Preface [Special Issue: International Symposium on Combinatorial Optimisation (CO2000)]

Preface [Special Issue containing a selection of papers presented at the International Symposium on Combinatorial Optimisation (CO2000) held at the University of Greenwich, London, from 12-14 July 2000.

Multilevel refinement for combinatorial optimisation problems

We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (sometimes for the original problem, sometimes the coarsest) and then iteratively refined at each level. As a general solution strategy, the multilevel paradigm has been in use for many years and has been applied to many problem areas (most notably in the form of multigrid techniques). However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial optimisation problems. In this paper we address the issue of multilevel refinement for such problems and, with the aid of examples and results in graph partitioning, graph colouring and the travelling salesman problem, make a case for its use as a metaheuristic. The results provide compelling evidence that, although the multilevel framework cannot be considered as a panacea for combinatorial problems, it can provide an extremely useful addition to the combinatorial optimisation toolkit. We also give a possible explanation for the underlying process and extract some generic guidelines for its future use on other combinatorial problems.

Multilevel refinement for combinatorial optimisation: boosting metaheuristic performance

The multilevel paradigm as applied to combinatorial optimisation problems is a simple one, which at its most basic involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found, usually at the coarsest level, and then iteratively refined at each level, coarsest to finest, typically by using some kind of heuristic optimisation algorithm (either a problem-specific local search scheme or a metaheuristic). Solution extension (or projection) operators can transfer the solution from one level to another. As a general solution strategy, the multilevel paradigm has been in use for many years and has been applied to many problem areas (for example multigrid techniques can be viewed as a prime example of the paradigm). Overview papers such as [] attest to its efficacy. However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial problems and in this chapter we discuss recent developments. In this chapter we survey the use of multilevel combinatorial techniques and consider their ability to boost the performance of (meta)heuristic optimisation algorithms.

Characterisation of pavement profile heights using accelerometer readings and a combinatorial optimisation technique

Pavement surface profiles induce dynamic ride responses in vehicles which can potentially be used to classify road surface roughness. A novel method is proposed for the characterisation of pavement roughness through an analysis of vehicle accelerations. A combinatorial optimisation technique is applied to the determination of pavement profile heights based on measured accelerations at and above the vehicle axle. Such an approach, using low-cost inertial sensors, would provide an inexpensive alternative to the costly laser-based profile measurement vehicles. The concept is numerically validated using a half-car roll dynamic model to infer measurements of road profiles in both the left and right wheel paths.

Combinatorial and Robust Optimisation Models and Algorithms for Railway Applications

This thesis deals with an investigation of combinatorial and robust optimisation models to solve railway problems. Railway applications represent a challenging area for operations research. In fact, most problems in this context can be modelled as combinatorial optimisation problems, in which the number of feasible solutions is finite. Yet, despite the astonishing success in the field of combinatorial optimisation, the current state of algorithmic research faces severe difficulties with highly-complex and data-intensive applications such as those dealing with optimisation issues in large-scale transportation networks. One of the main issues concerns imperfect information. The idea of Robust Optimisation, as a way to represent and handle mathematically systems with not precisely known data, dates back to 1970s. Unfortunately, none of those techniques proved to be successfully applicable in one of the most complex and largest in scale (transportation) settings: that of railway systems. Railway optimisation deals with planning and scheduling problems over several time horizons. Disturbances are inevitable and severely affect the planning process. Here we focus on two compelling aspects of planning: robust planning and online (real-time) planning.

A flexible optimisation model for the railway crew scheduling problem

Addressing the Crew Scheduling Problem (CSP) in transportation systems can be too complex to capture all details. The designed models usually ignore or simplify features which are difficult to formulate. This paper proposes an alternative formulation using a Mixed Integer Programming (MIP) approach to the problem. The optimisation model integrates the two phases of pairing generation and pairing optimisation by simultaneously sequencing trips into feasible duties and minimising total elapsed time of any duty. Crew scheduling constraints in which the crew have to return to their home depot at the end of the shift are included in the model. The flexibility of this model comes in the inclusion of the time interval of relief opportunities, allowing the crew to be relieved during a finite time interval. This will enhance the robustness of the schedule and provide a better representation of real-world conditions.

