A novel approach is proposed to quantify the similarity (or “synchrony”) of multiple multi-dimensional point processes. It is based on a generative stochastic model that describes how two or more point processes are related to each other. Inference in that model is carried out by integer programming. As an application, the problem of diagnosing Alzheimer’s disease (AD) from multi-channel EEG re...

A multi-product fish production planning produces simultaneously multi fish products from several classes of raw resources. The goal in production planning is to meet customer demand over a fixed time horizon divided into planning periods by optimizing the trade-off between economic objectives such as production cost and customer satisfaction level. The major decisions are production and invent...

The weekly cost-optimal generation of electric power in a hydrothermal generation system is modeled as a multistage mixed-integer stochastic program. The model incorporates uncertainties of electrical load forecasts, of inflows to pumped storage hydro plants and of fuel or electricity prices. For its solution a stochastic Lagrangian relaxation scheme is designed by assigning (stochastic) multip...

We discuss two families of valid inequalities for linear mixed integer programming problems with cone constraints of arbitrary order, which arise in the context of stochastic optimization with downside risk measures. In particular, we extend the results of Atamtürk and Narayanan (Math. Program., 2010, 2011), who developed mixed integer rounding cuts and lifted cuts for mixed integer programming...

We present a scheme for generating new valid inequalities for mixed integer programs by taking pairwise combinations of existing valid inequalities. Our scheme is related to mixed integer rounding and mixing. The scheme is in general sequence-dependent and therefore leads to an exponential number of inequalities. For some important cases, we identify combination sequences that lead to a managea...

We consider stochastic integer programming problems with probabilistic constraints. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce new methods for constructing lower and upper bounds for probabilistically constrained integer programs. We also show how limited information about the distribution can be ...

We propose a new class of stochastic integer programs whose special features are dominance constraints induced by mixed-integer linear recourse. For these models, we establish closedness of the constraint set mapping with the underlying probability measure as parameter. In the case of finite probability spaces, the models are shown to be equivalent to large-scale, block-structured, mixedinteger...

Classical and anomalous diffusion equations employ integer derivatives, fractional derivatives, and other pseudodifferential operators in space. In this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are Mittag-Leffler type. This leads to e...

This paper addresses a general class of two-stage stochastic programs with integer recourse and discrete distributions. We exploit the structure of the value function of the second-stage integer problem to develop a novel global optimization algorithm. The proposed scheme departs from those in the current literature in that it avoids explicit enumeration of the search space while guaranteeing f...

Airport gate assignment is a critical issue for the operation management of an airport. Airport gate assignment is to assign flights to gates according to their real-time arrival time and departure time, such that each flight is assigned to exactly one gate, and there is no conflict between two consecutive flights assigned to the same gate. We formulate the airport gate assignment as a stochast...