James T. Moore

A branch and bound algorithm for the bilevel programming problem

The bilevel programming problem is a static Stackelberg game in which two players try to maximize their individual objective functions. Play is sequential and uncooperative in nature. This paper presents an algorithm for solving the linear/quadratic case. In order to make the problem more manageable, it is reformulated as a standard mathematical program by exploiting the followers Kuhn–Tucker conditions. A branch and bound scheme suggested by Fortuny-Amat and McCarl is used to enforce the underlying complementary slackness conditions. An example is presented to illustrate the computations, and results are reported for a wide range of problems containing up to 60 leader variables, 40 follower variables, and 40 constraints. The main contributions of the paper are in the step-by-step details of the implementation, and in the scope of the testing.

The mixed integer linear bilevel programming problem

A two-person, noncooperative game in which the players move in sequence can be modeled as a bilevel optimization problem. In this paper, we examine the case where each player tries to maximize the individual objective function over a jointly constrained polyhedron. The decision variables are variously partitioned into continuous and discrete sets. The leader goes first, and through his choice may influence but not control the responses available to the follower. For two reasons the resultant problem is extremely difficult to solve, even by complete enumeration. First, it is not possible to obtain tight upper bounds from the natural relaxation; and second, two of the three standard fathoming rules common to branch and bound cannot be applied fully. In light of these limitations, we develop a basic implicit enumeration scheme that finds good feasible solutions within relatively few iterations. A series of heuristics are then proposed in an effort to strike a balance between accuracy and speed. The computational results suggest that some compromise is needed when the problem contains more than a modest number of integer variables.

An algorithm for the discrete bilevel programming problem

The bilevel programming problem (BLPP) is an example of a two-stage, noncooperative game in which the first player can influence but not control the actions of the second. This article addresses the linear formulation and presents a new algorithm for solving the zero-one case. We begin by converting the leaders objective function into a parameterized constraint, and then attempt to solve the resultant problem. This produces a candidate solution that is used to find a point in the BLPP feasible reagion. Incremental improvements are sought, which ultimately lead to a global optimum. An example is presented to highlight the computations and to demonstrate some basic characteristics of the solution. Computational experience indicates that the algorithm is capable of solving problems with up to 50 variables in a reasonable amount of time.

Reactive tabu search in unmanned aerial reconnaissance simulations

We apply a Reactive Tabu Search (RTS) heuristic within a discrete-event simulation to solve routing problems for unmanned aerial vehicles (UAVs). Our formulation represents this problem as a multiple traveling salesman problem with time windows (mTSPTW), with the objective of maximizing expected target coverage. Incorporating weather and probability of UAV survival at each target as random inputs, the RTS heuristic in the simulation searches for the best solution in each realization of the problem scenario in order to identify those routes that are robust to variations in weather, threat, or target service times. We present an object-oriented implementation of this approach using CACIs simulation language MODSIM.

The distributor's three-dimensional pallet-packing problem: a human intelligence-based heuristic approach

The distributors pallet-packing problem requires the loading of a pallet or container that has a fixed length, width and height with the objective to maximise utilisation of the pallets volume. We develop a new heuristic algorithm using novel heuristic rules and a dynamic data structure to mimic human intelligence, thus providing a new solution approach to 3-D pallet packing. Comprehensive empirical testing, to include new methods for generating problems with known optimal solutions, demonstrate that our algorithm achieves pallet volume utilisations comparable or better than the best-known solutions, while finding these solutions very quickly. Computer-independent complexity results are provided.

Problem reduction heuristic for the 0-1 multidimensional knapsack problem

This paper introduces new problem-size reduction heuristics for the multidimensional knapsack problem. These heuristics are based on solving a relaxed version of the problem, using the dual variables to formulate a Lagrangian relaxation of the original problem, and then solving an estimated core problem to achieve a heuristic solution to the original problem. We demonstrate the performance of these heuristics as compared to legacy heuristics and two other problem reduction heuristics for the multi-dimensional knapsack problem. We discuss problems with existing test problems and discuss the use of an improved test problem generation approach. We use a competitive test to highlight the performance of our heuristics versus the legacy heuristic approaches. We also introduce the concept of computational versus competitive problem test data sets as a means to focus the empirical analysis of heuristic performance.