Systematic delay-driven power optimisation and power-driven delay optimisation of combinational circuits

With the proliferation of mobile wireless communication and embedded systems, the energy efficiency becomes a major design constraint. The dissipated energy is often referred as the product of power dissipation and the input-output delay. Most of electronic design automation techniques focus on optimising only one of these parameters either power or delay. Industry standard design flows integrate systematic methods of optimising either area or timing while for power consumption optimisation one often employs heuristics which are characteristic to a specific design. In this work we answer three questions in our quest to provide a systematic approach to joint power and delay Optimisation. The first question of our research is: How to build a design flow which incorporates academic and industry standard design flows for power optimisation? To address this question, we use a reference design flow provided by Synopsys and integrate in this flow academic tools and methodologies. The proposed design flow is used as a platform for analysing some novel algorithms and methodologies for optimisation in the context of digital circuits. The second question we answer is: Is possible to apply a systematic approach for power optimisation in the context of combinational digital circuits? The starting point is a selection of a suitable data structure which can easily incorporate information about delay, power, area and which then allows optimisation algorithms to be applied. In particular we address the implications of a systematic power optimisation methodologies and the potential degradation of other (often conflicting) parameters such as area or the delay of implementation. Finally, the third question which this thesis attempts to answer is: Is there a systematic approach for multi-objective optimisation of delay and power? A delay-driven power and power-driven delay optimisation is proposed in order to have balanced delay and power values. This implies that each power optimisation step is not only constrained by the decrease in power but also the increase in delay. Similarly, each delay optimisation step is not only governed with the decrease in delay but also the increase in power. The goal is to obtain multi-objective optimisation of digital circuits where the two conflicting objectives are power and delay. The logic synthesis and optimisation methodology is based on AND-Inverter Graphs (AIGs) which represent the functionality of the circuit. The switching activities and arrival times of circuit nodes are annotated onto an AND-Inverter Graph under the zero and a non-zero-delay model. We introduce then several reordering rules which are applied on the AIG nodes to minimise switching power or longest path delay of the circuit at the pre-technology mapping level. The academic Electronic Design Automation (EDA) tool ABC is used for the manipulation of AND-Inverter Graphs. We have implemented various combinatorial optimisation algorithms often used in Electronic Design Automation such as Simulated Annealing and Uniform Cost Search Algorithm. Simulated Annealing (SMA) is a probabilistic meta heuristic for the global optimization problem of locating a good approximation to the global optimum of a given function in a large search space. We used SMA to probabilistically decide between moving from one optimised solution to another such that the dynamic power is optimised under given delay constraints and the delay is optimised under given power constraints. A good approximation to the global optimum solution of energy constraint is obtained. Uniform Cost Search (UCS) is a tree search algorithm used for traversing or searching a weighted tree, tree structure, or graph. We have used Uniform Cost Search Algorithm to search within the AIG network, a specific AIG node order for the reordering rules application. After the reordering rules application, the AIG network is mapped to an AIG netlist using specific library cells. Our approach combines network re-structuring, AIG nodes reordering, dynamic power and longest path delay estimation and optimisation and finally technology mapping to an AIG netlist. A set of MCNC Benchmark circuits and large combinational circuits up to 100,000 gates have been used to validate our methodology. Comparisons for power and delay optimisation are made with the best synthesis scripts used in ABC. Reduction of 23% in power and 15% in delay with minimal overhead is achieved, compared to the best known ABC results. Also, our approach is also implemented on a number of processors with combinational and sequential components and significant savings are achieved.

