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A Kaleodoscopic View of Fuzzy Stochastic Optimization*

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American Journal of Operations Research 2021年第6期11卷 283-308页

作者： Yves Tinda Mangongo justin dupar busili kampempe Monga Kalonda Luhandjula Département de Mathématiques et Informatique Université de Kinshasa Kinshasa Democratic Republic of the Congo Département de Mathématique-Informatique Université de Kisangani Kisangani Democratic Republic of the Congo

The last three decades have witnessed development of optimization under fuzziness and randomness also called Fuzzy Stochastic Optimization. The main objective of this new field is the need for basing many human decisions on information which is both fuzzily imprecise and probabilistically uncertain. Consistency indexes providing a union nexus between possibilities and probabilities of uncertain events exist in the literature. Nevertheless, there are no reliable transformations between them. This calls for new paradigms for coping with mathematical models involving both fuzziness and randomness. Fuzzy Stochastic Optimization (FSO) is an attempt to fulfill this need. In this paper, we present a panoramic view of Fuzzy Stochastic Optimization emphasizing the methodological aspects. The merits of existing methods are also briefly discussed along with some related theoretical aspects.

关键词： Optimization Randomness Fuzziness Fuzzy Random Variable

New Hybrid Algorithm Based on BicriterionAnt for Solving Multiobjective Green Vehicle Routing Problem

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American Journal of Operations Research 2023年第3期13卷 33-52页

作者： Emile Nawej Kayij Joél Lema Makubikua justin dupar kampempe busili Faculty of Technological and Sciences University of Kinshasa Kinshasa Democratic Republic of the Congo

The main objective of this paper is to propose a new hybrid algorithm for solving the Bi objective green vehicle routing problem (BGVRP) from the BicriterionAnt metaheuristic. The methodology used is subdivided as follows: first, we introduce data from the GVRP or instances from the literature. Second, we use the first cluster route second technique using the k-means algorithm, then we apply the BicriterionAntAPE (BicriterionAnt Adjacent Pairwise Exchange) algorithm to each cluster obtained. And finally, we make a comparative analysis of the results obtained by the case study as well as instances from the literature with some existing metaheuristics NSGA, SPEA, BicriterionAnt in order to see the performance of the new hybrid algorithm. The results show that the routes which minimize the total distance traveled by the vehicles are different from those which minimize the CO2 pollution, which can be understood by the fact that the objectives are conflicting. In this study, we also find that the optimal route reduces product CO2 by almost 7.2% compared to the worst route.

关键词： Metaheuristics Green Vehicle Routing Problem Ant Colony Algorithm Genetic Algorithms Green Logistics

Fuzzy Global Stability Analysis of the Dynamics of Malaria with Fuzzy Transmission and Recovery Rates

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American Journal of Operations Research 2021年第6期11卷 257-282页

作者： Yves Tinda Mangongo Joseph-Désiré Kyemba Bukweli justin dupar busili kampempe Department of Mathematics and Computer Science Faculty of Sciences University of Kinshasa Kinshasa D.R. Congo

In this paper, fuzzy techniques have been used to track the problem of malaria transmission dynamics. The fuzzy equilibrium of the proposed model was discussed for different amounts of parasites in the body. We proved that when the amounts of parasites are less than the minimum amounts required for disease transmission (), we reach the model disease-free equilibrium. Using Choquet integral, the fuzzy basic reproduction number through the expected value of fuzzy variable was introduced for the fuzzy Susceptible, Exposed, Infected, Recovered, susceptible-Susceptible, Exposed and Infected (SEIRS-SEI) malaria model. The fuzzy global stabilities were introduced and discussed. The disease-free equilibrium is globally asymptotically stable if or if the basic reproduction number is less than one (). Whe

关键词： Malaria Fuzzy Analysis Fuzzy Basic Reproduction Number Fuzzy Variable Credibility Measure Fuzzy Equilibrium Fuzzy Global Stability

A New Approach for Solving Fuzzy Linear Multi-Criterion Problems: An Approach Based on Minimization of the Errors Functions

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American Journal of Operations Research 2023年第1期13卷 1-17页

作者： Joél Lema Makubikua Amani Wema Yves Tinda Mangongo Joseph-Désiré Kyemba Bukweli justin dupar busili kampempe Département des Mathématiques et Informatique Université de Kinshasa Kinshasa The Democratic Republic of the Congo Conférence Congolaise de Recherche en Informatique et en Mathématiques Appliquées COCORIMA Kinshasa The Democratic Republic of the Congo

The main purpose of this paper is to build a new approach for solving a fuzzy linear multi-criterion problem by defining a function called “error function”. For this end, the concept of level set is used to construct the error function. In addition, we introduce the concept of deviation variable in the definition of the error function. The algorithm of the new approach is summarized in three main steps: first, we transform the original fuzzy problem into a deterministic one by choosing a specific level . second, we solve separately each uni-criteria problem and we compute the error function for each criteria. Finally, we minimize the sum of error functions in order to obtain the desired compromise solution. A numerical example is done for a comparative study with some existing approaches to show the effectiveness of the new approach.

关键词： Deviation Variable Compromise Solution Membership Function Error Function Decision-Making Function