We present an algorithm for constructing an optimal slate of sponsored search advertisements which respects the ordering that is the outcome of a generalized second price auction, but which must also accommodate complicating factors such as overall budget constraints. The algorithm is easily fast enough to use on the fly for typical problem sizes, or as a subroutine in an overall optimization.

This paper considers one of the optimization problems on graphs, namely, problem constructing parallel ordering vertices. Three cases anomalous deterioration value objective function with simultaneous improvement two initial parameters are investigated. The obtained results basis for further study subclasses graphs which such anomalies will always arise.

This paper presents new techniques for the trajectory design and control of nonlinear dynamical systems. The technique uses a convex polytope to bound range function associates with each vertex an auxiliary linear system. Provided controls associated systems can be generated satisfy ordering constraint, is computable by interpolation obtained optimization. theoretical result leads two numerical...

1 Supported by Chinese National Science Foundation and Chinese National Key Project funds: 69776027 and 96-738-01-08. Abstract: We proposed a new Global Routing algorithm solving the net ordering problem. The algorithm uses random optimization methods to keep the equality of earlier routed nets and later routed one in passing congested areas. It can find solution independent of net ordering in ...

Adaptive stochastic optimization (ASO) optimizes an objective function adaptively under uncertainty. It plays a crucial role in planning and learning under uncertainty, but is, unfortunately, computationally intractable in general. This paper introduces two conditions on the objective function, the marginal likelihood rate bound and the marginal likelihood bound, which, together with pointwise ...

This paper is a continuation of two previous papers where the authors used Genetic Algorithm with automated problem decomposition strategy for small scale capacitated vehicle routing problems (CVRP) and vehicle routing problem with time windows (VRPTW). In this paper they have extended their scheme to large scale capacitated vehicle routing problems by introducing selective search version of th...

In search based test data generation, the problem of test data generation is reduced to that of function minimization or maximization.Traditionally, for branch testing, the problem of test data generation has been formulated as a minimization problem. In this paper we define an alternate maximization formulation and experimentally compare it with the minimization formulation. We use genetic alg...

The ordering of variables can have a significant effect on the size of the reduced binary decision diagram (BDD) that represents the set of solutions to a combinatorial optimization problem. It also influences the quality of the objective function bound provided by a limited-width relaxation of the BDD. We investigate these effects for the maximum independent set problem. By identifying variabl...

Structure learning of Bayesian networks is an important problem that arises in numerous machine learning applications. In this work, we present a novel approach for learning the structure of Bayesian networks using the solution of an appropriately constructed traveling salesman problem. In our approach, one computes an optimal ordering (partially ordered set) of random variables using methods f...