A* Algorithm

Abstract

A heuristic search procedure that selects a node in its search tree for expansion such that the selected node has minimum value of the sum of the cost to reach the node plus a heuristic cost value for that node, where the heuristic cost underestimates the true minimum cost of completion. See ▶ Artificial IntelligenceReferences Hart, P. E., Nilsson, N. J., & Raphael, B. (1968). A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science and Cybernetics, 4, 100-107. Pearl, J. (1984). Heuristics. Reading, MA: Addison-Wesley. Acceptance Sampling ▶ Quality Control Acceptance-Rejection MethodIn stochastic or Monte Carlo simulation, a method for sampling from a given difficult target probability distribution by sampling from a distribution that is close to the target distribution and relatively easy to sample but possibly rejecting the generated output. Sometimes just called the rejection method. Activity LevelThe value taken by a structural variable in an intermediate or final solution to a linear programming problem. See ▶ Structural Variables Activity-Analysis ProblemA linear-programming problem of the form Maximize cx, subject to Ax b, x ! 0. The variables x j of the vector x are quantities of products to be produced. The b i coefficients of the resource vector b represent the amount of resource i that is available for production, the c j coefficients represent the value (profit) of one unit of output x j , and the coefficients a ij of the technological matrix A represent the amount of resource i required to produce one unit of product j. The a ij are termed technological or input-output coefficients. The objective function cx represents some measure of value of the total production. Adjacent (Neighboring) Extreme PointsTwo extreme points of a polyhedron that are connected by an edge of the polyhedron. Advertising IntroductionAdvertising research has focused on three substantive areas: sales response to advertising, optimal advertising policy (constant spending or pulsing), competitive reactions and over-time effects. The research has employed econometric, time-serioes, optimization and game theoretic analytical techniques to address the issues. The advent of enormous amounts of scanner panel and internet data has led to some fruitful modeling at the individual household level. Contributions in each one of the three areas are discussed. A thorough review of optimal control advertising models is given in Feichtinger, Hartl, and Sethi (1994). Mathematical programming also has been a useful technology. Since some early successful applications of this technology for media planning, the progress has been limited because of measurement problems relating to advertising response function (Little and Lodish 1969). Advances in research, however, provide reasons for optimism in identifying the response function (Little 1979; Eastlack and Rao 1986). Heuristic approaches have been developed to estimate the media characteristics of reach and frequency (Rust and Eechambadi 1989)...