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Minimal Representations of a Face of a Convex Polyhedron and Some Applications

ACTA MATHEMATICA VIETNAMICA 2021年第4期46卷 761-778页

作者： Tu, Ta Van Corvinus Univ Budapest Dept Operat Res H-1093 Budapest Hungary

In this paper, we propose a method for determining all minimal representations of a face of a polyhedron defined by a system of linear inequalities. Main difficulties for determining prime and minimal representations of a face are that the deletion of one redundant constraint can change the redundancy of other constraints and the number of descriptor index pairs for the face can be huge. To reduce computational efforts in finding all minimal representations of a face, we prove and use properties that deleting strongly redundant constraints does not change the redundancy of other constraints and all minimal representations of a face can be found only in the set of all prime representations of the face corresponding to the maximal descriptor index set for it. The proposed method is based on a top-down search strategy, is easy to implement, and has many computational advantages. Based on minimal representations of a face, a reduction of degeneracy degrees of the face and ideas to improve some known methods for finding all maximal efficient faces in multiple objective linear programming are presented. Numerical examples are given to illustrate the method.

关键词： Faces of a polyhedron Degeneracy degrees of faces Prime and minimal representations of a face Maximal descriptor index set multiple objective programming

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A Multi-objective Biased Random-Key Genetic Algorithm for Service Technician Routing and Scheduling Problem 12th

A Multi-objective Biased Random-Key Genetic Algorithm for Se...

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12th International Conference on Computational Logistics (ICCL)

作者： Damm, Ricardo de Brito Ronconi, Debora P. Univ Sao Paulo Polytech Sch Sao Paulo Brazil

ISBN: (纸本)9783030876722;9783030876715

Every day many service companies need to plan the tasks that will be carried out by its field staff. Maintenance service technicians have to perform a set of jobs at different locations in a city or state. This problem can be defined as the Service Technician Routing and Scheduling Problem in which tasks have different priorities and time windows, and technicians have different skills and working hours. Scheduling must account for technicians' lunch breaks, which must be respected. Each task is performed by only one technician. To ensure quality customer service and consumer rights are upheld, a novel approach is proposed: to address the problem in a multi-objective context aiming to execute the priority tasks and, simultaneously, to serve the customers at the beginning of their time windows. A Multi-objective Biased Random-Key Genetic Algorithm (BRKGA) was customized to tackle this NP-hard optimization problem and then compared with the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The analyzed methods showed similar performance for small instances, but for medium- and large-sized instances the proposed method presented superior performance and more robust results.

关键词： multiple objective programming Routing and scheduling technicians Time windows Biased Random-Key Genetic Algorithm NSGA-II

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A computationally efficient algorithm to approximate the pareto front of multi-objective linear fractional programming problem

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RAIRO-OPERATIONS RESEARCH 2019年第4期53卷 1229-1244页

作者： Stanojevic, Bogdana Stanojevic, Milan Serbian Acad Arts & Sci Math Inst Belgrade Serbia Univ Belgrade Fac Org Sci Belgrade Serbia

The main contribution of this paper is the procedure that constructs a good approximation to the non-dominated set of multiple objective linear fractional programming problem using the solutions to certain linear optimization problems. In our approach we propose a way to generate a discrete set of feasible solutions that are further used as starting points in any procedure for deriving efficient solutions. The efficient solutions are mapped into non-dominated points that form a 0th order approximation of the Pareto front. We report the computational results obtained by solving random generated instances, and show that the approximations obtained by running our procedure are better than those obtained by running other procedures suggested in the recent literature. We evaluated the quality of each approximation using classic metrics.

关键词： Fractional programming multiple objective programming efficient solution non-dominated point 0th order approximation

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Are soft skills conditioned by conflicting factors? A multiobjective programming approach to explore the trade-offs

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ECONOMIC ANALYSIS AND POLICY 2021年 72卷 18-40页

作者： Marcenaro-Gutierrez, O. D. Lopez-Agudo, L. A. Henriques, C. O. Univ Malaga Dept Appl Econ Stat & Econometr C Ejido 6 Malaga 29071 Spain Polytech Coimbra Coimbra Business Sch Res Ctr ISCAC Quinta Agr P-3040316 Coimbra Portugal Univ Coimbra INESC Coimbra DEEC P-3030290 Coimbra Portugal Univ Coimbra CeBER Fac Econ Av Dias Silva 165 P-3004512 Coimbra Portugal

Despite the relevance of noncognitive skills (i.e. soft skills) for individual development and for certain forms of employment, they tend to be overlooked in studies centred on educational performance. This study brings an additional contribution to the growing interest on these skills by exploring their main determinants and by providing an additional understanding of how they are influenced by socio-economic and family background. To this end, a multiobjective programming model has been developed, whose coefficients are instantiated by the results of several econometric estimations, in which distinct (and conflicting) aspects of multiple soft skills are considered. Hence, by coupling econometric with multiobjective optimisation modelling approaches we provide an overarching framework for assessing the trade-offs between the different dimensions of noncognitive skills. Data from the most populated region of Spain are used. Overall, our findings highlight the trade-off between different soft skills, which are particularly conditioned by students' gender. (C) 2021 Economic Society of Australia, Queensland. Published by Elsevier B.V.

