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A strategic view of University timetabling

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第1期266卷 35-45页

作者： Lindahl, Michael Mason, Andrew J. Stidsen, Thomas Sorensen, Matias Tech Univ Denmark Dept Management Engn Prod Storvet 426 DK-2800 Lyngby Denmark Univ Auckland Engn Sci 70 Symonds St Auckland 1010 New Zealand MaCom AS Vesterbrogade 48 DK-1620 Copenhagen Denmark

University timetabling has traditionally been studied as an operational problem where the goal is to assign lectures to rooms and timeslots and create timetables of high quality for students and teachers. Two other important decision problems arise before this can be solved: what rooms are necessary, and in which teaching periods? These decisions may have a large impact on the resulting timetables and are rarely changed or even discussed. This paper focuses on solving these two strategic problems and investigates the impact of these decisions on the quality of the resulting timetables. The relationship and differences between operational, tactical and strategic timetabling problems are reviewed. Based on the formulation of curriculum-based course timetabling and data from the Second International Timetabling Competition (ITC 2007), three new bi-objective mixed-integer models are formulated. We propose an algorithm based on the E-constraint method to solve them. The algorithm can be used to analyze the impact of having different resources available on most timetabling problems. Finally, we report results on how the three objectives rooms, teaching periods, and quality - influence one another. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Timetabling multiple objective programming Integer programming

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SUFFICIENT CONDITION FOR PARTIAL EFFICIENCY IN A BICRITERIA NONLINEAR CUTTING STOCK PROBLEM

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RAIRO-OPERATIONS RESEARCH 2017年第3期51卷 709-717页

作者： Arana-Jimenez, Manuel Salles Neto, L. L. Univ Cadiz Fac SSCC & Commun Dept Stat & Operat Res Ave Univ Jerez de la Frontera 11406 Spain Univ Fed Sao Paulo Dept Ciencia & Tecnol Sao Paulo Brazil

This work presents a sufficient criteria for partial efficient solutions of the cutting stock problem with two objectives. We consider two important objectives for an industry: number of processed objects (cost of raw materials) and number of different patterns (cost of setup). These optimality results are established through a new approach based on connections between discrete optimization and continuous vector optimization.

关键词： multiple objective programming optimality conditions continuous optimization cutting stock problem

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Finding compromise solutions in project portfolio selection with multiple experts by inverse optimization

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COMPUTERS & OPERATIONS RESEARCH 2016年 66卷 12-19页

作者： Roland, Julien Figueira, Jose Rui De Smet, Yves Univ Libre Bruxelles Ecole Polytech Bruxelles Serv Mathemat Gest CoDE SMG B-1050 Brussels Belgium Univ Lisbon Inst Super Tecn CEG IST P-1049001 Lisbon Portugal

This paper deals with project portfolio selection evaluated by multiple experts. The problem consists of selecting a subset of projects that satisfies a set of constraints and represents a compromise among the group of experts. It can be modeled as a multi-objective combinatorial optimization problem and solved by two procedures based on inverse optimization. It requires to find a minimal adjustment of the expert's evaluations such that a portfolio becomes ideal in the objective space. Several distance functions are considered to define a measure of the adjustment. The two procedures are applied to randomly generated instances of the knapsack problem and computational results are reported. Finally, two illustrative examples are analyzed and several theoretical properties are proved. (c) 2015 Elsevier Ltd. All rights reserved.

关键词： multiple objective programming Combinatorial optimization Inverse optimization

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Applying the approximation method PAINT and the interactive method NIMBUS to the multiobjective optimization of operating a wastewater treatment plant

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ENGINEERING OPTIMIZATION 2015年第3期47卷 328-346页

作者： Hartikainen, Markus E. Ojalehto, Vesa Sahlstedt, Kristian Univ Jyvaskyla Dept Math Informat Technol FI-40014 Jyvaskyla Finland Poyry Finland Ltd FI-01621 Vantaa Finland

Using an interactive multiobjective optimization method called NIMBUS and an approximation method called PAINT, preferable solutions to a five-objective problem of operating a wastewater treatment plant are found. The decision maker giving preference information is an expert in wastewater treatment plant design at the engineering company Poyry Finland Ltd. The wastewater treatment problem is computationally expensive and requires running a simulator to evaluate the values of the objective functions. This often leads to problems with interactive methods as the decision maker may get frustrated while waiting for new solutions to be computed. Thus, a newly developed PAINT method is used to speed up the iterations of the NIMBUS method. The PAINT method interpolates between a given set of Pareto optimal outcomes and constructs a computationally inexpensive mixed integer linear surrogate problem for the original wastewater treatment problem. With the mixed integer surrogate problem, the time required from the decision maker is comparatively short. In addition, a new IND-NIMBUS (R) PAINT module is developed to allow the smooth interoperability of the NIMBUS method and the PAINT method.

