Robert F. Dell

Using multiple searchers in constrained-path, moving-target search problems

The search theory open literature has paid little, if any, attention to the multiple-searcher, moving-target search problem. We develop an optimal branch-and-bound procedure and six heuristics for solving constrained-path problems with multiple searchers. Our optimal procedure outperforms existing approaches when used with only a single searcher. For more than one searcher, the time needed to guarantee an optimal solution is prohibitive. Our heuristics represent a wide variety of approaches: One solves partial problems optimally, two use paths based on maximizing the expected number of detections, two are genetic algorithm implementations, and one is local search with random restarts. A heuristic based on the expected number of detections obtains solutions within 2% of the best known for each one-, two-, and three-searcher test problem considered. For one- and two-searcher problems, the same heuristics solution time is less than that of other heuristics. For three-searcher problems, a genetic algorithm implementation obtains the best-known solution in as little as 20% of other heuristic solution times.

Web User Session Reconstruction Using Integer Programming

An important input for Web usage mining is Web user sessions that must be reconstructed from Web logs (sessionization) when such sessions are not otherwise identified. We present a novel approach for sessionization based on an integer program. We compare results of our approach with the timeout heuristic on Web logs from an academic Web site. We find our integer program provides sessions that better match an expected empirical distribution with about half of the standard error of the heuristic.

Optimizing Military Capital Planning

Planning United States military procurement commits a significant portion of our nations wealth and determines our ability to defend ourselves, our allies, and our principles over the long term. Our military pioneered and has long used mathematical optimization to unravel the distinguishing complexities of military capital planning. The succession of mathematical optimization models we present exhibits increasingly detailed features; such embellishments are always needed for real-world, long-term procurement decision models. Two case studies illustrate practical modeling tricks that are useful in helping decision makers decide how to spend about a trillion dollars.

Formulating Integer Linear Programs: A Rogues' Gallery

“Convincing yourself is easy, persuading a colleague is harder, but proving it to a computer is hardest of all!”---R. Hamming, ca 1985. The art of formulating linear and integer linear programs is, well, an art: It is hard to teach, and even harder to learn. To help demystify this art, we present a set of modeling building blocks that we call “formulettes.” Each formulette consists of a short verbal description that must be expressed in terms of variables and constraints in a linear or integer linear program. These formulettes can better be discussed and analyzed in isolation from the much more complicated models they comprise. Not all models can be built from the formulettes we present. Rather, these are chosen because they are the most frequent sources of mistakes. We also present Naval Postgraduate School NPS format; a define-before-use formulation guide we have followed for decades to express a complete formulation.

Solving the pallet loading problem

Abstract This paper presents new bounds, heuristics, and an exact algorithm for the Pallet Loading Problem (PLP). PLP maximizes the number of boxes placed on a rectangular pallet. All boxes have identical rectangular dimensions and, when placed, must be located completely within the pallet. Boxes may be rotated 90° so long as they are placed with edges parallel to the pallet’s edges. The set of all PLP instances with an area ratio (pallet area divided by box area) less than 101 boxes can be represented by 3,080,730 equivalent classes. Our G5-heuristic finds optimal solutions to 3,073,724 of these 3,080,730 classes and in the remaining 7006 classes only differs from the best known bound by one box. We develop three other heuristics that solve another 54 instances. Finally, we solve the 6952 remaining classes with our exact HVZ algorithm. Only a subset of these classes has been solved previously.

The minimum size instance of a Pallet Loading Problem equivalence class

Abstract The Pallet Loading Problem (PLP) maximizes the number of identical rectangular boxes placed within a rectangular pallet. Boxes may be rotated 90° so long as they are packed with edges parallel to the pallet’s edges, i.e., in an orthogonal packing. This paper defines the Minimum Size Instance (MSI) of an equivalence class of PLP, and shows that every class has one and only one MSI. We develop bounds on the dimensions of box and pallet for the MSI of any class. Applying our new bounds on MSI dimensions, we present an algorithm for MSI generation and use it to enumerate all 3,080,730 equivalence classes with an area ratio (pallet area divided by box area) smaller than 101 boxes. Previous work only provides bounds on the ratio of box dimensions and only considers a subset of all classes presented here.

How US Air Force Space Command Optimizes Long-Term Investment in Space Systems

United States Air Force Space Command spends billions of dollars each year acquiring and developing launch vehicles and space systems. The space systems in orbit must continually meet defensive and offensive requirements and remain interoperable over time. Space Command can launch additional space systems only if it has a launch vehicle of sufficient capability. Space planners using space and missile optimization analysis (SAMOA) consider a 24-year time horizon when determining which space assets and launch vehicles to fund and procure. A key tool within SAMOA is an integer linear program called the space command optimizer of utility toolkit (SCOUT) that Space Command uses for long-range planning. SCOUT gives planners insight into the annual funding profiles needed to meet Space Commands acquisition goals. The 1999 portfolio of 74 systems will cost about

Optimizing plant-line schedules and an application at Hidden Valley manufacturing company

310 billion and includes systems that can lift satellites into orbit; yield information on space, surface, and subsurface events, activities, and threats; and destroy terrestrial, airborne, and space targets.

Optimizing Army Base Realignment and Closure

A plant line schedule specifies a plants sustained batch operations over time with detail sufficient to manage all activities. Plantwide considerations include restrictions on how production centers can be formed from production lines, packaging lines, conveyers, and so forth; the cost and time of product-package item setups, changeovers, and shutdowns; honoring in-stock service levels, minimum inventory, and committed shipments; recognizing efficiency gains with longer batch runs; respecting crew constraints; and the costs of materials, labor, and carrying inventory. We developed a cost-minimizing optimization model, PROFITS, that features multiple independent time streams for various categories of events that mimic existing periodic reviews of operations. PROFITS is embedded in a graphical user interface that eases the grueling aspects of scheduling: preparing data, controlling scenarios, and visualizing results. At Hidden Valley Manufacturing Company, completing an eight-week plant-line schedule takes about an hour. This is much faster than manual scheduling was--and the schedules are better.

Optimally Stationing Army Forces

In April 1997, the United States Army announced that savings had finally overtaken costs in closing or realigning 803 of its installations worldwide. This milestone occurred in the ninth year of a 13-year program approved by Congress and Presidents Reagan, Bush, and Clinton. The cost of this program is