关键词： Noncognitive skills Econometric analysis multiple objective programming

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Industrial information integration method to vehicle routing optimization using grey target decision

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JOURNAL OF INDUSTRIAL INFORMATION INTEGRATION 2022年 27卷

作者： Guo, Kai Hu, Shanshan Zhu, Hai Tan, Wenan Henan Univ Sci & Technol Sch Management Luoyang 471023 Henan Peoples R China Henan Collaborat Innovat Ctr Nonferrous Met Luoyang 471000 Henan Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Comp Sci & Technol 29 Jiangjun Ave Nanjing 211106 Peoples R China Shanghai Polytech Univ Sch Comp & Informat Engn Shanghai 201209 Peoples R China

Industrial information integration can help companies develop supply chain systems and is a good framework for vehicle routing problem. To address the problems of excessive energy consumption, environmental pollution caused by carbon dioxide emission, and timeliness in the transportation process, a multi-objective vehicle routing optimization model was proposed to minimise transportation, carbon emission, and time window penalty costs. In the proposed model, an elitist nondominated sorting genetic algorithm was used to obtain the Pareto optimal solution. Furthermore, the optimal distribution path was selected by using multi-objective grey target decision making according to entropy value. Finally, a real distribution case was analysed, and the calculated optimal path was compared with the actual path of the case to verify the feasibility of the proposed model and algorithm. The results showed that the proposed model and algorithm can be effectively used to reduce the target cost.

关键词： Industrial information integration Grey target decision multiple objective programming Routing optimization Elitist nondominated sorting genetic algorithm

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UAV routing for reconnaissance mission: A multi-objective orienteering problem with time-dependent prizes and multiple connections

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COMPUTERS & OPERATIONS RESEARCH 2022年 145卷 1页

作者： Dasdemir, Erdi Batta, Rajan Koksalan, Murat Ozturk, Diclehan Tezcaner Hacettepe Univ Dept Ind Engn TR-06800 Ankara Turkey Univ Buffalo SUNY Dept Ind & Syst Engn Buffalo NY 14260 USA Middle East Tech Univ Dept Ind Engn TR-06800 Ankara Turkey Univ Michigan Ross Sch Business Ann Arbor MI 48109 USA

We address the route planning problem of an unmanned air vehicle (UAV) tasked with collecting information from a radar-monitored environment for a reconnaissance mission. The UAV takes off from a home base, visits a set of targets, and finishes its movement at a final base. Collectable information at a target depends on the time the target is visited by the UAV. There are multiple trajectory alternatives between the target pairs with different travel time and threat attributes. A route plan involves the selection of the targets to visit, the order of visit to the targets, and the trajectories to follow between the targets. multiple routing objectives, information collection, mission duration and mission safety, are considered to present the trade-offs among the objectives to the route planner. The problem is classified as a multi-objective orienteering problem with time-dependent prizes and multiple connection options. A mixed integer programming model that can be used for small-sized problems is formulated. Larger problems are addressed with a hybrid algorithm involving heuristics and exact approaches. A case study based on a terrain in the State of Colorado is presented. Finally, some practical issues for the UAV route planning problem is discussed.

关键词： multiple objective programming UAV routing Orienteering Time-dependent prizes Mixed integer programming

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Control of perishable inventory system with uncertain perishability process using neural networks and robust multicriteria optimization

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BULLETIN OF THE POLISH ACADEMY OF SCIENCES-TECHNICAL SCIENCES 2022年第3期70卷

作者： Cholodowicz, Ewelina Orlowski, Przemyslaw West Pomeranian Univ Technol Szczecin Fac Elect Engn Dept Automat & Robot Al Piastow 17 PL-70310 Szczecin Poland

