Kevin Y. K. Ng

A hybrid ‘dynamic programming/depth-first search’ algorithm, with an application to redundancy allocation

A hybrid ‘dynamic programming/depth-first search’ algorithm has been developed to solve non-linear integer programming problems arising in the reliability optimization of redundancy allocation. Initially, the technique solves the knapsack relaxation of the original mathematical programming problem using dynamic programming. Then, all solutions in some range of the relaxation problem are obtained via an enumerative depth-first search technique. The solutions are ranked and the optimal solution is given by the best one that satisfies the remaining constraints of the given problem. Computational complexity of the algorithm is also discussed. The salient features of our hybrid algorithm are its simplicity and ease of programming. Our algorithm also has an advantage over the traditional Lagrangian and surrogate dual approaches. It does not have to deal with the issue of ‘duality gap’ as in classical dual approaches, which is responsible for the failure to identify optimal solutions to the primal integer optimization problems. Of most importance, it guarantees to succeed in identifying an optimal solution.

Workforce configuration and workflow analysis of an information technology organization: a queueing network approach

This paper addresses two issues related to a hypothetical division in the Canadian Forces Geomatics Organization, which is devoted to the production of information in support of the U.S. National Imaging and Mapping Agencys (NIMA) Foundation Based Operations. First, the optimal configuration of the division is determined using queueing network and optimization principles. The second issue concerns the examination of the system behavior, given the system configuration. Bounding analysis, in classical queueing theory, is used to acquire insights into the problem. The contribution of the paper lies in the derivation of an alternative geomatics network architecture and the illustration that the L/sup /spl infin// norms on the expected steady-state waiting times between the two network representations, are equivalent. The objective of the revised architecture is that the theory of product-form solutions can be employed. In addition, the paper proposes a means to transform the nonlinear integer programming Internet protocol (IP) problem to a linear IP, using approximation techniques and pre-tabulated probability-related functions. Finally, in anticipation of the surge and volume of geomatics information in support of Joint Vision 2010, this workforce and workflow analysis is of utmost importance. This paper provides a timely contribution toward the resolution of some of these military organizational issues.

A new algorithm for solving certain variational problems

A technique for finding the solution of discrete, multistate dynamic programming problems is applied to solve certain variational problems. The algorithm is a method of successive approximations using a general two-stage solution. The advantage of the method is that it provides a means of reducing Bellmans “curse of dimensionality.” An example on the Plateau problem or the minimal surface area problem is considered, and the algorithm is found to be computationally efficient.

An automated surface surveillance system

This paper describes an automated surface surveillance system, developed on behalf of the Government of Canada to detect and track illegal vessels. The scenario involves a moving target having speed significantly less than the searcher speed, slowly approaching Canadas coastline. The crux of the surveillance problem is to determine the sequence of sub-regions to search in order to maximize the probability of target detection. The complexity of our surveillance problem lies in the absence of knowledge on the target location, speeds and course. Additionally, the searcher is frequently confronted with insufficient time to area search the sub-regions. The presence of false targets and the occurrence of irregular search area further compound the problem. Our decision support system is a combination of established theories on probability maps, barrier patrol and a novel construction of heuristics for area searching irregular regions. Our approach also involves extensive use of visualization tools to aid code debugging and validation. More importantly, our automated surveillance system provides a user-friendly environment for decision planners.

Regional surveillance of disjoint rectangles: a travelling salesman formulation

Mission planning for surveillance coverage is of both practical and theoretical interest. In brief, regional surveillance involves planning the search of certain given regions in the minimum possible time. The surveillance problem can therefore be described as a variant of the classical travelling salesman problem. The uniqueness of the problem lies in the different allowed entry and exit points. Additionally, the mission schedule has to ensure the probability of target detection must not be compromised. From the practical perspective, any reduction in travelling time provides immediate cost savings to the defence department. A dynamic programming formulation is derived for the regional surveillance problem. An example is included to illustrate the methodology.

Goal Programming, Method of Weighted Residuals, and Optimal Control Problems

The feasibility of utilizing goal programming, a management science originated technique, in solving optimal control problems is investigated. The basic idea is to recast the problem in a pre-emptive goal programming model via the use of hard and soft constraints (or stiff and weak springs) in linear programming (or mechanics). It is found that the goal programming technique for solving the optimal control problem is fundamentally more general than the method of weighted residuals. An example is included to illustrate the methodology.

An agent-based approach towards network-enabled capabilities – I: Simulation validation and illustrative examples

This paper presents an approach to understanding network-enabled operations using agent-based simulations. We describe the newly created agent-based software ABSNEC (Agent-Based System for Network Enabled Capabilities), highlighting some of its salient features: the ability to represent human factors towards the analysis of battle outcomes in network operations, and the ability to represent realistic force structures with tiered C2 architectures. We provide affirmative results of three validation techniques to date on the model. Finally, we demonstrate the utilization of ABSNEC to acquire meaningful insights for analysis through two examples: a study on the interrelationship between fratricide, human factors, and situation awareness; and the generation of alternative combat strategies for a military engagement.

Dynamic programming, reduction of dimensionality and eigenvalue problems

Abstract This paper develops an iterative algorithm, based on a priori deduction from Bellmans principle of optimality, for solving eigenvalue problems. During each iteration, the set of admissible states is restricted only to those stages that are “near” to the nominal trajectory. The algorithm is shown to use only minimal storage requirements. The significance of the method is that it provides a means of reducing Bellmans “curse of dimensionality” and broadens the scope of problems that can effectively be solved with the dynamic programming approach. The technique is then applied to evaluate the smallest eigenvalue for the differential equation arising in the mathematical modelling of the desorption from a liquid film.

Solution of Nonlinear Field Problems by Goal Programming

This survey paper reports on the application of goal programming techniques toward the solutions of nonlinear field problems. The proposed approach involves approximating the solution by a set of trial functions containing unknown coefficients. The technique then minimizes in a weighted residual sense the absolute deviations of the system equations and/or the performance function residuals by nonlinear goal programming. Since the approximate solutions will in general not be able to satisfy all conditions, such as the boundary and initial conditions and at the same time minimize the residual errors, our approach involves reformulating the field problem as a preemptive goal programming model via the use of hard and soft constrains (or stiff and weak springs) in linear programming (or mechanics). Examples from fluid dynamics and control theory will be employed to illustrate the methodolgy. In conclusion, the advantages, limitations and other related issues on the goal programming model in solving nonlinear problems will be discussed.

DYNAMIC PROGRAMMING, REDUCTION OF DIMENSIONALITY AND EIGENVALUE PROBLEMS—II. MULTIDIMENSIONAL CASE

Dynamic Programming as used in most optimal control applications relies heavily on the causal structure of the underlying dynamics. In this paper, we will show that noncausal problems, such as the Helmholtz equation, can be recast into causal form and then be handled as a vector multistage decision process using a modified version of dynamic programming. The proposed technique, documented in detail in a previous paper by Ng and Sancho5, is based on an a priori deduction from Bellmans principle of optimally. The significance of the method is that it provides a means of reducing Bellmans “curse of dimensionality” and broadens the scope of problems that can effectively be solved with the dynamic programming approach The outstanding feature of the technique is illustrated by its application to the evaluation of the dominant TM-mode of rectangular and ridge electric waveguides. The latter problem is particularly challenging because it involves singularities in the solution. The modified dynamic programming s...