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An algorithm to solve multi-objective integer quadratic programming problem

ANNALS OF OPERATIONS RESEARCH 2024年第1-3期332卷 433-459页

作者： Kushwah, Prerna Sharma, Vikas TIET Sch Math Patiala India

The multi-objective integer programming problem often occurs in multi-criteria decision making situations, where the decision variables are integers. In the present paper, we have discussed an algorithm for finding all efficient solutions of a multi-objective integer quadratic programming problem. The proposed algorithm is based on the aspect that efficient solutions of a multi-objective integer quadratic programming problem can be obtained by enumerating ranked solutions of an integer quadratic programming problem. For determining ranked solutions of an integer quadratic programming problem, we have constructed a related integer linear programming problem and from ranked solutions of this integer linear programming problem, ranked solutions of the original integer quadratic programming problem are generated. Theoretically, we have shown that the developed method generates the set of all efficient solutions in a finite number of steps, and numerically we have elaborated the working of our algorithm and compared our results with existing algorithms. Further, we have analyzed that the developed method is efficient for solving a multi-objective integer quadratic programming problem with a large number of constraints, variables and objectives.

关键词： Efficient set integer programming problem Multiple objective programming problem Quadratic programming problem

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On solving fuzzy rough multiobjective integer linear fractional programming problem

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2019年第5期37卷 6499-6511页

作者： Ammar, El Saeed Eljerbi, Tarek Tanta Univ Fac Sci Dept Math Tanta Egypt

In solving real life fractional programming problem, we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To overcome these limitations, the fuzzy rough approach is applied to this problem. In this paper, an efficient method is proposed for solving fuzzy rough multiobjective integer linear fractional programming problem where all the variables and parameters are fuzzy rough numbers. Here, the fuzzy rough multiobjective problem transformed into an equivalent multiobjective integer linear fractional programming problem. Furthermore, from the obtained problem, five crisp multiobjective integer linear fractional programming problems are constructed and the resultant problems are solved as a crisp integer linear programming problem by using Dinkelbach concept. Finally, the effectiveness of the proposed procedure is illustrated through numerical examples.

关键词： Fractional programming integer programming problem triangular fuzzy rough numbers fuzzy rough linear programming

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A STUDY ON HIERARCHICAL PRODUCTION PLANNING FRAMEWORK FOR ENGINEER-TO-ORDER PRODUCTION OF LARGE PRODUCTS

A STUDY ON HIERARCHICAL PRODUCTION PLANNING FRAMEWORK FOR EN...

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International Symposium on Flexible Automation (ISFA)

作者： Iwamura, Koji Morinaga, Eiji Hirahara, Yoshiyuki Fukuda, Masamitsu Niinuma, Ayumu Oshima, Hirotomo Namioka, Yasuo Osaka Metropolitan Univ Osaka Japan Toshiba Co Ltd Yokohama Kanagawa Japan

ISBN: (纸本)9780791887882

Engineer-to-order (ETO) production is a method in which products are designed and manufactured in response to customer orders. Typical products of ETO production targeted in this study are large products such as power plants, plants, and shipbuilding. These products have long lead times and delivery times, and production plans need to be generated for a year or more in advance. This study proposes a hierarchical production planning (HPP) framework to generate long-term, medium-term, and short-term production plans using common granularity of production equipment and unit time on production planning method for ETO production of large products. A load planning required for the long-term production plan is formulated as an integer programming problem, and the load plans are generated using a mathematical programming solver and a constraint programming solver.

关键词： Engineer-to-order production Hierarchical production planning Load planning integer programming problem

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Intersection traffic deadlock formation and its probability: A petri net-based modeling approach

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IET INTELLIGENT TRANSPORT SYSTEMS 2022年第10期16卷 1342-1363页

作者： Qi, HongSheng Yu, Yi Tang, Qing Hu, XianBiao Zhejiang Univ Coll Civil Engn & Architecture Hangzhou Peoples R China Penn State Univ Dept Civil & Environm Engn 212 Sackett Bldg University Pk PA 16801 USA