关键词： OR in natural resources simulation productivity and competitiveness multiple objective programming

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A one direction search method to find the exact nondominated frontier of biobjective mixed-binary linear programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第2期266卷 415-425页

作者： Fattahi, Ali Turkay, Metin Univ Calif Los Angeles Anderson Sch Management 110 Westwood Plaza Los Angeles CA 90095 USA Koc Univ Dept Ind Engn TR-34450 Istanbul Turkey

The nondominated frontier (NDF) of a biobjective optimization problem is defined as the set of feasible points in the objective function space that cannot be improved in one objective function value without worsening the other. For a biobjective mixed-binary linear programming problem (BOMBLP), the NDF consists of some combination of isolated points and open, closed, or half-open/half-closed line segments. Some algorithms have been proposed in the literature to find an approximate or exact representation of the NDF. We present a one direction search (ODS) method to find the exact NDF of BOMBLPs. We provide a theoretical analysis of the ODS method and show that it generates the exact NDF. We also conduct a comprehensive experimental study on a set of benchmark problems and show the solution quality and computational efficacy of our algorithm. (C) 2017 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Integer programming

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A length-based, multiple-resource formulation for shortest path network interdiction problems in the transportation sector

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INTERNATIONAL JOURNAL OF CRITICAL INFRASTRUCTURE PROTECTION 2013年第2期6卷 107-119页

作者： Yates, Justin Sanjeevi, Sujeevraja Texas A&M Univ Dept Ind & Syst Engn College Stn TX 77843 USA

This paper analyzes a variation of the shortest path network interdiction problem for homeland security scenarios pertaining to attacks on critical infrastructure and key resources that use highways in the transportation sector as conduits for gaining proximity to targets. The model represents a static Stackelberg game and may be formulated as a bi-level mixed integer program with two players: an attacker and a defender. Using highway segments as arcs, a set of predetermined highway entry points and a target set, the attacker seeks the path of maximum non-detection between any entry and target node. The defender impacts the minimum value of this maximum non-detection path through the allocation of a limited number of defense sensors that reduce the non-detection probabilities for arcs that fall within the range of influence of a sensor. Two types of sensors, static and dynamic sensors, are available to the defender and separate influence functions model their respective effects on arc non-detection. A geographic information system is used to collect, store and process network information and sensor influence information stored in a relational database. The results of the problem formulation are analyzed in a case study involving a California highway sub-network. The case study also examines the effects of sensor parameters, budget levels and target sets on the solutions that are obtained. Published by Elsevier B.V.

关键词： Shortest path network interdiction problem Highways Transportation sector Integer programming multiple objective programming

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Methods for constrained optimization of expensive mixed-integer multi-objective problems, with application to an internal combustion engine design problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期307卷 421-446页

作者： Duro, Joao A. Ozturk, Umud Esat Salomon, Shaul Oara, Daniel C. Lygoe, Robert J. Burke, Richard Purshouse, Robin C. Univ Sheffield Dept Automat Control & Syst Engn Sheffield England Univ Bath Inst Adv Automot Prop Syst Bath BA2 7AY England ORT Braude Coll Engn Karmiel Israel Ford Motor Co Ltd Dunton Tech Ctr UK Prod Dev Europe Laindon England