Heuristic approaches for multi-criteria optimisation in kidney exchange programs

The Kidney Exchange Problem (KEP) is an optimisation problem that was first discussed in Rapaport (1986) but has only more recently been the subject of much work by combinatorial optimisation re-searchers. This has been in parallel with its increased prevalence in the medical community. In the basic formulation of a KEP, each instance of the problem features a directed graph D = (V,A) . Each node i ∈ V represents an incompatible pair wherein the patient needs to trade kidneys with the patient of another incompatible pair. The goal is to find an optimal set of cycles such that as many patients as possible receive a transplant. The problem is further complicated by the imposition of a cycle-size constraint, usually considered to be 3 or 4. Kidney exchange programs around the world implement different algorithms to solve the allocation problem by matching up kidneys from potential donors to patients. In some systems all transplants are considered equally desirable, whereas in others, ranking criteria such as the age of the patient or distance they will need to travel are applied, hence the multi-criteria nature of the KEP. To address the multi-criteria aspect of the KEP, in this paper we propose a two-stage approach for the kidney exchange optimisation problem. In the first stage the goal is to find the optimal number of exchanges, and in the second stage the goal is to maximise the weighted sum of the kidney matches, subject to the added constraint that the number of exchanges must remain optimal. The idea can potentially be extended to multiple-objectives, by repeating the process in multiple runs. In our preliminary numerical experiments, we first find the maximum number of kidney matches by using an existing open source exact algorithm of Anderson et al. (2015). The solution will then be used as an initial solution for the stage two optimisation problem, wherein two heuristic methods, steepest ascent and random ascent, are implemented in obtaining good quality solutions to the objective of maximizing total weight of exchanges. The neighbourhood is obtained by two-swaps. It is our intention in the future to implement a varying neighbourhood scheme within the same two heuristic framework, or within other meta-heuristic framework.

Composite SaaS resource management in cloud computing using evolutionary computation

Cloud computing is an emerging computing paradigm in which IT resources are provided over the Internet as a service to users. One such service offered through the Cloud is Software as a Service or SaaS. SaaS can be delivered in a composite form, consisting of a set of application and data components that work together to deliver higher-level functional software. SaaS is receiving substantial attention today from both software providers and users. It is also predicted to has positive future markets by analyst firms. This raises new challenges for SaaS providers managing SaaS, especially in large-scale data centres like Cloud. One of the challenges is providing management of Cloud resources for SaaS which guarantees maintaining SaaS performance while optimising resources use. Extensive research on the resource optimisation of Cloud service has not yet addressed the challenges of managing resources for composite SaaS. This research addresses this gap by focusing on three new problems of composite SaaS: placement, clustering and scalability. The overall aim is to develop efficient and scalable mechanisms that facilitate the delivery of high performance composite SaaS for users while optimising the resources used. All three problems are characterised as highly constrained, large-scaled and complex combinatorial optimisation problems. Therefore, evolutionary algorithms are adopted as the main technique in solving these problems. The first research problem refers to how a composite SaaS is placed onto Cloud servers to optimise its performance while satisfying the SaaS resource and response time constraints. Existing research on this problem often ignores the dependencies between components and considers placement of a homogenous type of component only. A precise problem formulation of composite SaaS placement problem is presented. A classical genetic algorithm and two versions of cooperative co-evolutionary algorithms are designed to now manage the placement of heterogeneous types of SaaS components together with their dependencies, requirements and constraints. Experimental results demonstrate the efficiency and scalability of these new algorithms. In the second problem, SaaS components are assumed to be already running on Cloud virtual machines (VMs). However, due to the environment of a Cloud, the current placement may need to be modified. Existing techniques focused mostly at the infrastructure level instead of the application level. This research addressed the problem at the application level by clustering suitable components to VMs to optimise the resource used and to maintain the SaaS performance. Two versions of grouping genetic algorithms (GGAs) are designed to cater for the structural group of a composite SaaS. The first GGA used a repair-based method while the second used a penalty-based method to handle the problem constraints. The experimental results confirmed that the GGAs always produced a better reconfiguration placement plan compared with a common heuristic for clustering problems. The third research problem deals with the replication or deletion of SaaS instances in coping with the SaaS workload. To determine a scaling plan that can minimise the resource used and maintain the SaaS performance is a critical task. Additionally, the problem consists of constraints and interdependency between components, making solutions even more difficult to find. A hybrid genetic algorithm (HGA) was developed to solve this problem by exploring the problem search space through its genetic operators and fitness function to determine the SaaS scaling plan. The HGA also uses the problem's domain knowledge to ensure that the solutions meet the problem's constraints and achieve its objectives. The experimental results demonstrated that the HGA constantly outperform a heuristic algorithm by achieving a low-cost scaling and placement plan. This research has identified three significant new problems for composite SaaS in Cloud. Various types of evolutionary algorithms have also been developed in addressing the problems where these contribute to the evolutionary computation field. The algorithms provide solutions for efficient resource management of composite SaaS in Cloud that resulted to a low total cost of ownership for users while guaranteeing the SaaS performance.

