Metro maps are schematic diagrams of public transport networks that serve as visual aids for route planning and navigation tasks. It is a challenging problem in network visualization to automatically draw appealing me...
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Metro maps are schematic diagrams of public transport networks that serve as visual aids for route planning and navigation tasks. It is a challenging problem in network visualization to automatically draw appealing metro maps. There are two aspects to this problem that depend on each other: the layout problem of finding station and link coordinates and the labeling problem of placing nonoverlapping station labels. In this paper, we present a new integral approach that solves the combined layout and labeling problem (each of which, independently, is known to be NP-hard) using mixed-integer programming (MIP). We identify seven design rules used in most real-world metro maps. We split these rules into hard and soft constraints and translate them into an MIP model. Our MIP formulation finds a metro map that satisfies all hard constraints (if such a drawing exists) and minimizes a weighted sum of costs that correspond to the soft constraints. We have implemented the MIP model and present a case study and the results of an expert assessment to evaluate the performance of our approach in comparison to both manually designed official maps and results of previous layout methods.
We investigate the problem of designing energy-efficient timetables for railway traffic. More precisely, we slightly adapt a given timetable draft before it is published by moderately shifting the departure times of t...
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We investigate the problem of designing energy-efficient timetables for railway traffic. More precisely, we slightly adapt a given timetable draft before it is published by moderately shifting the departure times of the trains at the stations. To this end, we propose a mixed-integer programming model for feasible adaptations of the timetable draft and investigate its behaviour under different objective functions which fall into two classes: reducing the energy cost and increasing the stability of the power supply system. These tests are performed on real-world problem instances from our industry partner Deutsche Bahn AG. They show a significant potential for improvements in the existing railway timetables.
AimClimate change threatens the effectiveness of existing protected areas, pivotal, yet static, instruments to promote the persistence of biodiversity. The identification of the areas more likely to be used by multipl...
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AimClimate change threatens the effectiveness of existing protected areas, pivotal, yet static, instruments to promote the persistence of biodiversity. The identification of the areas more likely to be used by multiple species to track their most suitable changing climates is therefore an important step in conservation planning. Species persistence targets and budget limitation are two critical ingredients constraining target-based conservation area selection. However, defining adequate persistence targets under budget constraints is far from intuitive. LocationUnspecific. MethodsWe propose a two-staged mixed-integer linear programming model to determine optimized persistence targets for several species, for a given time horizon and climate change scenarios, under budgetary limitation. The first stage tunes pre-established targets for each species with a bound on the size of the area to select. The second stage identifies a set of areas of minimum cost that allows the persistence levels optimized in the first stage to be achieved. We apply a heuristic to test whether small deviations from optimal persistence settings (i.e., targets for multiple species) do influence cost-effectiveness of final solutions. Analyses were undertaken using a synthetic data set replicating changes of environmental suitability for several simulated species using several experimental designs. ResultsOur results showed that minor differences to the optimal persistence scores can result in large contraction of cost-effectiveness in final solutions. Main conclusionsPersistence targets should be carefully assessed case by case, and alternative species persistence settings should be considered, as they potentially result in important reductions of cost-effectiveness. Our model along with the respective heuristic can be used as a tool to efficiently promote species persistence under climate change.
We present a version of GMI (Gomory mixed-integer) cuts in a way so that they are derived with respect to a "dual form" mixed-integer optimization problem and applied on the standard-form primal side as colu...
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We present a version of GMI (Gomory mixed-integer) cuts in a way so that they are derived with respect to a "dual form" mixed-integer optimization problem and applied on the standard-form primal side as columns, using the primal simplex algorithm. This follows the general scheme of He and Lee, who did the case of Gomory pure-integer cuts. Our input mixed-integer problem is not in standard form, and so our cuts are derived rather differently from how they are normally derived. A convenient way to develop GMI cuts is from MIR (mixed-integer rounding) cuts, which are developed from 2-dimensional BMI (basic mixed-integer) cuts, which involve a nonnegative continuous variable and an integer variable. The non-negativity of the continuous variable is not the right tool for us, as our starting point (the "dual form" mixed-integer optimization problem) has no non-negativity. So we work out a different 2-dimensional starting point, a pair of somewhat arbitrary inequalities in one continuous and one integer variable. In the end, we follow the approach of He and Lee, getting now a finitely converging primal simplex column-generation algorithm for mixed-integer optimization problems.
Most computerized adaptive testing (CAT) applications in patient-reported outcomes (PRO) measurement to date are reliability-centric, with a primary objective of maximizing measurement efficiency. A key concern and a ...
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Most computerized adaptive testing (CAT) applications in patient-reported outcomes (PRO) measurement to date are reliability-centric, with a primary objective of maximizing measurement efficiency. A key concern and a potential threat to validity is that, when left unconstrained, individual CAT administrations could have items with systematically different attributes, e.g., sub-domain coverage. This paper aims to provide a solution to the problem from an optimal test design framework using the shadow-test approach to CAT. Following the approach, a case study was conducted using the PROMISA (R) (Patient-Reported Outcomes Measurement Information System) fatigue item bank both with empirical and simulated response data. Comparisons between CAT administrations without and with the enforcement of content and item pool usage constraints were examined. The unconstrained CAT exhibited a high degree of variation in items selected from different substrata of the item bank. Contrastingly, the shadow-test approach delivered CAT administrations conforming to all specifications with a minimal loss in measurement efficiency. The optimal test design and shadow-test approach to CAT provide a flexible framework for solving complex test-assembly problems with better control of their domain coverage than for the conventional use of CAT in PRO measurement. Applications in a wide array of PRO domains are expected to lead to more controlled and balanced use of CAT in the field.
