An O(n log n) heuristic for the Euclidean Steiner Minimal Tree (ESMT) problem is presented. The algorithm is based on a decomposition approach which first partitions the vertex set into triangles via the Delaunay triangulation, then "recomposes" the suboptimal Steiner Minimal Tree (SMT) according to the Voronoi diagram and Minimum Spanning Tree (MST) of the point set. The ESMT algorithm was implemented in FORTRAN-IV and tested on a number of randomly generated point sets in the plane drawn from a uniform distribution. Comparison of the O(n log n) algorithm with an O(n") algorithm clearlyindicates that the O(n log n) algorithm is as good as the previous O(n4) algorithm in achieving reductions in the ratio SMT/MST of the given vertex set. This is somewhat surprising since the O(n4) algorithm considers more potential Steiner points and alternative tree configurations. THE EUCLIDEAN STEINER MINIMAL TREE PROBLEMThe Euclidean Steiner Minimal Tree (ESMT) problem is the Steiner network problem which has classically received the most attention in the literature [ 2 , 5 , 8 , 1 0 , 1 3 , 14, 17-20]. The ESMT problem is as follows: for a given set V of points in the plane, where I.'= { u l , u21 . . . , un}, we wish t o construct a minimal length tree which connects these vertices. In order to minimize this total length, additional vertices S = {sl , s2, . . . , s, } are sometimes necessary. In this problem, the distance metric is the L2 metric function, better known as the Euclidean metric.Algebraically, we can represent the ESMT problem as follows:

In teaching nonlinear programming (NLP) to undergraduate and graduate students majoring in engineering or operations research, we have changed our instructional objectives, course content, and approaches to teaching because of recent dramatic improvements in optimization software and computer hardware. Our primary instructional innovation is to use cooperative active learning methods rather than a traditional lecture format.

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Cognitive research shows that student motivation, perception, comprehension, and recall is improved by using a variety of instructional strategies. After a discussion of how individuals learn through cognitive processing, this paper suggests the use of a variety of strategies for motivating students and enhancing learning. As a particular example, cooperative learning groups are described in detail. In these groups students assume responsibility not only for their own learning but also the learning of others.

Automatic control systems typically incorporate legacy code and components that were originally designed to operate independently. Furthermore, they operate under stringent safety and timing constraints. Current design strategies deal with these requirements and characteristics with ad hoc approaches. In particular, when designing control laws, implementation constraints are often ignored or cursorily estimated. Indeed, costly redesigns are needed after a prototype of the control system is built because of missed timing constraints and subtle transient errors. In this paper, we use the concepts of platform-based design to develop a methodology for the design of automatic control systems that builds in modularity and correct-by-construction procedures. We illustrate our strategy by describing the (successful) application of the methodology to the design of a time-based control system for a helicopter-based uninhabited aerial vehicle.

A model developed to aid a state-level resource allocation process in the United States Department of Agriculture Special Supplement Food Program for Women, Infants, and Children (WIC) is presented. The model is formulated as a linear integer goal program, utilizing service levels for six categories of WIC participants as goals. The model employs a methodical, consistent approach to the allocation process, yet allows ample flexibility for consideration of state-specific issues. By allowing the user to adjust the relative importance of each goal, the model can incorporate subjective attitudes of state-level WIC administrators. This is extremely important as these attitudes are the result of the administrators' familiarity with the WIC program in their states, and the significance of input of this nature should not be neglected. An application of the model to the Indiana WIC program is presented. Sensitivity of the model to changes in the objective function weights and in the target values for the goals is explored. Although orginally developed to allocate budget increases, the model may be used in allocating budget cuts as well; this form of the model is also presented. The model can be extended hierarchically to incorporate resource allocation at the federal level. This modeling approach should be useful in all public sector programs characterized by multiple objective and hierarchical decisionmaking.goal programming, health care, resource allocation, linear programming applications

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