Restricted Dynamic Programming Heuristic for Precedence Constrained Bottleneck Generalized TSP

We develop a restricted dynamical programming heuristic for a complicated traveling salesman problem: a) cities are grouped into clusters, resp. Generalized TSP; b) precedence constraints are imposed on the order of visiting the clusters, resp. Precedence Constrained TSP; c) the costs of moving to the next cluster and doing the required job inside one are aggregated in a minimax manner, resp. Bottleneck TSP; d) all the costs may depend on the sequence of previously visited clusters, resp. Sequence-Dependent TSP or Time Dependent TSP. Such multiplicity of constraints complicates the use of mixed integer-linear programming, while dynamic programming (DP) benefits from them; the latter may be supplemented with a branch-and-bound strategy, which necessitates a “DP-compliant” heuristic. The proposed heuristic always yields a feasible solution, which is not always the case with heuristics, and its precision may be tuned until it becomes the exact DP

AN INTEGER PROGRAMMING APPROACH FOR SINGLE TRUCK ROUTING-AND-SCHEDULING PROBLEMS TO ISLANDS WITH TIME-VARYING FERRY SCHEDULES

This study aims to develop a solving model for the single trucks routing-and-scheduling problems to islands with variations in ferry schedules. In this problem, the travel time is asymmetric and the truck routing is based on the sequence of island visits, known and unknown. The models are developed using an integer programming approach. Integer non-linear programming is formulated to solve problems where the sequence is unknown, whereas integer linear programming for the sequence is known. Besides, a delivery day scenario is built to determine the optimal route and schedule with minimum total travel time on each departure day. Numerical experiments were carried out on the case of a small distribution of a small industry in Central Moluccas, Indonesia. The results showed that the model developed could provide solutions to solve problems

OPERATIONAL PLANNING AND OPTIMIZATION OF SMALL DOMAIN SWARM DEFENSE STRATEGIES

This thesis considers the case of a drone defending a high-value target from a number of inbound attacking drones. The defending drone is equipped with short-range weapons and must destroy each of the attacking drones in the most efficient manner. This problem sits at the intersection of several open problems in applied mathematics, such as optimal motion planning in the presence of attrition, as well as solving a “traveling salesman problem” (TSP) with moving targets. The purpose of our research was to analyze this problem by decomposing it into the component problems and then presenting proof-of-concept solutions of each component. The primary results of this thesis include a modeling framework where optimization can be performed without requiring constraints; comparing the strengths of using different types of cost functions for optimization (e.g., minimizing the chance of high-value unit destruction versus a metric based on the path of the defender relative to attackers); and solving moving-target TSP in certain limits by mapping it onto standard TSP or using machine learning.Cruiser/ONRMajor, United States Marine CorpsApproved for public release. Distribution is unlimited

Scheduling aircraft landings - the static case

This is the publisher version of the article, obtained from the link below.In this paper, we consider the problem of scheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time for each plane such that each plane lands within a predetermined time window and that separation criteria between the landing of a plane and the landing of all successive planes are respected. We present a mixed-integer zero–one formulation of the problem for the single runway case and extend it to the multiple runway case. We strengthen the linear programming relaxations of these formulations by introducing additional constraints. Throughout, we discuss how our formulations can be used to model a number of issues (choice of objective function, precedence restrictions, restricting the number of landings in a given time period, runway workload balancing) commonly encountered in practice. The problem is solved optimally using linear programming-based tree search. We also present an effective heuristic algorithm for the problem. Computational results for both the heuristic and the optimal algorithm are presented for a number of test problems involving up to 50 planes and four runways.J.E.Beasley. would like to acknowledge the financial support of the Commonwealth Scientific and Industrial Research Organization, Australia

ANALYSIS OF IDEAL MANEUVERS FOR MISSION EXTENSION VEHICLE

Finding optimal maneuvers between spacecraft is computationally demanding. Targeting many spacecraft successively requires more computational power than commercially available. This thesis tested algorithms looking to reduce this computational burden. Algorithms claiming optimal two-impulse rendezvous solutions between any two arbitrary orbits were coded and compared through minimum delta-vs (fuel) and computational times. Orbit characteristics were varied across a multitude of scenarios to represent many possible applications. Assorted considerations were discussed, which provided a framework for designing multi-client on-orbit servicing missions.Lieutenant, United States NavyApproved for public release. Distribution is unlimited

Monitoring using Heterogeneous Autonomous Agents.

This dissertation studies problems involving different types of autonomous agents observing objects of interests in an area. Three types of agents are considered: mobile agents, stationary agents, and marsupial agents, i.e., agents capable of deploying other agents or being deployed themselves. Objects can be mobile or stationary. The problem of a mobile agent without fuel constraints revisiting stationary objects is formulated. Visits to objects are dictated by revisit deadlines, i.e., the maximum time that can elapse between two visits to the same object. The problem is shown to be NP-complete and heuristics are provided to generate paths for the agent. Almost periodic paths are proven to exist. The efficacy of the heuristics is shown through simulation. A variant of the problem where the agent has a finite fuel capacity and purchases fuel is treated. Almost periodic solutions to this problem are also shown to exist and an algorithm to compute the minimal cost path is provided. A problem where mobile and stationary agents cooperate to track a mobile object is formulated, shown to be NP-hard, and a heuristic is given to compute paths for the mobile agents. Optimal configurations for the stationary agents are then studied. Several methods are provided to optimally place the stationary agents; these methods are the maximization of Fisher information, the minimization of the probability of misclassification, and the minimization of the penalty incurred by the placement. A method to compute optimal revisit deadlines for the stationary agents is given. The placement methods are compared and their effectiveness shown using numerical results. The problem of two marsupial agents, one carrier and one passenger, performing a general monitoring task using a constrained optimization formulation is stated. Necessary conditions for optimal paths are provided for cases accounting for constrained release of the passenger, termination conditions for the task, as well as retrieval and constrained retrieval of the passenger. A problem involving two marsupial agents collecting information about a stationary object while avoiding detection is then formulated. Necessary conditions for optimal paths are provided and rectilinear motion is demonstrated to be optimal for both agents.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111439/1/jfargeas_1.pd