The Vehicle Routing Problem with Time windows (VRPTW) is an extension of the capacity constrained Vehicle Routing Problem (VRP). The VRPTW is NP-Complete and instances with 100 customers or more are very hard to solve optimally. We represent the VRPTW as a multi-objective problem and present a genetic algorithm solution using the Pareto ranking technique. We use a direct interpretation of the VRPTW as a multi-objective problem, in which the two objective dimensions are number of vehicles and total cost (distance). An advantage of this approach is that it is unnecessary to derive weights for a weighted sum scoring formula. This prevents the introduction of solution bias towards either of the problem dimensions. We argue that the VRPTW is most naturally viewed as a multi-objective problem, in which both vehicles and cost are of equal value, depending on the needs of the user. A result of our research is that the multi-objective optimization genetic algorithm returns a set of solutions that fairly consider both of these dimensions. Our approach is quite effective, as it provides solutions competitive with the best known in the literature, as well as new solutions that are not biased toward the number of vehicles. A set of well-known benchmark data are used to compare the effectiveness of the proposed method for solving the VRPTW.

Many difficult combinatorial optimization problems have been modeled as static problems. However, in practice, many problems are dynamic and changing, while some decisions have to be made before all the design data are known. For example, in the Dynamic Vehicle Routing Problem (DVRP), new customer orders appear over time, and new routes must be reconfigured while executing the current solution. Montemanni et al.[1] considered a DVRP as an extension to the standard vehicle routing problem (VRP) by decomposing a DVRP as a sequence of static VRPs, and then solving them with an ant colony system (ACS) algorithm. This paper presents a genetic algorithm (GA) methodology for providing solutions for the DVRP model employed in [1]. The effectiveness of the proposed GA is evaluated using a set of benchmarks found in the literature. Compared with a tabu search approach implemented herein and the aforementioned ACS, the proposed GA methodology performs better in minimizing travel costs.

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We investigate a class of multiagent planning problems termed multiagent expedition, where agents move around an open, unknown, partially observable, stochastic, and physical environment, in pursuit of multiple and alternative goals of different utility. Optimal planning in multiagent expedition is highly intractable. We introduce the notion of conditional optimality, decompose the task into a set of semi-independent optimization subtasks, and apply a decision-theoretic multiagent graphical model to solve each subtask optimally. A set of techniques are proposed to enhance modeling so that the resultant graphical model can be practically evaluated. Effectiveness of the framework and its scalability are demonstrated through experiments. Multiagent expedition can be characterized as decentralized partially observable Markov decision processes (Dec-POMDPs). Hence, this work contributes towards practical planning in Dec-POMDPs.

Frameworks for multiagent decision making may be divided into those where each agent is assigned a single variable (SVFs) and those where each agent carries an internal model, which can be further divided into loosely coupled frameworks (LCFs) and tightly coupled frameworks (TCFs). In TCFs, agent communication interfaces render their subdomains conditionally independent. In LCFs, either agents do not communicate or their messages are semantically less restricted. SVFs do not address the privacy issue well. LCF agents cannot draw from collective knowledge as well as TCF agents. However, disproportional effort has been dedicated to SVFs and LCFs, which can be attributed partially to unawareness of the computational advantages of TCFs over performance, efficiency and privacy. This work aims to provide empirical evidence of such advantages by comparing recursive modeling method (RMM) from LCFs and collaborative design network (CDN) from TCFs, both of which are decision-theoretic and the latter of which is a graphical model. We apply both to multiagent expedition (MAE), resolve technical issues encountered, and report our experimental evaluation.