Slack matching is an optimization that determines the amount of buffering that must be added to each channel of a slack elastic asynchronous system in order to reduce its cycle time to a specified target. We present t...
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Slack matching is an optimization that determines the amount of buffering that must be added to each channel of a slack elastic asynchronous system in order to reduce its cycle time to a specified target. We present two methods of expressing the slack matching problem as a mixed integer linear programming problem. The first method is applicable to systems composed of either full-buffers or half-buffers but not both. The second method is applicable to systems composed of any combination of full-buffers and half-buffers
In a placed circuit, there are a lot of movable cells that can be flipped to further reduce the total wirelength, without affecting the original placement solution. We aim at solving this flipping problem optimally. H...
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In a placed circuit, there are a lot of movable cells that can be flipped to further reduce the total wirelength, without affecting the original placement solution. We aim at solving this flipping problem optimally. However, solving such a problem optimally is non-trivial given the gigantic sizes of modern circuits. We are able to identify a large portion of cells (about 75%) of which the orientation (flipped or not flipped) can be determined independent of the orientations of all the other cells. We have derived three non-trivial conditions to identify those so called independent cells, strictly solvable cells and conditionally solvable cells. In this way, we can greatly reduce the number of cells whose orientations are dependent on each other. Finally, the cell flipping problem of the remaining dependent cells can be formulated as a mixed integer linear programming (MILP) problem and solved optimally. However, this may still be too slow for extremely large circuits and we have applied two other methods, linearprogramming (LP) and linearprogramming followed by mixed integer linear programming (LP+MILP) to solve the problem. Experimental results show that by identifying those independent and solvable cells first and applying the LP+MILP technique, we can solve this flipping problem effectively and obtain results just 0.01% more than the optimal. In addition, we can improve the wirelength and number of overflow tiles by 5% and 9% respectively on the floorplanning benchmarks
This paper proposes and demonstrates procedures to optimally design tensegrity structures actuation, based on closed loop shape control requirements, while at the same time a feasible path for realizing a desired shap...
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This paper proposes and demonstrates procedures to optimally design tensegrity structures actuation, based on closed loop shape control requirements, while at the same time a feasible path for realizing a desired shape is synthesized. The procedures are employing different optimization based formulations of a set of requirements needed for shape control. The specific procedure demonstrated is based on a mixed integer linear programming formulation, one of the simplest possible. It is possible to formulate the design problem more generally, but then the computations become more involved, inhibiting a real time implementation of the procedure. The demonstration is for a simple planar tensegrity, but the procedures can be applied to more general structures without modification
This paper presents a practical method by using mixed integer linear programming for the short-term hydro scheduling (STHS). The STHS is used to determine the optimal or near-optimal schedules for the dispatchable hyd...
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This paper presents a practical method by using mixed integer linear programming for the short-term hydro scheduling (STHS). The STHS is used to determine the optimal or near-optimal schedules for the dispatchable hydro plants in a hydro-dominant system for a user-definable study period at each time step while respecting all system and hydraulic constraints. The problem can be modeled in detail for a hydro system that contains both conventional and pumped-storage units. Discrete and dynamic constraints such as plant startup and shutdown statuses are also included in the model. The STHS problem is solved with a commercial-grade MILP solver. The usefulness of the proposed solution algorithm is illustrated by testing the problem with actual hydraulic system data. Numerical experiences show that the solution technique is computationally efficient, simple, and suitable for decision support of short-term hydro operations planning.
A method tar finding fuel-optimal trajectories for spacecraft subjected to avoidance requirements is introduced. These include avoidance of collisions with obstacles or other vehicles and prevention of thruster plumes...