Although traffic deadlock at an intersection is a common phenomenon during rush hours, the deadlock formation metrics such as formation probability and duration have not been derived yet. As Petri Net (PN)-based approach can formulate the deadlock formation in analytical form and has been applied in numerous traffic flow studies, the PN is employed to investigate the deadlock formation probability and duration. First, each of the four main components of an intersection is formulated, namely vehicle trajectory, traffic signal, vehicle arrivals, and conflict behaviour, as a Petri Net (or IntersectionPN), and name them CellularPN, TrafficLightPN, DemandPN, and ConflictPN, respectively. Together, the entire intersection becomes an IntersectionPN, on which the system's three classes of states are defined, namely the deadlock state, the trap state, and the live state. The deadlock occurrence is formulated as an integer programming problem, while the formation probability and duration are studied by constructing a reachability graph that leads to the Markov chain of the system. A case study shows that the developed model is able to reproduce an intersection deadlock, and that the focus is on two priority behaviours: "First Enter First Serve" and "Pure Stochastic". The results show that different behaviours lead to different deadlock formation metrics and that, when the saturation flow rate degrades (due to events such as severe weather conditions), a deadlock will occur more quickly. The research results provide the analysis tool for probabilistic deadlock formation. It can also be applied to the intersection deadlock prevention and control.

关键词： Markov chain IntersectionPN live state conflict behaviour deadlock state vehicle trajectory traffic information systems deadlock formation probability petri net-based approach integer programming pure stochastic CellularPN ConflictPN trap state rush hours reachability graph integer programming problem road traffic DemandPN Petri nets vehicle arrivals traffic signal TrafficLightPN deadlock occurrence intersection deadlock prevention probability Markov processes reachability analysis intersection traffic deadlock formation probabilistic deadlock formation first enter first serve

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A new model for curriculum-based university course timetabling

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OPTIMIZATION LETTERS 2021年第5期15卷 1601-1616页

作者： Colajanni, Gabriella Daniele, Patrizia Univ Catania Dept Math & Comp Sci Viale A Doria 6 I-95125 Catania Italy

The Curriculum Based university Course Timetabling (CCT) problem consists in determining the best scheduling of university course lessons in a given time interval, assigning the lessons of each course to classrooms and time periods, so that a series of constraints is satisfied. These constraints are divided into two categories: hard constraints, necessary so that the programming can actually be implemented, and soft constraints, which involve qualitative measures. This paper deals with the study of the CCT problem. We formulate a new and complete model that satisfies both the planning constraints and those on the compactness of the curricula, the distribution of the lessons (in the examined time frame), the teachers' preferences, the minimum number of working days, maximum capacity and stability of the classrooms (which aims to minimize the daily movements of students among classrooms) so that the resulting timetable is of high quality. The formulated model, with appropriate adaptations, has been applied to the real case study of the first year of the Mathematics Degree Course of the University of Catania, Italy.

关键词： University course timetable Curriculum based Scheduling integer programming problem

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Minimizing risk in Bayesian supply chain networks

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COMPUTERS & INDUSTRIAL ENGINEERING 2022年 169卷

作者： Ruskey, Brendan Rosenberg, Eric Lehigh Univ Bethlehem PA USA Georgian Court Univ Lakewood NJ USA

We develop an approach for minimizing expected unmet demand in a supply chain modelled using a Bayesian network. We allow for nodes to be upgraded, subject to a budget constraint, to reduce the probability that the node becomes non-operational. We formulate the problem of selecting an optimal set of node upgrades as a linear binary integer program (BIP). Ours is the first formulation of expected loss minimization in Bayesian-modelled supply chains as a BIP. Unlike previous published formulations, our formulation allows for the conditional probability table of each node in the Bayesian network to be quite general, including allowing an upgraded node to have a nonzero probability of failure, and allowing multiple types of upgrades for a node. This reflects real world scenarios, including those in which node upgrades do not completely eliminate risk. We present computational results for small problems and illustrate how the solution set changes with the budget. Results for a larger food supply chain with 44 nodes and 63 arcs are also discussed. Finally, we present a preprocessing method for reducing the number of constraints needed for the BIP formulation, and evaluate the savings in run time achieved by applying our constraint reduction method.

关键词： Bayesian networks Supply chain networks Risk mitigation integer programming problem

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Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2020年第1期11卷 189-222页

作者： Kumar, P. Senthil Navodaya Inst Technol Dept Humanities & Sci Bijanagera Rd PB 26Navodaya Nagar Raichur 584103 Karnataka India

In this article, the crisp, fuzzy and intuitionistic fuzzy optimization problem is formulated. The basic definitions and notations related to optimization problems are given in the preliminaries section. Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set is presented in this article. Then, with the help of the proposed algorithm the optimal solution of the crisp, fuzzy and intuitionistic fuzzy optimization problems are determined. A new theorem related to type-2 fuzzy/type-2 intuitionistic fuzzy optimization problems is proposed and proved. Some new and concrete results related to type-2 fuzzy/type-2 intuitionistic fuzzy optimization problems are presented. To illustrate the proposed method, some real-life numerical examples are presented. The proposed article provides seven fully worked examples with screenshots of output summaries from the software used in the computations for better understanding. The advantages of the proposed approach as compared to other existing work are also specified. Detail analyses of the comparative study as well the discussion are given. To show the advantages of the proposed approach, superiority analysis is discussed. Comparison analysis and the advantages of the proposed operators are also discussed. Some managerial applications and the advantages of the proposed approach are given. Finally, conclusion and future research directions are also given.

