An epsilon‐constraint method for fully fuzzy multiobjective linear programming

Pérez‐Cañedo, Boris; Verdegay, José L.; Pérez, Ridelio Miranda

doi:10.1002/int.22219

Cited by 23 publications

(19 citation statements)

References 43 publications

(117 reference statements)

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“…

-constraint is a broadly applied method to get the exact solutions for multi-objective problems [57] . Plenty of successful applications have been reported to solve various problems for this method [58] .…”

Section: Solution Methodsmentioning

confidence: 99%

A stochastic bi-objective simulation–optimization model for plasma supply chain in case of COVID-19 outbreak

Shirazi

Kia

Ghasemi

2021

Applied Soft Computing

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As of March 24, 2020, the Food and Drug Administration (FDA) authorized to bleed the newly recovered from Coronavirus Disease 2019 (COVID-19), i.e., the ones whose lives were at risk, separate Plasma from their blood and inject it to COVID-19 patients. In many cases, as observed the plasma antibodies have cured the disease. Therefore, a four-echelon supply chain has been designed in this study to locate the blood collection centers, to find out how the collection centers are allocated to the temporary or permanent plasma-processing facilities, how the temporary facilities are allocated to the permanent ones, along with determining the allocation of the temporary and permanent facilities to hospitals. A simulation approach has been employed to investigate the structure of COVID-19 outbreak and to simulate the quantity of plasma demand. The proposed bi-objective model has been solved in small and medium scales using -constraint method, Strength Pareto Evolutionary Algorithm II (SPEA-II), Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi-Objective Grey Wolf Optimizer (MOGWO) and Multi Objective Invasive Weed Optimization algorithm (MOIWO) approaches. One of the novelties of this research is to study the system dynamic structure of COVID-19’s prevalence so that to estimate the required plasma level by simulation. Besides, this paper has focused on blood substitutability which is becoming increasingly important for timely access to blood. Due to shorter computational time and higher solution quality, MOIWO is selected to solve the proposed model for a large-scale case study in Iran. The achieved results indicated that as the plasma demand increases, the amount of total system costs and flow time rise, too. The proposed simulation model has also been able to calculate the required plasma demand with 95% confidence interval.

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Section: Solution Methodsmentioning

confidence: 99%

A stochastic bi-objective simulation–optimization model for plasma supply chain in case of COVID-19 outbreak

Shirazi

Kia

Ghasemi

2021

Applied Soft Computing

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“…Pérez-Cañedo et al [15] showed that the transformation of FFMOLP problems into crisp multi-objective linear programming problems by means of linear ranking functions does not guarantee Pareto optimal fuzzy solutions. Thus, taking as a starting point the lexicographic method for fully fuzzy single-objective linear programming presented in Section 2.3.6, in [15], the authors extended the classical definitions of dominance and Pareto optimality to the fuzzy case using lexicographic ranking criteria, and proposed a fuzzy epsilon-constraint method that guarantees Pareto optimal fuzzy solutions. In what follows, we briefly present their approach only considering the minimization case.…”

Section: Fuzzy Epsilon-constraint Methodsmentioning

confidence: 99%

“…Despite being widely used, linear ranking functions have little discriminative capabilities, as they may map different FNs into the same real number, which, in turn, may yield unreasonable results [14]. Lexicographic ranking criteria can overcome this issue by defining multiple comparison indices arranged in a hierarchical fashion [15]. This fact has motivated the development of lexicographic methods for FLP.…”

Section: Introductionmentioning

confidence: 99%

Lexicographic Methods for Fuzzy Linear Programming

2020

Self Cite

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Fuzzy Linear Programming (FLP) has addressed the increasing complexity of real-world decision-making problems that arise in uncertain and ever-changing environments since its introduction in the 1970s. Built upon the Fuzzy Sets theory and classical Linear Programming (LP) theory, FLP encompasses an extensive area of theoretical research and algorithmic development. Unlike classical LP, there is not a unique model for the FLP problem, since fuzziness can appear in the model components in different ways. Hence, despite fifty years of research, new formulations of FLP problems and solution methods are still being proposed. Among the existing formulations, those using fuzzy numbers (FNs) as parameters and/or decision variables for handling inexactness and vagueness in data have experienced a remarkable development in recent years. Here, a long-standing issue has been how to deal with FN-valued objective functions and with constraints whose left- and right-hand sides are FNs. The main objective of this paper is to present an updated review of advances in this particular area. Consequently, the paper briefly examines well-known models and methods for FLP, and expands on methods for fuzzy single- and multi-objective LP that use lexicographic criteria for ranking FNs. A lexicographic approach to the fuzzy linear assignment (FLA) problem is discussed in detail due to the theoretical and practical relevance. For this case, computer codes are provided that can be used to reproduce results presented in the paper and for practical applications. The paper demonstrates that FLP that is focused on lexicographic methods is an active area with promising research lines and practical implications.

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“…Traditional optimization algorithms are generally aimed at structural problems, most of which fall into the category of convex optimization [9]. The essence of the algorithm is to transform multiple objective functions into a single objective function based on some rules and then solve the MOP by a single-objective optimization method [10,11]. Although the traditional optimization algorithm has a fast convergence speed and a clear termination criterion, it can only find one of the Pareto solution sets of the optimization problem at a time, and the solution results are strongly dependent on the initial values.…”

Section: Introductionmentioning

confidence: 99%

An Improved Multi-Objective Artificial Physics Optimization Algorithm Based on Multi-Strategy Fusion

Sun

Fan

et al. 2022

IEEE Access

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The elements of the population of the artificial physics optimization (APO) algorithm are assigned mass, velocity, and displacement attributes. It is a new type of heuristic algorithm, but it still has defects such as low efficiency of non-dominated solution selection and unbalanced search capacity of global and local. This paper introduces the mechanism of improved fast non-dominant sorting and partitionguided individual evolution into the APO algorithm to overcome this imperfection. An improved multiobjective artificial physics optimization algorithm based on fast non-dominated sorting (IFNS-MOAPO) is proposed, which is the result of integrating numerous strategies into the APO algorithm. Firstly, an improved fast non-dominated sorting strategy is introduced. This strategy can increase the efficiency of selecting non-dominated solutions and decrease the running time of the algorithm. Secondly, the mechanism of individual evolution guided by partition is proposed. For individuals in infeasible and feasible domains, different mass functions and virtual force calculation rules are adopted to update the algorithm iteratively to boost the convergence performance. To verify the comprehensive performance of the IFNS-MOAPO algorithm, seven benchmark test problems are selected for simulation experiments and compared with five algorithms in terms of runtime duration, Pareto front plots, and metric values. The results show that the IFNS-MOAPO algorithm has good distribution and can converge to the true Pareto front quickly. It is a useful tool for solving constrained multi-objective optimization problems (CMOPs).

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An epsilon‐constraint method for fully fuzzy multiobjective linear programming

Cited by 23 publications

References 43 publications

A stochastic bi-objective simulation–optimization model for plasma supply chain in case of COVID-19 outbreak

A stochastic bi-objective simulation–optimization model for plasma supply chain in case of COVID-19 outbreak

Lexicographic Methods for Fuzzy Linear Programming

An Improved Multi-Objective Artificial Physics Optimization Algorithm Based on Multi-Strategy Fusion

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