Vicky H. Mak-Hau

On the kidney exchange problem: cardinality constrained cycle and chain problems on directed graphs: a survey of integer programming approaches

The Kidney Exchange Problem (KEP) is a combinatorial optimization problem and has attracted the attention from the community of integer programming/combinatorial optimisation in the past few years. Defined on a directed graph, the KEP has two variations: one concerns cycles only, and the other, cycles as well as chains on the same graph. We call the former a Cardinality Constrained Multi-cycle Problem (CCMcP) and the latter a Cardinality Constrained Cycles and Chains Problem (CCCCP). The cardinality for cycles is restricted in both CCMcP and CCCCP. As for chains, some studies in the literature considered cardinality restrictions, whereas others did not. The CCMcP can be viewed as an Asymmetric Travelling Salesman Problem that does allow subtours, however these subtours are constrained by cardinality, and that it is not necessary to visit all vertices. In existing literature of the KEP, the cardinality constraint for cycles is usually considered to be small (to the best of our knowledge, no more than six). In a CCCCP, each vertex on the directed graph can be included in at most one cycle or chain, but not both. The CCMcP and the CCCCP are interesting and challenging combinatorial optimization problems in their own rights, particularly due to their similarities to some travelling salesman- and vehicle routing-family of problems. In this paper, our main focus is to review the existing mathematical programming models and solution methods in the literature, analyse the performance of these models, and identify future research directions. Further, we propose a polynomial-sized and an exponential-sized mixed-integer linear programming model, discuss a number of stronger constraints for cardinality-infeasible-cycle elimination for the latter, and present some preliminary numerical results.

A unified mixed-integer programming model for simultaneous fluence weight and aperture optimization in VMAT, Tomotherapy, and Cyberknife

In this paper, we propose and study a unified mixed-integer programming model that simultaneously optimizes fluence weights and multi-leaf collimator (MLC) apertures in the treatment planning optimization of VMAT, Tomotherapy, and CyberKnife. The contribution of our model is threefold: (i) Our model optimizes the fluence and MLC apertures simultaneously for a given set of control points. (ii) Our model can incorporate all volume limits or dose upper bounds for organs at risk (OAR) and dose lower bound limits for planning target volumes (PTV) as hard constraints, but it can also relax either of these constraint sets in a Lagrangian fashion and keep the other set as hard constraints. (iii) For faster solutions, we propose several heuristic methods based on the MIP model, as well as a meta-heuristic approach. The meta-heuristic is very efficient in practice, being able to generate dose- and machinery-feasible solutions for problem instances of clinical scale, e.g., obtaining feasible treatment plans to cases with 180 control points, 6750 sample voxels and 18,000 beamlets in 470seconds, or cases with 72 control points, 8000 sample voxels and 28,800 beamlets in 352seconds. With discretization and down-sampling of voxels, our method is capable of tackling a treatment field of 8000 - 64 , 000 cm 3 , depending on the ratio of critical structure versus unspecified tissues.

Packet Faking Attack: A Novel Attack and Detection Mechanism in OppNets

Security is a major challenge in Opportunistic Networks (OppNets) due to its characteristics of being an open medium with dynamic topology, there is neither a centralized management nor clear lines of defence. A packet dropping attack is one of the major security threats in OppNets as neither source nodes nor destination nodes have any knowledge of when or where a packet will be dropped. In this paper, we present a novel attack and detection mechanism against a special type of packet dropping where the malicious node drops one packet or more and injects a new fake packet instead. Our novel detection mechanism is very powerful and has very high accuracy. It relies on a very simple yet powerful idea, the creation time of each packet. Significant results show this robust mechanism achieves a very high accuracy and detection rate.

An Exact Method for Minimizing the Total Treatment Time in Intensity-Modulated Radiotherapy

In this paper, we solve a combinatorial optimization problem that arises from the treatment planning of a type of radiotherapy where intensity is modulated by multileaf collimators (MLC) in a step-and-shoot manner. In Ernst et al [INFORMS Journal on Computing 21 (4) (2009): 562–574], we proposed an exact method for minimizing the number of MLC apertures needed for a treatment. Our method outperformed the fastest algorithms available at the time. We refer to our method as the CPI method. We now attempt to minimize the total treatment time by modifying our CPI method. This modification involves non-trivial work, as some of the search space elimination schemes used in the CPI method cannot be applied in here. In our numerical experiments, we again compare our new method with the fastest algorithms currently available. There has been significant recent research in this area; hence we compare our method with those published in Wake et al [Computers and Operations Research 36 (2009): 795–810], Taşkin et al [Operations Research 58 (3) (2010): 674–690] and Cambazard et al [CPAIRO (2010): 1–16]. The numerical comparisons indicate that our method generally outperformed the first two, while being competitive with the third.

