Solving fuzzy multi-objective shortest path problem based on data envelopment analysis approach

A deterministic and nature-inspired algorithm for the fuzzy multi-objective path optimization problem

Increasing evaluation indexes have been involved in the network modeling, and some parameters cannot be described precisely. Fuzzy set theory becomes a promising mathematical method to characterize such uncertain parameters. This study investigates the fuzzy multi-objective path optimization problem (FMOPOP), in which each arc has multiple crisp and fuzzy weights simultaneously. Fuzzy weights are characterized by triangular fuzzy numbers or trapezoidal fuzzy numbers. We adopt two fuzzy number ranking methods based on their fuzzy graded mean values and distances from the fuzzy minimum number. Motivated by the ripple spreading patterns on the natural water surface, we propose a novel ripple-spreading algorithm (RSA) to solve the FMOPOP. Theoretical analyses prove that the RSA can find all Pareto optimal paths from the source node to all other nodes within a single run. Numerical examples and comparative experiments demonstrate the efficiency and robustness of the newly proposed RSA. Moreover, in the first numerical example, the processes of the RSA are illustrated using metaphor-based language and ripple spreading phenomena to be more comprehensible. To the best of our knowledge, the RSA is the first algorithm for the FMOPOP that can adopt various fuzzy numbers and ranking methods while maintaining optimality.

Fuzzy efficiency evaluation in relational network data envelopment analysis: application in gas refineries

In contrast to classical data envelopment analysis (DEA), network DEA has attention to the internal structure of a production system and reveals the relationship between the efficiency of system and efficiencies of the processes. However, the flexibility of weights and the need for crisp input and output data in the evaluation process are two major shortcomings of classical network DEA models. This paper presents a common weights approach for a relational network DEA model in a fuzzy environment to measure the efficiencies of the system and the component processes. The proposed approach first finds upper bounds on input and output weights for a given cut level and then it determines a common set of weights (CSW) for all decision-making units (DMUs). Hence, the fuzzy efficiencies of all processes and systems for all DMUs are obtained based on the resulting CSW. The developed fuzzy relational network DEA and the proposed common weights approach are illustrated with a numerical example. The obtained results confirm that the fuzzy data affects over the efficiency scores and complete ranking of DMUs. The applicability of the proposed network model is illustrated by performance evaluation of gas refineries in Iran.

An estimation of distribution algorithm with clustering for scenario-based robust financial optimization

One important problem in financial optimization is to search for robust investment plans that can maximize return while minimizing risk. The market environment, namely the scenario of the problem in optimization, always affects the return and risk of an investment plan. Those financial optimization problems that the performance of the investment plans largely depends on the scenarios are defined as scenario-based optimization problems. This kind of uncertainty is called scenario-based uncertainty. The consideration of scenario-based uncertainty in multi-objective optimization problem is a largely under explored domain. In this paper, a nondominated sorting estimation of distribution algorithm with clustering (NSEDA-C) is proposed to deal with scenario-based robust financial problems. A robust group insurance portfolio problem is taken as an instance to study the features of scenario-based robust financial problems. A simplified simulation method is applied to measure the return while an estimation model is devised to measure the risk. Applications of the NSEDA-C on the group insurance portfolio problem for real-world insurance products have validated the effectiveness of the proposed algorithm.

Using context-dependent DEA to analyze the efficiency of highly funded scientists in China

Funding inputs and research outputs have always been two central issues in the science of science. In recent decades, research funding plays an increasingly important role in scientific research. Thus, it is progressively significant for management authorities to measure the research efficiency of highly funded scientists, which can be helpful for them to make effective policies. However, few researchers use quantitative analysis to study these issues. To promote the research in this field, we begin with collecting a dataset. This dataset contains research funding and other information from 345 highly funded scientists in Mainland China. Next, we use the dataset to measure the efficiency of highly funded scientists based on the data envelopment analysis. In this way, highly funded scientists are placed into several levels according to their research inputs and outputs. We also give their attractiveness and progress scores compared to other grades. The learning path for less efficient scientists is also provided. We find that highly funded scientists have relatively high efficiency in three kinds of projects, such as the Major Research Plan. Besides, the career length and career start year are demonstrated to have a limited impact on the highly funded scientists. These patterns are beneficial for the development of the scientific community and management authorities to make policies.