Russell Bent

A Two-Stage Hybrid Local Search for the Vehicle Routing Problem with Time Windows

The vehicle routing problem with time windows is a hard combinatorial optimization problem that has received considerable attention in the last decades. This paper proposes a two-stage hybrid algorithm for this transportation problem. The algorithm first minimizes the number of vehicles, using simulated annealing. It then minimizes travel cost by using a large neighborhood search that may relocate a large number of customers. Experimental results demonstrate the effectiveness of the algorithm, which has improved 10 (17%) of the 56 best published solutions to the Solomon benchmarks, while matching or improving the best solutions in 46 problems (82%). More important perhaps, the algorithm is shown to be very robust. With a fixed configuration of its parameters, it returns either the best published solutions (or improvements thereof) or solutions very close in quality on all Solomon benchmarks. Very preliminary results on the extended Solomon benchmarks are also given.

Online stochastic optimization under time constraints

This paper considers online stochastic combinatorial optimization problems where uncertainties, i.e., which requests come and when, are characterized by distributions that can be sampled and where time constraints severely limit the number of offline optimizations which can be performed at decision time and/or in between decisions. It proposes online stochastic algorithms that combine the frameworks of online and stochastic optimization. Online stochastic algorithms differ from traditional a priori methods such as stochastic programming and Markov Decision Processes by focusing on the instance data that is revealed over time. The paper proposes three main algorithms: expectation E, consensus C, and regret R. They all make online decisions by approximating, for each decision, the solution to a multi-stage stochastic program using an exterior sampling method and a polynomial number of samples. The algorithms were evaluated experimentally and theoretically. The experimental results were obtained on three applications of different nature: packet scheduling, multiple vehicle routing with time windows, and multiple vehicle dispatching. The theoretical results show that, under assumptions which seem to hold on these, and other, applications, algorithm E has an expected constant loss compared to the offline optimal solution. Algorithm R reduces the number of optimizations by a factor |R|, where R is the number of requests, and has an expected ρ(1+o(1)) loss when the regret gives a ρ-approximation to the offline problem.

A simple and deterministic competitive algorithm for online facility location

This paper presents a deterministic and efficient algorithm for online facility location. The algorithm is based on a simple hierarchical partitioning and is extremely simple to implement. It also applies to a variety of models, i.e., models where the facilities can be placed anywhere in the region, or only at customer sites, or only at fixed locations. The paper shows that the algorithm is O(log n)-competitive under these various models, where n is the total number of customers. It also shows that the algorithm is O(1)-competitive with high probability and for any arrival order when customers are uniformly distributed or when they follow a distribution satisfying a smoothness property. Experimental results for a variety of scenarios indicate that the algorithm behaves extremely well in practice.

Sub-optimality approximations

The sub-optimality approximation problem considers an optimization problem O, its optimal solution σ*, and a variable x with domain {d1,...,dm} and returns approximations to O[x←d1],...,O[x←dm], where O[x←d1] denotes the problem O with x assigned to di. The sub-optimality approximation problem is at the core of online stochastic optimization algorithms and it can also be used for solution repair and approximate filtering of optimization constraints. This paper formalizes the problem and presents sub-optimality approximation algorithms for metric TSPs, packet scheduling, and metric k-medians that run faster than the optimal or approximation algorithms. It also presents results on the hardness/easiness of sub-optimality approximations.

Online stochastic and robust optimization

This paper considers online stochastic optimization problems where uncertainties are characterized by a distribution that can be sampled and where time constraints severely limit the number of offline optimizations which can be performed at decision time and/or in between decisions. It reviews our recent progress in this area, proposes some new algorithms, and reports some new experimental results on two problems of fundamentally different nature: packet scheduling and multiple vehicle routing (MVR). In particular, the paper generalizes our earlier generic online algorithm with precomputation, least-commitment, service guarantees, and multiple decisions, all which are present in the MVR applications. Robustness results are also presented for multiple vehicle routing.

Online stochastic reservation systems

This paper considers online stochastic reservation problems, where requests come online and must be dynamically allocated to limited resources in order to maximize profit. Multi-knapsack problems with or without overbooking are examples of such online stochastic reservations. The paper studies how to adapt the online stochastic framework and the consensus and regret algorithms proposed earlier to online stochastic reservation systems. On the theoretical side, it presents a constant sub-optimality approximation of multi-knapsack problems, leading to a regret algorithm that evaluates each scenario with a single mathematical programming optimization followed by a small number of dynamic programs for one-dimensional knapsacks. On the experimental side, the paper demonstrates the effectiveness of the regret algorithm on multi-knapsack problems (with and without overloading) based on the benchmarks proposed earlier.

A two-stage hybrid algorithm for pickup and delivery vehicle routing problems with time windows

This paper presents a two-stage hybrid algorithm for pickup and delivery vehicle routing problems with time windows and multiple vehicles (PDPTW). The first stage uses a simple simulated annealing algorithm to decrease the number of routes, while the second stage uses LNS to decrease total travel cost. Experimental results show the effectiveness of the algorithm which has produced many new best solutions on problems with 100, 200, and 600 customers. In particular, it has improved 47% and 76% of the best solutions on the 200 and 600-customer benchmarks, sometimes by as much as 3 vehicles. These results further confirm the benefits of two-stage approaches in vehicle routing. They also answer positively the open issue in the original LNS paper, which advocated the use of LNS for the PDPTW and argue for the robustness of LNS with respect to side-constraints.

Using Network Metrics to Achieve Computationally Efficient Optimal Transmission Switching

Recent studies have shown that dynamic removal of transmission lines from operation (“Transmission Switching”) can reduce costs associated with power system operation. Smart Grid systems introduce flexibility into the transmission network topology and enable co-optimization of generation and network topology. The optimal transmission switching (OTS) problem has been posed in on small test systems, but problem complexity and large system sizes make OTS intractable. Our previous work suggests that most economic benefits of OTS arise through switching a small number of lines, so pre-screening has the potential to produce good solutions in less time. We explore the use of topological and electrical graph metrics to increase solution speed via solution space reduction. We find that screening based on line outage distribution factors outperforms other methods. When compared to un-screened OTS on the RTS-96 and IEEE 118-Bus networks, the sensitivity-based screen generates near optimal solutions in a fraction of the time.

Efficient Synchronization Stability Metrics for Fault Clearing

Direct methods can provide rapid screening of the dynamical security of large numbers fault and contingency scenarios by avoiding extensive time simulation. We introduce a computationally-efficient direct method based on optimization that leverages efficient cutting plane techniques. The method considers both unstable equilibrium points and the effects of additional relay tripping on dynamical security[1]. Similar to other direct methods, our approach yields conservative results for dynamical security, however, the optimization formulation potentially lends itself to the inclusion of additional constraints to reduce this conservatism.

Probabilistic N-k failure-identification for power systems

This paper considers a probabilistic generalization of the