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Decision-making with rules of thumb in relation to dynamic decision problems is studied and compared to dynamic programming. A fixed mapping from a subset of states into actions was used as a definition of a rule. The rules were then compared by averaging over past experiences which resulted in favoring rules which were only applicable in good states. Solving the dynamic program was done for the correction of the good state bias.

The subset sum problem is considered in terms of an exact algorithm introducing a new core problem based on an improved version of Bellman's recursion.

In this paper, we present a new approach for object boundary extraction, called the watersnake. It is a two-step snake algorithm whose energy functional is minimized by the dynamic programming method. It is more robust to local minima because it finds the solution by searching the entire energy space. To reduce the complexity of the minimization process, the watershed transformation and a coarse-to-fine strategy are used. The new technique is compared to standard methods for accuracy in synthetic data and is applied to segmentation of white blood cells in bone marrow images. Index Terms--Active contour model, snakes, watershed algorithm, dynamic programming, energy minimization, white blood cell detection.

Research investigating optimal resource allocation procedures is presented. Particular attention is given to maximum and minimum activation levels and fixed costs. A portfolio optimization problem with application to project financing is analysed.

Research is presented describing the study of statistical and economic environment changes on the management of cash systems using Markov decision processing.

Research is presented concerning the the development of a dynamic programming algorithm to model the local access network expansion problems associated with a telecommunication network.

Algorithms for the data set reconstruction problem, based on dynamic programming, are presented.

A search game in discrete time and space is investigated.

A new study investigates the problem of optimal stopping and expected utility maximization.

A study has been conducted to examine generalized semi-infinite optimization problems (GSIP) and to try to illustrate the difference between GSIP and standard semi-infinite problems (SIP). Illustrated examples reveal that Chebyshev approximation problems lead to semi-infinite problems and GSIP. Finding indicate that the numerical solution of GSIP can be more difficult than the solution for SIP. The transformation of GSIP to SIP may be possible if in all points of Y(x) the Mangasarian Fromovitz Constraint Qualification is satisfied.

A new approach was created to solve the multiple-objective resource allocation problem. The approach, which utilizes dynamic programming, involves the development of a fuzzy evaluation and fuzzy optimization methodology for multiple-objective systems. Fuzzy evaluation and fuzzy optimization method is integrated with the conventional dynamic programming technique to create a dynamic optimization algorithm. Further development of such algorithm enables it to be used in multiple-objective resource allocation problems with qualitative objectives.

An optimal stopping problem with recall cost was presented in which some of the cost must be paid to accept the best offer y. The model's optimal decision rule may possess a property called the double reservation value in which two different critical values exist for at least one current offer. In the model, the recall cost is viewed as a vital factor and is reasonable to consider such cost. Such cost substantially decreases the value of a past offer.

The MULKNAP algorithm, which is based on the MTM framework of Martello and Toth, is the first algorithm capable of solving large sized cases up to n=100,000 with data range of as much as R=10,000. MULKNAP uses specialized algorithms to derive both lower bounds and upper bounds as well as solve the Subset-sum Problem. It has been demonstrated that despite the unsuitability of Multiple Knapsack Problem in dynamic programming, dynamic programming algorithms can be used to provide the needed solutions.

In a companion paper [6] we presented theoretical analysis of an analog network for fixed-point computation. This paper applies these results to several applications from numerical analysis and combinatorial optimization, in particular: 1) solving systems of linear equations; 2) nonlinear programming; 3) dynamic programing; and 4) network flow computations. Schematic circuits are proposed for representative cases and implementation issues are discussed. Exponential convergence is established for a fixed-point computation that determines the stationary probability vector for a Markov chain. A fixed-point formulation of the single source shortest path problem (SPP) that will always converge to the exact shortest path is described. A proposed implementation, on a 2-[Mu] complementary metal-oxide-semiconductor (CMOS) process, for a fully connected eight-node network is described in detail. The accuracy and settling time issues associated with the proposed design approach are presented.

Dynamic programming is a general technique for solving optimization problems. It is based on the division of problems into simpler subproblems that can be computed separately. In this paper, we show that Datalog with aggregates and other nonmonotonic constructs can express classical dynamic programming optimization problems in a natural fashion, and then we discuss the important classes of queries and applications that benefit from these techniques. Index Terms - Deductive databases, nonmonotonic reasoning, aggregates, optimization.