The NP-hard problem of scheduling jobs on unrelated parallel machines with the objective of minimizing the makespan is addressed. A variable neighborhood descent heuristic hybridized with mathematical programming is p...
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The NP-hard problem of scheduling jobs on unrelated parallel machines with the objective of minimizing the makespan is addressed. A variable neighborhood descent heuristic hybridized with mathematical programming is proposed. A new constructive heuristic is also introduced to seed the search with a solution residing in a promising region. The strength of the approach lies in the adoption of appropriately chosen optimization criteria that avoid early local optimum entrapment and in the hybridization of the heuristic with mathematical programming for the exploration of the large neighborhood structures. Experimental results on a large set of benchmark problem instances attest to the efficacy of the proposed approach.
A convex set with nonempty interior is maximal lattice-free if it is inclusion maximal with respect to the property of not containing integer points in its interior. Maximal lattice-free convex sets are known to be po...
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A convex set with nonempty interior is maximal lattice-free if it is inclusion maximal with respect to the property of not containing integer points in its interior. Maximal lattice-free convex sets are known to be polyhedra. The precision of a rational polyhedron P in R-d is the smallest natural number s such that sP is an integral polyhedron. In this paper we show that, up to affine mappings preserving Z(d), the number of maximal lattice-free rational polyhedra of a given precision s is finite. Furthermore, we present the complete list of all maximal lattice-free integral polyhedra in dimension three. Our results are motivated by recent research on cutting plane theory in mixed-integer linear optimization.
Quantum annealers such as D-Wave machines are designed to propose solutions for quadratic unconstrained binary optimization (QUBO) problems by mapping them onto the quantum processing unit, which tries to find a solut...
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Quantum annealers such as D-Wave machines are designed to propose solutions for quadratic unconstrained binary optimization (QUBO) problems by mapping them onto the quantum processing unit, which tries to find a solution by measuring the parameters of a minimum-energy state of the quantum system. While many NP-hard problems can be easily formulated as binary quadratic optimization problems, such formulations almost always contain one or more constraints, which are not allowed in a QUBO. Embedding such constraints as quadratic penalties is the standard approach for addressing this issue, but it has drawbacks such as the introduction of large coefficients and using too many additional qubits. In this paper, we propose an alternative approach for implementing constraints based on a combinatorial design and solving mixed-integer linear programming (MILP) problems in order to find better embeddings of constraints of the type Sigma xi=k for binary variables xi. Our approach is scalable to any number of variables and uses a linear number of ancillary variables for a fixed k.
This paper analyzes the energy replacement potential for high-speed passenger vessels. Emphasis is on whether better planning of services can mitigate technical and economic barriers to zero emission transport. A nove...
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This paper analyzes the energy replacement potential for high-speed passenger vessels. Emphasis is on whether better planning of services can mitigate technical and economic barriers to zero emission transport. A novel mixed-integer programming problem for battery electric vessel services that jointly minimizes operator and passenger costs subject to strategic (fleet selection and land-based infrastructure location), tactical (frequency), and operational decisions (sailing pattern) is proposed. The planning problem is utilized to estimate technology replacement potential and associated costs for two existing services/routes in Norway and based on four hypothetical demand scenarios derived from the same two services. The results showcase that constraints related to battery range and charging limit the replacement potential and make energy conservation more pertinent. Abatement cost estimates range between 3 000 and 18 000 NOK per ton CO2, placing them well above the social cost of carbon calculated at 2 000 NOK per ton by 2030.
Hydropower producers must submit bids to electricity market auctions where they state their willingness to produce power. These bids may be determined using a mixed-integer linear stochastic program. However, for larg...
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Hydropower producers must submit bids to electricity market auctions where they state their willingness to produce power. These bids may be determined using a mixed-integer linear stochastic program. However, for large interconnected river systems, this program may be too complex to be solved within the time limits set by current market rules. This paper investigates whether a linear approximation to start-ups can be used to reduce the computational burden without significantly degrading the solution quality. In order to investigate the trade-off of time versus solution quality, linear approximation is compared to a formulation that uses binary variables in a case study that simulates the operation of a reservoir system over time.
Recent studies by electric utility companies indicate that maximum benefits of distributed solar photovoltaic (PV) units can be reaped when siting and sizing of PV systems is optimized. This paper develops a two-stage...