A hybrid constructive heuristic and simulated annealing for railway crew scheduling

Railway crew scheduling problem is the process of allocating train services to the crew duties based on the published train timetable while satisfying operational and contractual requirements. The problem is restricted by many constraints and it belongs to the class of NP-hard. In this paper, we develop a mathematical model for railway crew scheduling with the aim of minimising the number of crew duties by reducing idle transition times. Duties are generated by arranging scheduled trips over a set of duties and sequentially ordering the set of trips within each of duties. The optimisation model includes the time period of relief opportunities within which a train crew can be relieved at any relief point. Existing models and algorithms usually only consider relieving a crew at the beginning of the interval of relief opportunities which may be impractical. This model involves a large number of decision variables and constraints, and therefore a hybrid constructive heuristic with the simulated annealing search algorithm is applied to yield an optimal or near-optimal schedule. The performance of the proposed algorithms is evaluated by applying computational experiments on randomly generated test instances. The results show that the proposed approaches obtain near-optimal solutions in a reasonable computational time for large-sized problems.

The Linear Ordering Problem Revisited

The Linear Ordering Problem is a popular combinatorial optimisation problem which has been extensively addressed in the literature. However, in spite of its popularity, little is known about the characteristics of this problem. This paper studies a procedure to extract static information from an instance of the problem, and proposes a method to incorporate the obtained knowledge in order to improve the performance of local search-based algorithms. The procedure introduced identifies the positions where the indexes cannot generate local optima for the insert neighbourhood, and thus global optima solutions. This information is then used to propose a restricted insert neighbourhood that discards the insert operations which move indexes to positions where optimal solutions are not generated. In order to measure the efficiency of the proposed restricted insert neighbourhood system, two state-of-the-art algorithms for the LOP that include local search procedures have been modified. Conducted experiments confirm that the restricted versions of the algorithms outperform the classical designs systematically. The statistical test included in the experimentation reports significant differences in all the cases, which validates the efficiency of our proposal.

Extending Distance-based Ranking Models In Estimation of Distribution Algorithms

Recently, probability models on rankings have been proposed in the field of estimation of distribution algorithms in order to solve permutation-based combinatorial optimisation problems. Particularly, distance-based ranking models, such as Mallows and Generalized Mallows under the Kendall’s-t distance, have demonstrated their validity when solving this type of problems. Nevertheless, there are still many trends that deserve further study. In this paper, we extend the use of distance-based ranking models in the framework of EDAs by introducing new distance metrics such as Cayley and Ulam. In order to analyse the performance of the Mallows and Generalized Mallows EDAs under the Kendall, Cayley and Ulam distances, we run them on a benchmark of 120 instances from four well known permutation problems. The conducted experiments showed that there is not just one metric that performs the best in all the problems. However, the statistical test pointed out that Mallows-Ulam EDA is the most stable algorithm among the studied proposals.

Multilevel approaches applied to the capacitated clustering problem

This paper presents two multilevel refinement algorithms for the capacitated clustering problem. Multilevel refinement is a collaborative technique capable of significantly aiding the solution process for optimisation problems. The central methodologies of the technique are filtering solutions from the search space and reducing the level of problem detail to be considered at each level of the solution process. The first multilevel algorithm uses a simple tabu search while the other executes a standard local search procedure. Both algorithms demonstrate that the multilevel technique is capable of aiding the solution process for this combinatorial optimisation problem.