With the rapid development of airlines, airports today become much busier and more complicated than previous days. During airlines daily operations, assigning the available gates to the arriving aircrafts based on the fixed schedule is a very important issue, which motivates researchers to study and solve Airport Gate Assignment Problems (AGAP) with all kinds of state-of-the-art combinatorial optimization techniques. In this paper, we study the AGAP and propose a novel hybrid mathematical model based on the method of constraint programming and 0 - 1 mixed-integer programming. With the objective to minimize the number of gate conflicts of any two adjacent aircrafts assigned to the same gate, we build a mathematical model with logical constraints and the binary constraints. For practical considerations, the potential objective of the model is also to minimize the number of gates that airlines must lease or purchase in order to run their business smoothly. We implement the model in the Optimization Programming Language (OPL) and carry out empirical studies with the data obtained from online timetable of Continental Airlines, Houston Gorge Bush Intercontinental Airport IAH, which demonstrate that our model can provide an efficient evaluation criteria for the airline companies to estimate the efficiency of their current gate assignments.

Various tasks in decision making and decision support systems require selecting a preferred subset of a given set of items. Here we focus on problems where the individual items are described using a set of characterizing attributes, and a generic preference specification is required, that is, a specification that can work with an arbitrary set of items. For example, preferences over the content of an online newspaper should have this form: At each viewing, the newspaper contains a subset of the set of articles currently available. Our preference specification over this subset should be provided offline, but we should be able to use it to select a subset of any currently available set of articles, e.g., based on their tags. We present a general approach for lifting formalisms for specifying preferences over objects with multiple attributes into ones that specify preferences over subsets of such objects. We also show how we can compute an optimal subset given such a specification in a relatively efficient manner. We provide an empirical evaluation of the approach as well as some worst-case complexity results.

We present an online method for estimating the cost of solving SAT problems. Modern SAT solvers present several challenges to estimate search cost including non-chronological backtracking, learning and restarts. Our method uses a linear model trained on data gathered at the start of search. We show the effectiveness of this method using random and structured problems. We demonstrate that predictions made in early restarts can be used to improve later predictions. We also show that we can use such cost estimations to select a solver from a portfolio.

This paper presents comparison of several stochastic optimization algorithms developed by authors in their previous works for the solution of some problems arising in Civil Engineering. The introduced optimization methods are: the integer augmented simulated annealing (IASA), the real-coded augmented simulated annealing (RASA), the differential evolution (DE) in its original fashion developed by R. Storn and K. Price and simplified real-coded differential genetic algorithm (SADE). Each of these methods was developed for some specific optimization problem; namely the Chebychev trial polynomial problem, the so called type 0 function and two engineering problems - the reinforced concrete beam layout and the periodic unit cell problem respectively. Detailed and extensive numerical tests were performed to examine the stability and efficiency of proposed algorithms. The results of our experiments suggest that the performance and robustness of RASA, IASA and SADE methods are comparable, while the DE algorithm performs slightly worse. This fact together with a small number of internal parameters promotes the SADE method as the most robust for practical use.

Moreover, the investor, the oncologist, and the airline manager are all in a situation where the number of available options or alternatives is very large or even infinite. There are infinitely many ways to invest money and infinitely many possible radiotherapy treatments, but the number of feasible crew schedules is finite, albeit astronomical in practice. The alternatives are therefore described by constraints, rather than explicitly known: the sums invested in every stock must equal the total invested; the radiotherapy treatment must meet physical and clinical constraints; crew schedules must ensure that each flight has exactly one crew assigned to operate it. Mathematically, the alternatives are described by vectors in variable or decision space; the set of all vectors satisfying the constraints is called the feasible set in decision space. The consequences or attributes of the alternatives are described as vectors in objective or outcome space, where outcome (objective) vectors are a function of the decision (variable) vectors.

The compact Genetic Algorithm (cGA) is an Estimation of Distribution Algorithm that generates offspring population according to the estimated probabilistic model of the parent population instead of using traditional recombination and mutation operators. The cGA only needs a small amount of memory; therefore, it may be quite useful in memory-constrained applications. This paper introduces a theoretical framework for studying the cGA from the convergence point of view in which, we model the cGA by a Markov process and approximate its behavior using an Ordinary Differential Equation (ODE). Then, we prove that the corresponding ODE converges to local optima and stays there. Consequently, we conclude that the cGA will converge to the local optima of the function to be optimized.

We combine two threads of research on approximate dynamic programming: random sampling of states and using local trajectory optimizers to globally optimize a policy and associated value function. This combination allows us to replace a dense multidimensional grid with a much sparser adaptive sampling of states. Our focus is on finding steady state policies for the deterministic time invariant discrete time control problems with continuous states and actions often found in robotics. In this paper we show that we can now solve problems we couldn't solve previously with regular grid-based approaches.

Most models of decision-making in neuroscience assume an infinite horizon, which yields an optimal solution that integrates evidence up to a fixed decision threshold; however, under most experimental as well as naturalistic behavioral settings, the decision has to be made before some finite deadline, which is often experienced as a stochastic quantity, either due to variable external constraints or internal timing uncertainty. In this work, we formulate this problem as sequential hypothesis testing under a stochastic horizon. We use dynamic programming tools to show that, for a large class of deadline distributions, the Bayes-optimal solution requires integrating evidence up to a threshold that declines monotonically over time. We use numerical simulations to illustrate the optimal policy in the special cases of a fixed deadline and one that is drawn from a gamma distribution.

We consider the ensemble clustering problem where the task is to'aggregate' multiple clustering solutions into a single consolidated clustering that maximizes the shared information among given clustering solutions. We obtain several new results for this problem. First, we note that the notion of agreement under such circumstances can be better captured using an agreement measure based on a 2D string encoding rather than voting strategy based methods proposed in literature. Using this generalization, we first derive a nonlinear optimization model to maximize the new agreement measure. We then show that our optimization problem can be transformed into a strict 0-1 Semidefinite Program (SDP) via novel convexification techniques which can subsequently be relaxed to a polynomial time solvable SDP. Our experiments indicate improvements not only in terms of the proposed agreement measure but also the existing agreement measures based on voting strategies. We discuss evaluations on clustering and image segmentation databases.

We investigate the use of message-passing algorithms for the problem of finding the max-weight independent set (MWIS) in a graph. First, we study the performance of loopy max-product belief propagation. We show that, if it converges, the quality of the estimate is closely related to the tightness of an LP relaxation of the MWIS problem. We use this relationship to obtain sufficient conditions for correctness of the estimate. We then develop a modification of max-product - one that converges to an optimal solution of the dual of the MWIS problem. We also develop a simple iterative algorithm for estimating the max-weight independent set from this dual solution. We show that the MWIS estimate obtained using these two algorithms in conjunction is correct when the graph is bipartite and the MWIS is unique. Finally, we show that any problem of MAP estimation for probability distributions over finite domains can be reduced to an MWIS problem. We believe this reduction will yield new insights and algorithms for MAP estimation.