Defense against packet collusion attacks in opportunistic networks

Security is a major challenge in Opportunistic Networks (OppNets) because of its characteristics such as an open medium, dynamic topology, no centralized management and absent clear lines of defense. A packet dropping attack is one of the major security threats in OppNets since neither source nor destination nodes have control over the behaviour of intermediate nodes in the network. Consequently, the knowledge of where or when packets are/will be dropped is difficult to gather. In this paper, we present a novel attack and traceback mechanism against a special type of packet dropping attacks packet collusion attacks, where the malicious node(s) drops some or all packets and then injects new fake packets in their place to mask the packet dropping. Our novel detection and traceback mechanism is based on the concept of a Merkle (or hash) tree and simulation results show it to be highly effective and accurate in terms of detecting attack instances and tracing back to the malicious node(s) in the network that is the attack source.

An Efficient Detection Mechanism Against Packet Faking Attack in Opportunistic Networks

Security is a major challenge in Opportunistic Networks (OppNets) because of its characteristics, such as open medium, dynamic topology, no centralized management and absent clear lines of defense. A packet dropping attack is one of the major security threats in OppNets since neither source nodes nor destination nodes have the knowledge of where or when the packet will be dropped. In our previous novel attack (Packet Faking Attack [1]) we presented a special type of packet dropping where the malicious node drops one or more packets and then injects new fake packets instead. In this paper, we present an efficient detection mechanism against this type of attack where each node can detect the attack instead of the destination node. Our detection mechanism is very powerful and has very high accuracy. It relies on a very simple yet powerful idea, that is, the packet creation time of each packet. Simulation results show this robust mechanism achieves a very high accuracy, detection rate and good network traffic reduction.

A parallel optimisation approach for the realisation problem in intensity modulated radiotherapy treatment planning

We propose a parallel algorithm for computing exact solutions to the problem of minimizing the number of multileaf collimator apertures needed in step-and-shoot intensity modulated radiotherapy. These problems are very challenging particularly as the problem size increases. Here, we investigate how advanced parallel computing methods can be applied to these problems with a focus on the issues that are peculiar to parallel search algorithms and do not arise in their serial counterparts. A previous paper by the authors presented the MU–RD method for solving such problems using a serial constraint programming based search method. This method is being used as the starting point for a parallel implementation. The key challenges in creating a parallel implementation are ensuring that the CPUs are not starved of work and avoiding unnecessary computation due to the rearrangement of the search order in the parallel version. We show that efficient parallel optimisation is possible by dynamically changing the way work is split with potentially multiple tree search processes as well as parallel search of nodes. A weakly sorted queueing system is used to ensure appropriate prioritisation of tasks. Numerical results are presented to demonstrate the effectiveness of our algorithms in scaling from 8 to 64 CPUs.

A Quick Practical Guide to Polyhedral Analysis in Integer Programming

Polyhedral analysis is one of the most interesting elements of integer programming and has been often overlooked. It plays an important role in finding exact solutions to an integer program. In this paper, we will discuss what polyhedral analysis is, and how some constraints for an integer programming model are “ideal” in the sense that if the model contains all of these “ideal” constraints, then the integer optimal solution can be obtained by simply solving a linear programming relaxation of the integer program. This paper serves as a quick guide for young researchers and PhD students.

An Exact Algorithm for the Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Three-Dimensional Loading Constraints

One of our industry partners distributes a multitude of orders of fibre boards all over each of the Australian capital cites, a problem that has been formalised as the Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Three-Dimensional Loading Constraints (3L-HFVRPTW). The fleet consists of two types of trucks with flat loading surfaces and slots for spacers that allow a subdivision into stacks of different sizes. A customer’s delivery can be positioned on more than one partition, but the deliveries have to be loaded in a strict LIFO order. Optimising the truck loads beyond the 75% that can be achieved manually provides value to the company because the deliveries are generally last-minute orders and the customers depend on the deliveries for their contract work on refurbishments. This paper presents an exact integer linear programming model that serves two purposes: (1) providing exact solutions for problems of a modest size as a basis for comparing the quality of heuristic solution methodologies, and (2) for further exploration of various relaxations, stack generation, and decomposition strategies that are based on the ILP model. We solved a few real-life instances by obtaining the exact optimal solution using CPLEX 12.61, whereas previously, the problem was solved manually by staff members of the furniture company.

Identifying items for moderation in a peer assessment framework

Abstract Peer assessment can be considered in the framework of group decision making and hence take advantage of many of the proposed methods and evaluation processes. Despite the potential of peer assessment to greatly reduce the workload of educators, a key hurdle to its uptake is its perceived reliability, with there being the preconception that peers may not be as reliable or fair as ‘experts’. In this contribution, we consider approaches to moderation with the aim of increasing the accuracy of scores given while reducing the total workload of the subject experts (or lecturers in the university context). Firstly, we propose several indices, which, in combination can be used to estimate the reliability of peer markers. Secondly, we consider the consensus of scores received by peers. We hence approach the problem of reliability from two angles, and from these considerations can identify a subset of peers whose results should be flagged for moderation. We conduct some numerical experiments to investigate the potential for these techniques in the context of peer assessment with heterogeneous marking behaviors.