP Neural Network Model Based on Genetic Algorithm for Comprehensive Evaluation