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Recent studies by electric utility companies indicate that maximum benefits of distributed solar photovoltaic (PV) units can be reaped when siting and sizing of PV systems is optimized. This paper develops a two-stage stochastic program that serves as a tool for optimally determining the placing and sizing of PV units in distribution systems. The PV model incorporates the mapping from solar irradiance to AC power injection. By modeling the uncertainty of solar irradiance and loads by a finite set of scenarios, the goal is to achieve minimum installation and network operation costs while satisfying necessary operational constraints. First-stage decisions are scenario-independent and include binary variables that represent the existence of PV units, the area of the PV panel, and the apparent power capability of the inverter. Second-stage decisions are scenario-dependent and entail reactive power support from PV inverters, real and reactive power flows, and nodal voltages. Optimization constraints account for inverter's capacity, PV module area limits, the power flow equations, as well as voltage regulation. A comparison between two designs, one where the DC:AC ratio is pre-specified, and the other where the maximum DC:AC ratio is specified based on historical data, is carried out. It turns out that the latter design reduces costs and allows further reduction of the panel area. The applicability and efficiency of the proposed formulation are numerically demonstrated on the IEEE 34-node feeder, while the output power of PV systems is modeled using the publicly available PVWatts software developed by the National Renewable Energy Laboratory. The overall framework developed in this paper can guide electric utility companies in identifying optimal locations for PV placement and sizing, assist with targeting customers with appropriate incentives, and encourage solar adoption.
In this paper we present a nonlinear model predictive control strategy for dynamic reconfiguration of electrical power distribution systems with distributed generation and storage. Even though power distribution syste...
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In this paper we present a nonlinear model predictive control strategy for dynamic reconfiguration of electrical power distribution systems with distributed generation and storage. Even though power distribution systems are physically built as interconnected meshed networks, as a rule, they operate in a radial topology. The network topology can be modified by changing status of the line switches (opened/closed). The goal of the proposed control strategy is to find the optimal radial network topology and the optimal power references for the controllable generators and energy storage units that will minimize cumulative active power losses while satisfying operating constraints. By utilizing recent results on convex relaxation of the power flow constraints, the proposed dynamic reconfiguration algorithm can be formulated as a mixed-integer second order cone program. Furthermore, if polyhedral approximations of second order cones are used then the underlying optimization problem can be solved as a mixed-integer linear program. Performance of the algorithm is illustrated on a small simulation case study based on actual meteorological and consumption data.
Magnetic resonance imaging (MRI) is a powerful diagnostic tool that has become the imaging modality of choice for soft-tissue visualization in radiation therapy. Emerging technologies aim to integrate MRI with a medic...
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Magnetic resonance imaging (MRI) is a powerful diagnostic tool that has become the imaging modality of choice for soft-tissue visualization in radiation therapy. Emerging technologies aim to integrate MRI with a medical linear accelerator to form novel cancer therapy systems (MR-linac), but the design of these systems to date relies on heuristic procedures. This paper develops an exact, optimization-based approach for magnet design that 1) incorporates the most accurate physics calculations to date, 2) determines precisely the relative spatial location, size, and current magnitude of the magnetic coils, 3) guarantees field homogeneity inside the imaging volume, 4) produces configurations that satisfy, for the first time, small-footprint feasibility constraints required for MR-linacs. Our approach leverages modern mixed-integer programming (MIP), enabling significant flexibility in magnet design generation, e.g., controlling the number of coils and enforcing symmetry between magnet poles. Our numerical results demonstrate the superiority of our method versus current mainstream methods.
In the cutting stock problem, we are given a set of objects of different types, and the goal is to pack them all in the minimum possible number of identical bins. All objects have integer lengths, and objects of diffe...
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In the cutting stock problem, we are given a set of objects of different types, and the goal is to pack them all in the minimum possible number of identical bins. All objects have integer lengths, and objects of different types have different sizes. The total length of the objects packed in a bin cannot exceed the capacity of the bin. In this paper, we consider the version of the problem in which the number of different object types is constant, and we present a polynomial-time algorithm that computes a solution using at most one more bin than an optimum solution.
Waste collection is one of the most important processes in the main cities. Its current volume obliges governments to establish efficient measures to satisfy the collection offer. Over 70% of waste can be recycled. It...
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Waste collection is one of the most important processes in the main cities. Its current volume obliges governments to establish efficient measures to satisfy the collection offer. Over 70% of waste can be recycled. It is necessary to identify the collection centers, the routes to be followed either by minor collectors and/or vehicles, the specific day of collection, and an estimate of the volumes of waste to recycling. The problem has been mathematically modeled in the literature. However, they suffer from the differentiation of the type of waste and the day of collection. This paper presents a new variant of the classical routing problem, called the Periodic Location-Routing with Selective Recycling Problem. It considers collection centers, types of containers by-product, day of collection, and subsequent routing. Besides, two solution approaches are presented: first, a model based on mixed-integer programming, and second, a greedy constructive heuristic. Several sets of instances are proposed. Preliminary results are favorable, achieving to solve instances with up to 15 customers for the exact approach and experimenting up to 1000 customers with the heuristics. The model and the solution technique are scalable.
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