Related papers: Modern column generation for estimating single- an…
We study consumer demand in large-scale retail settings with many products, multiple categories and repeated purchase behavior. While inertia and brand loyalty are well documented, existing discrete choice models typically focus on single…
This paper investigates the column generation (CG) for solving cutting stock problems (CSP). Traditional CG method, which repeatedly solves a restricted master problem (RMP), often suffers from two critical issues in practice -- the loss of…
Column generation (CG) is one of the most successful approaches for solving large-scale linear programming (LP) problems. Given an LP with a prohibitively large number of variables (i.e., columns), the idea of CG is to explicitly consider…
The team formation and routing problem is a challenging optimization problem with several real-world applications in fields such as airport, healthcare, and maintenance operations. To solve this problem, exact solution methods based on…
Column generation is an iterative method used to solve a variety of optimization problems. It decomposes the problem into two parts: a master problem, and one or more pricing problems (PP). The total computing time taken by the method is…
Submodular optimization is a special class of combinatorial optimization arising in several machine learning problems, but also in cooperative control of complex systems. In this paper, we consider agents in an asynchronous, unreliable and…
Space missions, particularly complex, large-scale exploration campaigns, can often involve many discrete decisions or events in their concepts of operations. Whilst a variety of methods exist for the optimisation of continuous variables in…
Predicting future consumer behaviour is one of the most challenging problems for large scale retail firms. Accurate prediction of consumer purchase pattern enables better inventory planning and efficient personalized marketing strategies.…
We study the problems of multi-person pose segmentation in natural images and instance segmentation in biological images with crowded cells. We formulate these distinct tasks as integer programs where variables correspond to poses/cells. To…
Capacity sharing networks are typical heterogeneous communication networks widely applied in information and communications technology (ICT) field. In such networks, resources like bandwidth, spectrum, computation and storage are shared…
Product ranking is the core problem for revenue-maximizing online retailers. To design proper product ranking algorithms, various consumer choice models are proposed to characterize the consumers' behaviors when they are provided with a…
With the abundance of available data, many enterprises seek to implement data-driven prescriptive analytics to help them make informed decisions. These prescriptive policies need to satisfy operational constraints, and proactively eliminate…
We study a class of nested path problems, in which every path-based variable can be decomposed into a sequence of subpaths. Subpaths must satisfy local resources, while paths must satisfy additional global resources. This paper develops a…
Bin packing problem examines the minimum number of identical bins needed to pack a set of items of various weights. This problem arises in various areas of the artificial intelligence demanding derivation of the exact solutions in the…
This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…
In this article we introduce Graph Generation, an enhanced Column Generation (CG) algorithm for solving expanded linear programming relaxations of mixed integer linear programs. To apply Graph Generation, we must be able to map any given…
We consider the problem of coordinating a fleet of robots in a warehouse so as to maximize the reward achieved within a time limit while respecting problem and robot specific constraints. We formulate the problem as a weighted set packing…
This paper proposes a novel column generation framework for combinatorial software testing. In particular, it combines Mathematical Programming and Constraint Programming in a hybrid decomposition to generate covering arrays. The approach…
We consider a class of linear-programming based estimators in reconstructing a sparse signal from linear measurements. Specific formulations of the reconstruction problem considered here include Dantzig selector, basis pursuit (for the case…
Discrete-choice models are used in economics, marketing and revenue management to predict customer purchase probabilities, say as a function of prices and other features of the offered assortment. While they have been shown to be…