Kwong Meng Teo

Vehicle routing problem with time windows and a limited number of vehicles

Abstract This paper introduces a variant of the vehicle routing problem with time windows where a limited number of vehicles is given (m-VRPTW). Under this scenario, a feasible solution is one that may contain either unserved customers and/or relaxed time windows. We provide a computable upper bound to the problem. To solve the problem, we propose a tabu search approach characterized by a holding list and a mechanism to force dense packing within a route. We also allow time windows to be relaxed by introducing the notion of penalty for lateness. In our approach, customer jobs are inserted based on a hierarchical objective function that captures multiple objectives. Computational results on benchmark problems show that our approach yields solutions that are competitive to best-published results on VRPTW. On m-VRPTW instances, experiments show that our approach produces solutions that are very close to computed upper bounds. Moreover, as the number of vehicles decreases, the routes become more densely packed monotically. This shows that our approach is good from both the optimality as well as stability point of view.

Robust Optimization for Unconstrained Simulation-Based Problems

In engineering design, an optimized solution often turns out to be suboptimal when errors are encountered. Although the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse if the cost function is nonconvex. In this work, we present a robust optimization method that is suited for unconstrained problems with a nonconvex cost function as well as for problems based on simulations, such as large partial differential equations (PDE) solver, response surface, and Kriging metamodels. Moreover, this technique can be employed for most real-world problems because it operates directly on the response surface and does not assume any specific structure of the problem. We present this algorithm along with the application to an actual engineering problem in electromagnetic multiple scattering of aperiodically arranged dielectrics, relevant to nanophotonic design. The corresponding objective function is highly nonconvex and resides in a 100-dimensional design space. Starting from an “optimized” design, we report a robust solution with a significantly lower worst-case cost, while maintaining optimality. We further generalize this algorithm to address a nonconvex optimization problem under both implementation errors and parameter uncertainties.

Vehicle routing problem with a heterogeneous fleet and time windows

In this paper, a problem variant of the vehicle routing problem with time windows is introduced to consider vehicle routing with a heterogeneous fleet, a limited number of vehicles and time windows. A method that extends an existing tabu search procedure to solve the problem is then proposed. To evaluate the performance of the proposed method, experiments are conducted on a large set of test cases, which comprises several benchmark problems from numerous problem variants of the vehicle routing problem with a heterogeneous fleet. It is observed that the proposed method can be used to give reasonably good results for these problem variants. In addition, some ideas are presented to advance the research in heuristics, such as fair reporting standards, publication of benchmark problems and executable routines developed for algorithmic comparison.

Nonconvex Robust Optimization for Problems with Constraints

We propose a new robust optimization method for problems with objective functions that may be computed via numerical simulations and incorporate constraints that need to be feasible under perturbations. The proposed method iteratively moves along descent directions for the robust problem with nonconvex constraints and terminates at a robust local minimum. We generalize the algorithm further to model parameter uncertainties. We demonstrate the practicability of the method in a test application on a nonconvex problem with a polynomial cost function as well as in a real-world application to the optimization problem of intensity-modulated radiation therapy for cancer treatment. The method significantly improves the robustness for both designs.

Robust optimization in electromagnetic scattering problems

In engineering design, the physical properties of a system can often only be described by numerical simulation. Optimization of such systems is usually accomplished heuristically without taking into account that there are implementation errors that lead to very suboptimal, and often, infeasible solutions. We present a robust optimization method for electromagnetic scattering problems with large degrees of freedom and report on results when this technique is applied to optimization of aperiodic dielectric structures. The spatial configuration of 50 dielectric scattering cylinders is optimized to match a desired target function such that the optimal arrangement is robust against placement and prototype errors. Our optimization method inherently improves the robustness of the optimized solution with respect to relevant errors and is suitable for real-world design of materials with unconventional electromagnetic functionalities, as relevant to nanophotonics.