Devising a quick-running heuristic for an unmanned aerial vehicle (UAV) routing system

UAVs provide reconnaissance support for the US military and often need operational routes immediately; current practice involves manual route calculation that can involve hundreds of targets and a complex set of operational restrictions. Our research focused on providing an operational UAV routing system. This system required development of a reasonably effective, quick running routing heuristic. We present the statistical methodology used to devise a quick-running routing heuristic that provides reasonable solutions. We consider three candidate local search heuristic approaches, conduct an empirical analysis to parameterize each heuristic, competitively test each candidate heuristic, and provide statistical analysis on the performance of each candidate heuristic to include comparison of the results of the best candidate heuristic against a compilation of the best-known solutions for standard test problems. Our heuristic is a component of the final UAV routing system and provides the UAV operators a tool to perform their route development tasks quickly and efficiently.

Trust Management and Security in the Future Communication-Based "Smart" Electric Power Grid

New standards and initiatives in the U.S. electric power grid are moving in the direction of a smarter grid. Media attention has focused prominently on smart meters in distribution systems, but big changes are also occurring in the domains of protection, control, and Supervisory Control and Data Acquisition (SCADA) systems. These changes promise to enhance the reliability of the electric power grid and to allow it to safely operate closer to its limits, but there is also a real danger concerning the introduction of network communication vulnerabilities to so-called cyber attacks. This article advocates the use of a reputation-based trust management system as one method to mitigate such attacks. A simulated demonstration of the potential for such systems is illustrated in the domain of backup protection systems. The simulation results show the promise of this proposed technique.

Exploiting empirical knowledge for bi-dimensional knapsack problem heuristics

The Multidimensional Knapsack Problem (MKP) has been used to model a variety of practical applications. Due to its combinatorial nature, heuristics are often employed to quickly find good solutions to MKPs. There have been a variety of heuristics proposed for MKP and a plethora of empirical studies comparing the performance of these heuristics. However, little has been done to garner a deeper understanding of why certain heuristics perform well on certain types of problems and others do not. Using a broad range of practical MKP test problems, we use three representative heuristics and conduct an empirical study aimed at gaining a deeper understanding of heuristic procedure performance as a function of test problem constraint characteristics. Our focus is on the Two-dimensional Knapsack Problem (2KP). New insights developed regarding greedy heuristic performance are exploited to yield two new heuristics whose performance is more robust than that of three legacy heuristics on our test problem set and on benchmark sets of MKP problems. A competitive test of these new heuristics against a set of legacy heuristics, using both existing test problem sets and a new systematically developed test problem set demonstrate the superior, robust performance of our new heuristics.

Maximizing strike aircraft planning efficiency for a given class of ground targets

Strike planning is one of the fundamental tasks of an advanced Air Force and involves the assignment of strike aircraft to ground targets with a maximum level of efficiency. Therefore, planning an optimal strike based on the preferences of the decision maker is crucial. The efficiency of the strike plan in this paper implies attacking the maximum number of targets while considering target priority and the desired level of damage on each target. The other objective is to minimize the cost of the strike plan. This paper develops a methodology that maximizes the efficiency of the strike plan. Given this efficiency, the aircraft and weapon costs plus the distance flown is then minimized. The methodology also considers the capacities for different types of aircraft and weapons at each aircraft base to avoid assigning aircraft to targets from a base where there are insufficient resources to do so. Computational results are presented that analyze the sensitivity of the model solution times to solver optimality tolerance and aircraft and weapon capacities. Results also suggest substantial cost savings are possible while still maintaining the effectiveness of the strike package.