A Hybrid Genetic Algorithm for the min-max Multiple Traveling Salesman Problem

This paper proposes a hybrid genetic algorithm for solving the Multiple Traveling Salesman Problem (mTSP) to minimize the length of the longest tour. The genetic algorithm utilizes a TSP sequence as the representation of each individual, and a dynamic programming algorithm is employed to evaluate the individual and find the optimal mTSP solution for the given sequence of cities. A novel crossover operator is designed to combine similar tours from two parents and offers great diversity for the population. For some of the generated offspring, we detect and remove intersections between tours to obtain a solution with no intersections. This is particularly useful for the min-max mTSP. The generated offspring are also improved by a self-adaptive random local search and a thorough neighborhood search. Our algorithm outperforms all existing algorithms on average, with similar cutoff time thresholds, when tested against multiple benchmark sets found in the literature. Additionally, we improve the best-known solutions for 21 out of 89 instances on four benchmark sets

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

A vehicle routing model with split delivery and stop nodes

In this work, a new variant of the Capacitated Vehicle Routing Problem (CVRP) is presented where the vehicles cannot perform any route leg longer than a given length L (although the routes can be longer). Thus, once a route leg length is close to L, the vehicle must go to a stop node to end the leg or return to the depot. We introduce this condition in a variation of the CVRP, the Split Delivery Vehicle Routing Problem, where multiple visits to a customer by different vehicles are allowed. We present two formulations for this problem which we call Split Delivery Vehicle Routing Problem with Stop Nodes: a vehicle flow formulation and a commodity flow formulation. Because of the complexity of this problem, a heuristic approach is developed. We compare its performance with and without the stop nodesSplit delivery vehicle routing problem, Stop node, Granular neighborhood, Tabu search

Dynamic vehicle routing problems: Three decades and counting

Since the late 70s, much research activity has taken place on the class of dynamic vehicle routing problems (DVRP), with the time period after year 2000 witnessing a real explosion in related papers. Our paper sheds more light into work in this area over more than 3 decades by developing a taxonomy of DVRP papers according to 11 criteria. These are (1) type of problem, (2) logistical context, (3) transportation mode, (4) objective function, (5) fleet size, (6) time constraints, (7) vehicle capacity constraints, (8) the ability to reject customers, (9) the nature of the dynamic element, (10) the nature of the stochasticity (if any), and (11) the solution method. We comment on technological vis-à-vis methodological advances for this class of problems and suggest directions for further research. The latter include alternative objective functions, vehicle speed as decision variable, more explicit linkages of methodology to technological advances and analysis of worst case or average case performance of heuristics.© 2015 Wiley Periodicals, Inc

The Traveling Salesman Problem with Stochastic and Correlated Customers

It is well-known that the cost of parcel delivery can be reduced by designingroutes that take into account the uncertainty surrounding customers’ presences. Thus far, routing problems with stochastic customer presences have relied on the assumption that all customer presences are independent from each other. However, the notion that demographic factors retain predictive power for parcel-delivery efficiency suggests that shared characteristics can be exploited to map dependencies between customer presences. This paper introduces the correlated probabilistic traveling salesman problem (CPTSP). The CPTSP generalizes the traveling salesman problem with stochastic customer presences, also known as the probabilistic traveling salesman problem (PTSP), to account for potentialcorrelations between customer presences. I propose a generic and flexible model formulation for the CPTSP using copulas that maintains computational and mathematical tractability in high-dimensional settings. I also present several adaptations of existing exact and heuristic frameworks to solve the CPTSP effectively. Computational experiments on real-world parcel-delivery data reveal that correlations between stochastic customer presences do not always affect route decisions, but could have a considerable impact on route costestimates