The inventory systems are highly variable and uncertain due to market demand instability, increased environmental impact, and perishability processes. The reduction of waste and minimization of holding and shortage costs are the main topics studied within the inventory management area. The main difficulty is the variability of perishability and other processes that occurred in inventory systems and the solution for a trade-off between sufficient inventory level and waste of products. In this paper, the approach for resolving this trade-off is proposed. The presented approach assumes the application of a state-feedback neural network controller to generate the optimal quantity of orders considering an uncertain deterioration process and the FIFO issuing policy. The development of the control system is based on state-space close loop control along with neural networks. For modelling the perishability process Weibull distribution and FIFO policy are applied. For the optimization of the designed control system, the evolutionary NSGA-II algorithm is used. The robustness of the proposed approach is provided using the minimax decision rule. The worst-case scenario of an uncertain perishability process is considered. For assessing the proposed approach, simulation research is conducted for different variants of controller structure and model parameters. We perform extensive numerical simulations in which the assessment process of obtained solutions is conducted using hypervolume indicator and average absolute deviation between results obtained for the learning and testing set. The results indicate that the proposed approach can significantly improve the performance of the perishable inventory system and provides robustness for the uncertain changes in the perishability process.

关键词： multiple objective programming optimal control genetic algorithm perishable inventories inventory control

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Multiobjective Integer programming: Synergistic Parallel Approaches

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INFORMS JOURNAL ON COMPUTING 2020年第2期32卷 461-472页

作者： Pettersson, William Ozlen, Melih Univ Glasgow Sch Comp Sci Glasgow G12 8QQ Lanark Scotland RMIT Univ Sch Sci Melbourne Vic 3000 Australia

Exactly solving multiobjective integer programming (MOIP) problems is often a very time-consuming process, especially for large and complex problems. Parallel computing has the potential to significantly reduce the time taken to solve such problems but only if suitable algorithms are used. The first of our new algorithms follows a simple technique that demonstrates impressive performance for its design. We then go on to introduce new theory for developing more efficient parallel algorithms. The theory utilises elements of the symmetric group to apply a permutation to the objective functions to assign different workloads and applies to algorithms that order the objective functions lexicographically. As a result, information and updated bounds can be shared in real time, creating a synergy between threads. We design and implement two algorithms that take advantage of such a theory. To properly analyse the running time of our three algorithms, we compare them against two existing algorithms from the literature and against using multiple threads within our chosen integer programming solver, CPLEX. This survey of six different parallel algorithms, to our knowledge the first of its kind, demonstrates the advantages of parallel computing. Across all problem types tested, our new algorithms are on par with existing algorithms on smaller cases and massively outperform the competition on larger cases. These new algorithms, and freely available implementations, allow the investigation of complex MOIP problems with four or more objectives.

关键词： multiple objective programming parallel computing integer programming combinatorial optimisation

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A concave optimization-based approach for sparse multiobjective programming

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OPTIMIZATION LETTERS 2020年第3期14卷 535-556页

作者： Cocchi, Guido Levato, Tommaso Liuzzi, Giampaolo Sciandrone, Marco Univ Firenze Dipartimento Ingn Informaz Via Santa Marta 3 I-50139 Florence Italy CNR Ist Anal Sistemi & Informat Via Taurini 19 I-00185 Rome Italy

The paper is concerned with multiobjective sparse optimization problems, i.e. the problem of simultaneously optimizing several objective functions and where one of these functions is the number of the non-zero components (or the 0-norm) of the solution. We propose to deal with the 0-norm by means of concave approximations depending on a smoothing parameter. We state some equivalence results between the original nonsmooth problem and the smooth approximated problem. We are thus able to define an algorithm aimed to find sparse solutions and based on the steepest descent framework for smoothmultiobjective optimization. The numerical results obtained on a classical application in portfolio selection and comparison with existing codes show the effectiveness of the proposed approach.

关键词： multiple objective programming Sparse optimization Concave programming Multiobjective steepest descent methods

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A possibilistic optimization over an integer efficient set within a fuzzy environment

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RAIRO-OPERATIONS RESEARCH 2020年第5期54卷 1437-1452页

作者： Menni, Assia Chaabane, Djamal USTHB Dept Operat Res Fac Math AMCD RO Lab Bp 32 El Alia Algiers 16121 Algeria

Optimizing a linear function over the efficient set of a multiple objective Integer Linear programming (MOILP) problem is known as a difficult problem to deal with, since a discrete efficient set is generally not convex and not explicitly known. Such problem becomes more and more difficult when parameters are defined with uncertainty. In this work, we deal with problems of this type for which parameters are imprecise and are assumed to be trapezoidal fuzzy numbers. The method is based on possibility and necessity measures introduced in the literature by D. Dubois and H. Prade.

关键词： multiple objective programming discrete optimization Fuzzy parameters possibility measure necessity measure

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