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A method tar finding fuel-optimal trajectories for spacecraft subjected to avoidance requirements is introduced. These include avoidance of collisions with obstacles or other vehicles and prevention of thruster plumes from one spacecraft impinging on another spacecraft. The necessary logical constraints for avoidance are appended to a fuel-optimizing linear program by including binary variables in the optimization. The resulting problem is a mixed-integerlinear program (MILP) that can be solved using available software. The logical constraints can also be used to express the configuration requirements for maneuvers where only the final relative alignment of the vehicles is important and the assignment of spacecraft within the fleet is not specified. The collision avoidance, trajectory optimization, and fleet assignment problems can be combined into a single MILE to obtain the optimal solution for these maneuvers. The MILE problem formulation, including these various avoidance constraints, is presented, and then several examples of their application to spacecraft maneuvers, including reconfiguration of a satellite formation and close inspection of the International Space Station by a microsatellite, are shown. These examples clearly show that the trajectory design methods presented are particularly well suited to proposed formation flying missions that involve multiple vehicles operating in close proximity.
In this paper we consider policies for free-flight management of air traffic. We consider instantaneous and bounded heading angle deviation as conflict avoidance maneuvers. The corresponding model, resulting in a mixe...
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In this paper we consider policies for free-flight management of air traffic. We consider instantaneous and bounded heading angle deviation as conflict avoidance maneuvers. The corresponding model, resulting in a mixed integer linear programming (MILP) problem allow to solve both conflict detection and conflict resolution problems. The developed algorithm proved successful in a centralized implementation with a large number of cooperating aircraft. However, the application of such algorithm to a free flight environment, where cooperation can only be expected from neighboring aircraft, poses many challenges. We consider a model of the decentralized conflict resolution strategy that is based on a hybrid system, and sufficient conditions under which a 3-aircraft free flight MILP-based scheme guarantees safety of flight are provided.
Describes a method for finding optimal trajectories for multiple aircraft avoiding collisions. Developments in spacecraft path-planning have shown that trajectory optimization including collision avoidance can be writ...
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Describes a method for finding optimal trajectories for multiple aircraft avoiding collisions. Developments in spacecraft path-planning have shown that trajectory optimization including collision avoidance can be written as a linear program subject to mixedinteger constraints, known as a mixed-integerlinear program (MILP). This can be solved using commercial software written for the operations research community. In the paper, an approximate model of aircraft dynamics using only linear constraints is developed, enabling the MILP approach to be applied to aircraft collision avoidance. The formulation can also be extended to include multiple waypoint path-planning, in which each vehicle is required to visit a set of points in an order chosen within the optimization.
The Vehicle Routing Problem with Backhauling deals with the supply of finished goods from a depot to a number of delivery points, and picking up returnable items and bringing them back to the depot using a fleet of tr...
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The Vehicle Routing Problem with Backhauling deals with the supply of finished goods from a depot to a number of delivery points, and picking up returnable items and bringing them back to the depot using a fleet of trucks. Traditionally, the objective of the problem has been to determine the truck routes such that the total number of trucks and/or the total distance traveled/total route cost are minimized. Most of the papers available in the literature in this connection deal with problems where the linehaul (having a demand for finished goods) and backhaul (having items to be returned to the depot) customers axe different, and a customer may be visited by at most one truck limiting demand and returns at a location by the capacity of the truck. In this paper, we allow the linehaul and backhaul customers to be the same leading to simultaneous delivery and pickup at a customer location, and also there is no restriction on the quantity demanded at (to be returned from) a customer location. As such a customer may be visited by more than one truck and more than once by the same truck. We developed a mixed integer linear programming (MILP) formulation of the problem and a route construction heuristic. The heuristic averaged 80 ms for 110 problems tested, and in 78 of them the heuristic costs were either equal to the optimal costs or at most equal to the upper bounds on the optimal costs obtained after running the optimization package for 30 min. Optimal solutions were obtained for 28 problems at an average time of 295 ms. The heuristic could match the optimal solutions for 22 of these problems at, an average time of 71 ms.
We address the problem of assigning forces to jacking positions in order to weaken stress at points where an aircraft maintenance operation has to be performed. We introduce a mixed-integerlinearprogramming model an...
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We address the problem of assigning forces to jacking positions in order to weaken stress at points where an aircraft maintenance operation has to be performed. We introduce a mixed-integerlinearprogramming model and report encouraging computational experiments on historical data. Our methodology is currently under the process of industrial implementation at Airbus, where it will be used as a maintenance decision-analysis tool.
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