关键词： Fuzzy set Fuzzy number TFN TrFN Intuitionistic fuzzy set Intuitionistic fuzzy number TIFN TrIFN Type-2 FTP Type-2 IFTP Type-2 IFSTP FAP IFAP IFSAP Linear programming method integer programming problem Optimal solution Optimal assignment PSK theorem

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An Adaptive Discrete Brain Storm Algorithm Solves 3D Protein Structure Prediction

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INTERNATIONAL JOURNAL OF ADVANCED COMPUTER SCIENCE AND APPLICATIONS 2021年第8期12卷 850-859页

作者： Fahim, Alaa Abdelraheem, Nehad Assiut Univ Fac Sci Math Dept Assiut Egypt Assiut Univ Fac Comp Sci & Informat Syst Assiut Egypt

Brain Storm Optimization (BSO) is one of the major effective swarm intelligence algorithms that simulate the human brainstorming process to find optimality for optimization problems. BSO method has successfully been applied to many real-world problems. This study employs BSO method, called BSO-IP, to solve the integer programming problem. Our method collects best solutions to generate new solutions that then search for optimal solutions in all areas of search *** BSO-IP method solves some benchmark integer programming problems to test its efficiency. The BSO-IP is used to simulate the 3D protein structure prediction problem, which is mathematically presented as an integer programming problem to approve the viability and helpfulness of our proposed Algorithm. The experimental results of different benchmarks protein structure show that our proposed method is superior in high performance, convergence, and stability in predicting protein structure. We examined our strategy results to be promising compared to other results.

关键词： Brain storm optimization integer programming problem three dimensional protein structure prediction

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Energy-efficient hierarchical cooperative caching optimisation for 5G networks

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IET COMMUNICATIONS 2019年第6期13卷 687-695页

作者： Xie, Renchao Tang, Qinqin Huang, Tao Beijing Univ Posts & Telecommun State Key Lab Networking & Switching Technol Beijing Peoples R China

The caching in fifth generation (5G) networks has been considered as a promising technique to reduce the duplicate traffic transmission and improve the users' quality of experience (QoE). Although many works have been done for caching in 5G networks, most of them focus on the content caching policy design to optimise the users' QoE, the issue to realise the energy efficiency of the whole network is not fully considered. Therefore, in this study, by introducing the hierarchical cooperative caching property, i.e. the core gateway and the base stations can cooperative cache the content, the authors study the problem of the hierarchical cooperative caching policy to realise the energy efficiency. They then formulate the hierarchical cooperative content placement problem as an integer programming problem to minimise the total energy consumption. Also, to reduce the computation complexity, the optimisation algorithm based on the idea of quantum-inspired evolutionary is proposed, which has the fast convergence and approximate to the optimal solution. Finally, extensive simulation results are illustrated to demonstrate the performance of the proposed scheme.

关键词： evolutionary computation cooperative communication cache storage integer programming 5G mobile communication telecommunication computing duplicate traffic transmission content caching policy design energy efficiency total energy consumption energy-efficient hierarchical 5G networks fifth-generation networks user QoE user quality-of-experience integer programming problem

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A DNA Computer Model to Solve integer programming problem

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JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE 2011年第2期8卷 274-281页

作者： Gang, Fang Yan, Zhu Xian Univ Arts & Sci Dept Life Sci Xian 710065 Peoples R China Xian Univ Arts & Sci Dept Comp Sci Xian 710065 Peoples R China

A special DNA computer is designed to solve the integer programming problem. The main body of this kind of DNA computer is piezoelectric genosensor which combines the sensitivity of piezoelectric sensor and DNA hybridization reaction amplified by functionalized magnetic nano-microspheres. It has the merits of simple construction, label-free feature, time-saving detection speed, and conveniently available information. When used in DNA computing, compared with conventional DNA chip, its information is easier to process automatically. Thus it can be used conveniently to construct an automatic computing machine to solve more complicated problems in operational researches. Based on the piezoelectric genosensor and surface DNA computing theory, a new DNA computer model is proposed in this paper. It is suggested that the piezoelectric genosensor can be used as a potential DNA computing chip to construct an automatic DNA computer.

关键词： DNA Computer Functionalized Magnetic Nano-Microspheres integer programming problem Piezoelectric Genosensor

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