On optimizing over lift-and-project closures

The lift-and-project closure is the relaxation obtained by computing all lift-and-project cuts from the initial formulation of a mixed integer linear program or equivalently by computing all mixed integer Gomory cuts read from all tableau's corresponding to feasible and infeasible bases. In this paper, we present an algorithm for approximating the value of the lift-and-project closure. The originality of our method is that it is based on a very simple cut generation linear programming problem which is obtained from the original linear relaxation by simply modifying the bounds on the variables and constraints. This separation LP can also be seen as the dual of the cut generation LP used in disjunctive programming procedures with a particular normalization. We study some properties of this separation LP in particular relating it to the equivalence between lift-and-project cuts and Gomory cuts shown by Balas and Perregaard. Finally, we present some computational experiments and comparisons with recent related works

Program representation size in an intermediate language with intersection and union types

The CIL compiler for core Standard ML compiles whole programs using a novel typed intermediate language (TIL) with intersection and union types and flow labels on both terms and types. The CIL term representation duplicates portions of the program where intersection types are introduced and union types are eliminated. This duplication makes it easier to represent type information and to introduce customized data representations. However, duplication incurs compile-time space costs that are potentially much greater than are incurred in TILs employing type-level abstraction or quantification. In this paper, we present empirical data on the compile-time space costs of using CIL as an intermediate language. The data shows that these costs can be made tractable by using sufficiently fine-grained flow analyses together with standard hash-consing techniques. The data also suggests that non-duplicating formulations of intersection (and union) types would not achieve significantly better space complexity.National Science Foundation (CCR-9417382, CISE/CCR ESS 9806747); Sun grant (EDUD-7826-990410-US); Faculty Fellowship of the Carroll School of Management, Boston College; U.K. Engineering and Physical Sciences Research Council (GR/L 36963, GR/L 15685

Vehicle Routing with Traffic Congestion and Drivers' Driving and Working Rules

For the intensively studied vehicle routing problem (VRP), two real-life restrictions have received only minor attention in the VRP-literature: traffic congestion and driving hours regulations. Traffic congestion causes late arrivals at customers and long travel times resulting in large transport costs. To account for traffic congestion, time-dependent travel times should be considered when constructing vehicle routes. Next, driving hours regulations, which restrict the available driving and working times for truck drivers, must be respected. Since violations are severely fined, also driving hours regulations should be considered when constructing vehicle routes, even more in combination with congestion problems. The objective of this paper is to develop a solution method for the VRP with time windows (VRPTW), time-dependent travel times, and driving hours regulations. The major difficulty of this VRPTW extension is to optimize each vehicle’s departure times to minimize the duty time of each driver. Having compact duty times leads to cost savings. However, obtaining compact duty times is much harder when time-dependent travel times and driving hours regulations are considered. We propose a restricted dynamic programming (DP) heuristic for constructing the vehicles routes, and an efficient heuristic for optimizing the vehicle’s departure times for each (partial) vehicle route, such that the complete solution algorithm runs in polynomial time. Computational experiments emonstrate the trade-off between travel distance minimization and duty time minimization, and illustrate the cost savings of extending the depot opening hours such that traveling before the morning peak and after the evening peak becomes possible

Wound healing and hyper-hydration - a counter intuitive model

Winters seminal work in the 1960s relating to providing an optimal level of moisture to aid wound healing (granulation and re-epithelialisation) has been the single most effective advance in wound care over many decades. As such the development of advanced wound dressings that manage the fluidic wound environment have provided significant benefits in terms of healing to both patient and clinician. Although moist wound healing provides the guiding management principle confusion may arise between what is deemed to be an adequate level of tissue hydration and the risk of developing maceration. In addition, the counter-intuitive model ‘hyper-hydration’ of tissue appears to frustrate the moist wound healing approach and advocate a course of intervention whereby tissue is hydrated beyond what is a normally acceptable therapeutic level. This paper discusses tissue hydration, the cause and effect of maceration and distinguishes these from hyper-hydration of tissue. The rationale is to provide the clinician with a knowledge base that allows optimisation of treatment and outcomes and explains the reasoning behind wound healing using hyper-hydration