Engineering design optimization problems increasingly require computationally expensive high-fidelity simulation models to evaluate candidate designs. The evaluation budget may be small, limiting the effectiveness of conventional multi-objective evolutionary algorithms. Bayesian optimization algorithms (BOAs) are an alternative approach for expensive problems but are underdeveloped in terms of support for constraints and non-continuous design variables-both of which are prevalent features of real-world design problems. This study investigates two constraint handling strategies for BOAs and introduces the first BOA for mixed-integer problems, intended for use on a real-world engine design problem. The new BOAs are empirically compared to their closest competitor for this problem-the multi-objective evolutionary algorithm NSGA-II, itself equipped with constraint handling and mixed-integer components. Performance is also analysed on two benchmark problems which have similar features to the engine design problem, but are computationally cheaper to evaluate. The BOAs offer statistically significant convergence improvements of between 5.9% and 31.9% over NSGA-II across the problems on a budget of 500 design evaluations. Of the two constraint handling methods, constrained expected improvement offers better convergence than the penalty function approach. For the engine problem, the BOAs identify improved feasible designs offering 36.4% reductions in nitrogen oxide emissions and 2.0% reductions in fuel consumption when compared to a notional baseline design. The use of constrained mixed-integer BOAs is recommended for expensive engineering design optimization problems. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://***/licenses/by/4.0/ )

关键词： multiple objective programming Bayesian optimization Mixed continuous and discrete variables Constraint handling Gasoline engine

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Multi-objective time-cost trade-off in dynamic PERT networks using an interactive approach

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第3期180卷 1186-1200页

作者： Azaron, Amir Tavakkoli-Moghaddam, Reza Natl Univ Ireland Univ Coll Cork Dept Comp Sci Cork Constraint Computat Ctr Cork Ireland Univ Tehran Fac Engn Dept Ind Engn Tehran Iran

We develop a multi-objective model for the time-cost trade-off problem in a dynamic PERT network using an interactive approach. The activity durations are exponentially distributed random variables and the new projects are generated according to a renewal process and share the same facilities. Thus, these projects cannot be analyzed independently. This dynamic PERT network is represented as a network of queues, where the service times represent the durations of the corresponding activities and the arrival stream to each node follows a renewal process. At the first stage, we transform the dynamic PERT network into a proper stochastic network and then compute the project completion time distribution by constructing a continuous-time Markov chain. At the second stage, the time-cost trade-off problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. Then, the STEM method is used to solve a discrete-time approximation of the original problem. Finally, the proposed methodology is extended to the generalized Erlang activity durations. (c) 2006 Elsevier B.V. All rights reserved.

关键词： multiple objective programming queueing project management and scheduling Markov processes optimal control

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A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第3期232卷 479-488页

作者： Kirlik, Gokhan Sayin, Serpil Koc Univ Grad Sch Sci & Engn TR-34450 Istanbul Turkey Koc Univ Coll Adm Sci & Econ TR-34450 Istanbul Turkey

Most real-life decision-making activities require more than one objective to be considered. Therefore, several studies have been presented in the literature that use multiple objectives in decision models. In a mathematical programming context, the majority of these studies deal with two objective functions known as bicriteria optimization, while few of them consider more than two objective functions. In this study, a new algorithm is proposed to generate all nondominated solutions for multiobjective discrete optimization problems with any number of objective functions. In this algorithm, the search is managed over (p - 1)-dimensional rectangles where p represents the number of objectives in the problem and for each rectangle two-stage optimization problems are solved. The algorithm is motivated by the well-known epsilon-constraint scalarization and its contribution lies in the way rectangles are defined and tracked. The algorithm is compared with former studies on multiobjective knapsack and multiobjective assignment problem instances. The method is highly competitive in terms of solution time and the number of optimization models solved. (C) 2013 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Integer programming Efficient set epsilon-Constraint method

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The effect of transformations on the approximation of univariate (convex) functions with applications to Pareto curves

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2008年第2期189卷 347-362页

作者： Siem, A. Y. D. den Hertog, D. Hoffmann, A. L. Tilburg Univ Dept Economet & Operat Res Ctr Econ Res NL-5000 LE Tilburg Netherlands Radboud Univ Nijmegen Med Ctr Dept Radiat Oncol NL-6525 GA Nijmegen Netherlands

In the literature, methods for the construction of piecewise linear upper and lower bounds for the approximation of univariate convex functions have been proposed. We study the effect of the use of transformations on the approximation of univariate (convex) functions. In this paper, we show that these transformations can be used to construct upper and lower bounds for nonconvex functions. Moreover, we show that by using such transformations of the input variable or the output variable, we obtain tighter upper and lower bounds for the approximation of convex functions than without these approximations. We show that these transformations can be applied to the approximation of a (convex) Pareto curve that is associated with a (convex) bi-objective optimization problem. (C) 2007 Elsevier B.V. All rights reserved.

关键词： approximation convex programming convex/concave transformation multiple objective programming Pareto curve

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