In this paper, we provide a mixed-integer programming approach for solving the problem of minimizing a real-valued function over the efficient set of a multiple objective linear program problem. Instead of solving the...
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In this paper, we provide a mixed-integer programming approach for solving the problem of minimizing a real-valued function over the efficient set of a multiple objective linear program problem. Instead of solving the problem directly, we introduce a new problem of minimizing the objective function subject to some linear constraints with additional binary variables. We show under certain conditions that the two problems are equivalent. When the objective function of the original problem is a linear or convex function, the new problem is a linear or convex programming problem, respectively, with some binary variables. These problems can be solved as mixed-integer programs with current state-of-art mixed-integer programming solvers.
Genome-scale models have expanded beyond their metabolic origins. Multiple modeling frameworks are required to combine metabolism with enzymatic networks, transcription, translation, and regulation. Mathematical progr...
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Genome-scale models have expanded beyond their metabolic origins. Multiple modeling frameworks are required to combine metabolism with enzymatic networks, transcription, translation, and regulation. Mathematical programming offers a powerful set of tools for tackling these “multi-modality” models, although special attention must be paid to the connections between modeling types. This chapter reviews common methods for combining metabolic and discrete logical models into a single mathematical programming framework. Best practices, caveats, and recommendations are presented for the most commonly used software packages. Methods for troubleshooting large sets of logical rules are also discussed. less
This paper reports the development of a two-level optimization methodology to help design a tri-generation system for a given district which satisfies the heating, cooling, and hot water demands and at the same time, ...
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This paper reports the development of a two-level optimization methodology to help design a tri-generation system for a given district which satisfies the heating, cooling, and hot water demands and at the same time, minimize the annual total costs and CO2 emissions. An optimization methodology is proposed and tested on a virtual district with eight buildings where three of them can host the district technologies including heat pump, gas engine, and lake cooling. Within the building, some backup technologies may be implemented including an air/water heat pump, a water/water heat pump, a boiler, and electric chillers. Analysis of the Pareto optimal frontier results in several distinct groups of configuration based on the selected district conversion technologies and their capacities. Solution to the sub-problems including design and operation of the district energy system is carried out by applying a mixedintegerprogramming (MIP) technique. Several different clusters are defined and studied regarding the cost and CO2 emission. A reference configuration is defined for the purpose of comparison in which electricity is supplied by the grid, heating and hot water by a boiler, and cooling by an electric chiller. Compared to this configuration, the best solution with respect to CO2 emissions causes 59% emission and 75% cost of the reference configuration. In this case, 53% of the total cost is associated with the initial investment cost while the rest 47% is associated with the operational cost. The optimal configuration with respect to the annual costs causes 86% more emission than the reference configuration and 38% less annual costs. In this case, 22% of the total cost is associated with initial investment cost while 78% of the total cost is associated with the operational cost. Implementation of a two-pipe system instead of a four-pipe system results in nearly 5% reduction in total annual cost.
This paper presents integrating the Battery-based Energy Storage Transportation (BEST) into optimization of generation and transmission planning in electric power system. BEST is the transportation of modular battery-...
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ISBN:
(纸本)9781509045358
This paper presents integrating the Battery-based Energy Storage Transportation (BEST) into optimization of generation and transmission planning in electric power system. BEST is the transportation of modular battery-based energy storage (BES) with gird-connection capabilities on train cars via existing railroad tracks to grid locations. BEST not only provides energy storage, but also transport the energy from source to load center. This makes BEST a better way to substitute generation and transmission planning within its ability. The objective function of this problem is minimizing the total system planning cost which consisted with the investment cost of candidate generation units, transmission lines and BES, operation cost of all running generation units and BES, and penalty of loss of load. A 6-bus system with 3 stations which can charging/discharging with grid is used in the numerical simulations, and the results shows the flexibility and optimization of BES compared to generation and transmission planning only. Renewable energy sources (RES) as one kind of candidate units will be added to the problem.
Evacuation planning algorithms are critical tools for assisting authorities in orchestrating large-scale evacuations while ensuring optimal utilization of resources. To be deployed in practice, these algorithms must i...
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ISBN:
(纸本)9783319661582;9783319661575
Evacuation planning algorithms are critical tools for assisting authorities in orchestrating large-scale evacuations while ensuring optimal utilization of resources. To be deployed in practice, these algorithms must include a number of constraints that dramatically increase their complexity. This paper considers the zone-based non-preemptive evacuation planning problem in which each evacuation zone is assigned a unique evacuation path to safety and the flow of evacuees over time for a given zone follows one of a set of specified response curves. The starting point of the paper is the recognition that the first and only optimization algorithm previously proposed for zone-based non-preemptive evacuation planning may produce non-elementary paths, i.e., paths that visit the same node multiple times over the course of the evacuation. Since non-elementary paths are undesirable in practice, this paper proposes a column-generation algorithm where the pricing subproblem is a least-cost path under constraints. The paper investigates a variety of algorithms for solving the subproblem as well as their hybridization. Experimental results on a real-life case study show that the new algorithm produces evacuation plans with elementary paths of the same quality as the earlier algorithm in terms of the number of evacuees reaching safety and the completion time of the evacuation, at the expense of a modest increase in CPU time.
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