Michael J. Hirsch

Global optimization by continuous grasp

We introduce a novel global optimization method called Continuous GRASP (C-GRASP) which extends Feo and Resende’s greedy randomized adaptive search procedure (GRASP) from the domain of discrete optimization to that of continuous global optimization. This stochastic local search method is simple to implement, is widely applicable, and does not make use of derivative information, thus making it a well-suited approach for solving global optimization problems. We illustrate the effectiveness of the procedure on a set of standard test problems as well as two hard global optimization problems.

Speeding up continuous GRASP

Continuous GRASP (C-GRASP) is a stochastic local search metaheuristic for finding cost-efficient solutions to continuous global optimization problems subject to box constraints (Hirsch et al., 2007). Like a greedy randomized adaptive search procedure (GRASP), a C-GRASP is a multi-start procedure where a starting solution for local improvement is constructed in a greedy randomized fashion. In this paper, we describe several improvements that speed up the original C-GRASP and make it more robust. We compare the new C-GRASP with the original version as well as with other algorithms from the recent literature on a set of benchmark multimodal test functions whose global minima are known. Harts sequential stopping rule (1998) is implemented and C-GRASP is shown to converge on all test problems.

A biased random-key genetic algorithm for road congestion minimization

One of the main goals in transportation planning is to achieve solutions for two classical problems, the traffic assignment and toll pricing problems. The traffic assignment problem aims to minimize total travel delay among all travelers. Based on data derived from the first problem, the toll pricing problem determines the set of tolls and corresponding tariffs that would collectively benefit all travelers and would lead to a user equilibrium solution. Obtaining high-quality solutions for this framework is a challenge for large networks. In this paper, we propose an approach to solve the two problems jointly, making use of a biased random-key genetic algorithm for the optimization of transportation network performance by strategically allocating tolls on some of the links of the road network. Since a transportation network may have thousands of intersections and hundreds of road segments, our algorithm takes advantage of mechanisms for speeding up shortest-path algorithms.

Cooperative Tracking of Multiple Targets by a Team of Autonomous UAVs

This research is concerned with dynamically determining appropriate flight patterns for a set of autonomous UAVs in an urban environment, for persistent and accurate tracking of moving ground targets. The authors assume that there are limited communication capabilities between the UAVs, and that there exist possible line of sight constraints between the UAVs and the targets. Each UAV (i) operates its own dynamic feedback loop, in a receding horizon framework, incorporating local information on the targets (from UAV i perspective) as well as remote information on the targets (from the perspective of the ‘neighbor’ UAVs) to determine the optimal flight path of UAV i over the planning horizon. This results in a decentralized and more realistic model of the real-world situation. As the flight-plan optimization formulation is NP-hard, a new heuristic for continuous global optimization is applied to solve for the flight plan. Results show that efficient flight patterns for the UAVs can be achieved.

Sensor Registration in a Sensor Network by Continuous GRASP

One of the main reasons in forming a sensor network is to combine the information seen from different sensors to produce a single integrated picture that is an accurate representation of the scene of interest. An often overlooked problem in network design is the proper registration of the sensors in the network. Sensor registration can be seen as the process of removing (accounting for) non-random errors, or biases, in the sensor data. Without properly accounting for these errors, the quality of the composite picture can, and oftentimes does, degrade. In this paper, we present an approach for solving the sensor registration problem, based on a new continuous meta-heuristic, when not all data is seen by all sensors, and the correspondence of data seen by the different sensors is not known a priori. Considering a real problem from the defense industry, we show that this approach performs better than other approaches in the literature.

On the minimization of traffic congestion in road networks with tolls

Population growth and the massive production of automotive vehicles have lead to the increase of traffic congestion problems. Traffic congestion today is not limited to large metropolitan areas, but is observed even in medium-sized cities and highways. Traffic engineering can contribute to lessen these problems. One possibility, explored in this paper, is to assign tolls to streets and roads, with the objective of inducing drivers to take alternative routes, and thus better distribute traffic across the road network. This assignment problem is often referred to as the tollbooth problem and it is NP-hard. In this paper, we propose mathematical formulations for two versions of the tollbooth problem that use piecewise-linear functions to approximate congestion cost. We also apply a biased random-key genetic algorithm on a set of real-world instances, analyzing solutions when computing shortest paths according to two different weight functions. Experimental results show that the proposed piecewise-linear functions approximate the original convex function quite well and that the biased random-key genetic algorithm produces high-quality solutions.

A continuous GRASP to determine the relationship between drugs and adverse reactions

Adverse drag reactions (ADRs) are estimated to be one of the leading causes of death. Many national and international agencies have set up databases of ADR reports for the express purpose of determining the relationship between drugs and adverse reactions that they cause. We formulate the drug‐reaction relationship problem as a continuous optimization problem and utilize C‐GRASP, a new continuous global optimization heuristic, to approximately determine the relationship between drugs and adverse reactions. Our approach is compared against others in the literature and is shown to find better solutions.

A stochastic optimization framework for resource management and course of action analysis

We consider a course of action (COA) problem domain with the support of information fusion technologies. We assume that level 1 and 2 fusion technologies have provided a set of suspicious/abnormal situations currently occurring and associated dasiaobjects of interestpsila participating in these situations, along with likelihoods of participation. We further assume that there are limited resources available to gather additional information on these objects of interest. COA analysis and resource management (RM) prescribe placement of resources to accomplish desired information gathering tasks. Thus the goal of COA/RM is ldquoputting the right resource in the right place and time to perform the appropriate information gathering task on the appropriate objects of interest.rdquo Our research focuses on formulating the COA/RM problem from a stochastic optimization framework, resulting in an NP-hard problem. An efficient heuristic is developed and demonstrated on an illustrative scenario from maritime domain awareness.

Multi-depot vessel routing problem in a direction dependent wavefield

Considerable research has been done on the vehicle routing problem and its variants; however only limited amount of existing work deals with possible environmental conditions and their effects on the vehicle routes. This paper presents the multiple-depot vehicle routing problem for surface vessels, where the vehicles must traverse a time-invariant direction-dependent medium. Our model captures environmental effects and vessel dynamics on the considered paths. Three heuristic solution methods are developed and tested on simulated scenarios. The first approach exactly solves an approximate formulation of the problem, the second approximately solves an approximate problem formulation, while the third approximately solves the exact problem. Performance of the algorithms are compared to assess the tradeoff between computational cost and quality of the found solutions.

End-to-End Applications and Algorithm Integration (E2A2I) Method and Architecture

DoD manned and unmanned air systems require multiple mission phases, each with unique procedures, algorithms and checklists that are implemented through a variety of hardware and software mechanisms, all within the same mission. This approach is not efficient with respect to mission processing, staffing, and training. The End-to-End Applications and Algorithm Integration (E2A2I) Method and Architecture addresses this issue using a checklist application that receives a complete mission checklist for all mission phases (e.g., pre-mission, launch and recovery, on-mission, post-mission, and maintenance) from a data broker enforcement entity that has access to a data store. This data store contains many checklists in support of multiple diverse missions. The E2A2I application automatically executes the checklists, invoking other mission applications in order of their mission usage. The E2A2I application runs on a mobile computing device with software services that invoke one mobile application from another so that the same applications can be used in multiple mission phases and for multiple missions.