Online System Identification of an Autonomous Underwater Vehicle Via In-Field Experiments

The dynamic characteristic of an autonomous underwater vehicle (AUV) is affected when it is reconfigured with different payloads. It is desirable to have an updated model, such that the control and guidance law can be redesigned to obtain better performance. Hence, we develop a method to enable online identification of AUV dynamics via in-field experiments, where the AUV is commanded to execute a compact set of maneuvers under doublet excitation. The identification process has two stages. In the training stage, state variable filter and recursive least square (SVF-RLS) estimator is used to estimate the unknown parameters. In the validation stage, the prediction capability of the model is checked using a fresh data set. The parameters converged within 12 s in the experiments using five different thrusts. Validation results show that the identified models are able to explain 78% to 92% of the output variation. Next, we compare the SVF-RLS estimator with the conventional offline identification method. The comparison shows that the SVF-RLS estimator is better in terms of prediction accuracy, computational cost and training time. The usefulness of the identified models is highlighted in two applications. We use it to estimate the turning radius of the AUV at different speeds, and to design a gain-scheduled controller.

Satisficing measure approach for vehicle routing problem with time windows under uncertainty

The complexity of evaluating chance constraints makes chance-constrained programming problem difficult to solve. One way to handle this complexity is by devising satisficing measures for the relevant uncertainties. This paper focuses on solving the stochastic vehicle routing problem with time windows (VRPTW) by Satisficing Measure Approach (SMA) that mitigates the dissatisfaction experienced by the customers. Satisficing measures are first proposed for the VRPTW with stochastic demand on various distributions to demonstrate the dependency of customers’ satisfaction towards lack of inventory based on the vehicles capacity. Similar satisficing measures are extended to VRPTW with stochastic travel times. We integrate the proposed satisficing measures into an existing tabu-search heuristics to solve a set of generalized Solomon instances in a short amount of computation time. Compared with best-known results, the SMA saves the effort to design recourse actions, applicable to many popular probability distributions and produces very competitive results.

Commuter cycling policy in Singapore: a farecard data analytics based approach

Peak-hour week-day traffic congestion is a common challenge in urban mobility. Promotion of commuter cycling can help in alleviating this problem in many cities. This paper takes a data analytics approach to propose policies for promoting commuter cycling in Singapore. It uses farecard data to assess the commuter cycling potential and develops a data-driven approach to policy making. A spatio-temporal analysis of farecard data helps in finding patterns in the potential demand for first-mile as well as end-to-end cycling. This analysis is used to suggest policies like cycling towns to promote first-mile cycling and cycling regions to enable end-to-end cycling by linking together the cycling towns. Furthermore, an optimization model is developed to make efficient choice of cycling towns and links for a given budget so as to maximize the potential number of commuter cyclists.

Minimum Speed Seeking Control for Nonhovering Autonomous Underwater Vehicles

Most autonomous underwater vehicles AUVs are propelled by a single thruster, use elevators and rudders as control surfaces, and are torpedo-shaped. Furthermore, they are positively buoyant to facilitate recovery during an emergency. For this class of nonhovering AUVs, there is a minimum speed at which the AUV must travel for stable depth control. Otherwise, the extra buoyancy will bring the AUV up to the surface when the fin loses its effectiveness at low speeds. Hence, we develop a novel algorithm such that the AUV is automatically controlled to travel at its minimum speed while maintaining a constant depth. This capability is important in a number of practical scenarios, including underwater loitering with minimum energy consumption, underwater docking with minimum impact, and high-resolution sensing at minimum speed. First, we construct a depth dynamic model to explain the mechanism of the minimum speed, and we show its relationship with the buoyancy, the righting moment, and the fins effectiveness of the AUV. Next, we discuss the minimum speed seeking problem under the framework of extremum seeking. We extend the framework by introducing a new definition of steady-state mapping that imposes new structure on the seeking algorithm. The proposed algorithm employs a fuzzy inference system, which is driven by the real-time measurements of pitch error and elevator deflection. The effectiveness of the algorithm in seeking the minimum speed is validated in both simulations and field experiments.

Reliability of surveillance mission with unmanned aerial vehicles

This paper has modeled the reliability of surveillance mission with unmanned aerial vehicles (UAVs). In order to surveil a number of targets, some UAVs can be assigned to visit the targets. It is assumed that if a UAV is shot down during the mission all the targets assigned to the UAV cannot be surveilled. The mission is regarded as successful if all the targets are assigned and successfully surveilled. An optimization framework is presented to solve the UAV routing plan with the consideration of mission reliability.