We combine mixed integer linear programming (MILP) and constraint programming (CP) to minimize tardiness in planning and scheduling. Tasks are allocated to facilities using MILP and scheduled using CP, and the two are linked via logic-based Benders decomposition. We consider two objectives: minimizing the number of late tasks, and minimizing total tardiness. Our main theoretical contribution is...

Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations. First-order logic (FOL), on the other hand, excels at reasoning about classes of objects, but lacks a rich representation of uncertainty. While representing propo...

Branch and bound algorithms for Mixed-Integer Linear Programming (MILP) almost universally branch on a single variable to create disjunctions. General linear expressions involving multiple variables are another option for branching disjunctions, but are not used for two main reasons: (i) descendent LPs tend to solve more slowly because of the added constraints, so the overall solution time is i...

A coarse registration method using Mixed Integer Linear Programming (MILP) is described that finds global optimal registration parameter values that are independent of the values of invariant features. We formulate the range image registration problem using MILP. Our algorithm using MILP formulation finds the best balanced optimal registration for robustly aligning two range images with the bes...

To overcome the inability of Description Logics (DLs) to represent vague or imprecise information, several fuzzy extensions have been proposed in the literature. In this context, an important family of reasoning algorithms for fuzzy DLs is based on a combination of tableau algorithms and Operational Research (OR) problems, specifically using Mixed Integer Linear Programming (MILP). In this pape...

Though the logical correctness of an asynchronous circuit is independent of implementation delays, the cycle time of an asynchronous circuit is of great importance to the designer. Oftentimes, the insertion of buffers to such circuits reduces the cycle time of the circuit without affecting the logical correctness of the circuit. This optimization is called slack matching. In this thesis the sla...

We study an assignment type resource-constrained project scheduling problem with resources being multi-skilled personnel to minimize the total staffing costs. We develop a hybrid Benders decomposition (HBD) algorithm that combines the complimentary strengths of both mixed-integer linear programming (MILP) and constraint programming (CP) to solve this NP-hard optimization problem. An effective c...

OBJECTIVE To support the selection of food items for FFQs in such a way that the amount of information on all relevant nutrients is maximised while the food list is as short as possible. DESIGN Selection of the most informative food items to be included in FFQs was modelled as a Mixed Integer Linear Programming (MILP) model. The methodology was demonstrated for an FFQ with interest in energy,...

One way to address multi-scale optimisation problems is by integrating logic and optimisation. For example, a scheduling problem may have two levels: (i) assigning orders to machines and (ii) sequencing orders on each machine. In a minumum cost model, assigning orders to machines is a mixed-integer optimisation problem, sequencing orders is a constraint satisfaction problem. The entire problem ...

In this paper, we study the security of SM4 block cipher against (related-key) differential cryptanalysis by making use of the Mixed Integer Linear Programming (MILP) method. SM4 is the first commercial block cipher standard of China, which attracts lots of attentions in cryptography. To analyze the security of SM4 against differential attack, we exploit a highly automatic MILP method to determ...