# Andreas T. ErnstMonash University (Australia) · School of Mathematics, Clayton

Andreas T. Ernst

PhD

## About

175

Publications

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6,552

Citations

Citations since 2016

Introduction

## Publications

Publications (175)

Constraint programming (CP) is an effective technique for solving constraint satisfaction and optimization problems. CP solvers typically use a variable ordering strategy to select which variable to explore first in the solving process, which has a large impact on the efficacy of the solvers. In this paper, we propose a novel variable ordering stra...

The operating theatre is the most crucial and costly department in a hospital due to its expensive resources and high patient admission rate. Efficiently allocating operating theatre resources to patients provides hospital management with better utilization and patient flow. In this paper, we tackle both tactical and operational planning over short...

Resource constrained project scheduling is an important combinatorial optimisation problem with many practical applications. With complex requirements such as precedence constraints, limited resources, and finance-based objectives, finding optimal solutions for large problem instances is very challenging even with well-customised meta-heuristics an...

Cyclic scheduling is of vital importance in a repetitive discrete manufacturing environment. We investigate scheduling in the context of general cyclic job shops with blocking where there are no intermediate buffers between the machines. We also consider sequence-dependent setups (anticipatory and nonanticipatory), which commonly appear in differen...

We investigate an important research question for solving the car sequencing problem, that is, which characteristics make an instance hard to solve? To do so, we carry out an instance space analysis for the car sequencing problem, by extracting a vector of problem features to characterize an instance. In order to visualize the instance space, the f...

Solving large-scale Mixed Integer Programs (MIP) can be difficult without advanced algorithms such as decomposition based techniques. Even if a decomposition technique might be appropriate, there are still many possible decompositions for any large MIP and it may not be obvious which will be the most effective. This paper presents a comprehensive a...

Column Generation (CG) is an effective method for solving large-scale optimization problems. CG starts by solving a subproblem with a subset of columns (i.e., variables) and gradually includes new columns that can improve the solution of the current subproblem. The new columns are generated as needed by repeatedly solving a pricing problem, which i...

This paper aims to predict optimal solutions for combinatorial optimization problems (COPs) via machine learning (ML). To find high-quality solutions efficiently, existing methods use a ML model to predict the optimal solution and use the ML prediction to guide the search. Prediction of the optimal solution to sufficient accuracy is critical, howev...

When shipping ports are colocated with major population centers, the exclusive use of road transport for moving shipping containers across the metropolitan area is undesirable from both social and economic perspectives. Port shuttles, an integrated road and short-haul rail transport modality, are thereby gaining significant interest from government...

This paper introduces an enhanced meta-heuristic (ML-ACO) that combines machine learning (ML) and ant colony optimization (ACO) to solve combinatorial optimization problems. To illustrate the underlying mechanism of our ML-ACO algorithm, we start by describing a test problem, the orienteering problem. In this problem, the objective is to find a rou...

Column Generation (CG) is an effective method for solving large-scale optimization problems. CG starts by solving a sub-problem with a subset of columns (i.e., variables) and gradually includes new columns that can improve the solution of the current subproblem. The new columns are generated as needed by repeatedly solving a pricing problem, which...

Combinatorial optimization plays an important role in real-world problem solving. In the big data era, the dimensionality of a combinatorial optimization problem is usually very large, which poses a significant challenge to existing solution methods.
In this paper, we examine the generalization capability of a machine learning model for problem red...

When solving hard multicommodity network flow problems using an LP-based approach, the number of commodities is a driving factor in the speed at which the LP can be solved, as it is linear in the number of constraints and variables. The conventional approach to improve the solve time of the LP relaxation of a Mixed Integer Programming (MIP) model t...

When solving hard multicommodity network flow problems using an LP-based approach, the number of commodities is a driving factor in the speed at which the LP can be solved, as it is linear in the number of constraints and variables. The conventional approach to improve the solve time of the LP relaxation of a Mixed Integer Programming (MIP) model t...

This paper presents a new method to solve the Maximum Edge Disjoint Paths (MEDP) problem. Given a set of node pairs within a network, the MEDP problem is the task of finding the largest number of pairs that can be connected by paths, using each edge within the network at most once. We present a heuristic algorithm that builds a hybridisation of Lag...

This book constitutes the proceedings of the Joint 2018 National Conferences of the Australian Society for Operations Research (ASOR) and the Defence Operations Research Symposium (DORS). Offering a fascinating insight into the state of the art in Australian operations research, this book is of great interest to academics and other professional res...

In this paper, we investigate an important research question in the car sequencing problem, that is, what characteristics make an instance hard to solve? To do so, we carry out an Instance Space Analysis for the car sequencing problem, by extracting a vector of problem features to characterize an instance and projecting feature vectors onto a two-d...

Fuel and fuel-related expenses constitute a major part of the operating costs of railway companies. Hence, improvements in fuel management often lead to significant annual operational cost savings. The traditional approach to reduce the fueling costs is to fill the locomotives at inexpensive stations to bypass the more expensive stations. However,...

Matheuristics have been gaining in popularity for solving combinatorial optimisation problems in recent years. This new class of hybrid method combines elements of both mathematical programming for intensification and metaheuristic searches for diversification. A recent approach in this direction has been to build a neighbourhood for integer progra...

This paper introduces an enhanced meta-heuristic (ML-ACO) that combines machine learning (ML) and ant colony optimization (ACO) to solve combinatorial optimization problems. To illustrate the underlying mechanism of our enhanced algorithm, we start by describing a test problem -- the orienteering problem -- used to demonstrate the efficacy of ML-AC...

Combinatorial optimization plays an important role in real-world problem solving. In the big data era, the dimensionality of a combinatorial optimization problem is usually very large, which poses a significant challenge to existing solution methods. In this paper, we examine the generalization capability of a machine learning model for problem red...

In this paper, we investigate problem reduction techniques using stochastic sampling and machine learning to tackle large-scale optimization problems. These techniques heuristically remove decision variables from the problem instance, that are not expected to be part of an optimal solution. First we investigate the use of statistical measures compu...

The resource constraint job scheduling problem considered in this work is a difficult optimization problem that was defined in the context of the transportation of minerals from mines to ports. The main characteristics are that all jobs share a common limiting resource and that the objective function concerns the minimization of the total weighted...

Conventional mixed-integer programming (MIP) solvers can struggle with many large-scale combinatorial problems, as they contain too many variables and constraints. Meta-heuristics can be applied to reduce the size of these problems by removing or aggregating variables or constraints. Merge search algorithms achieve this by generating populations of...

We investigate the problem of scheduling a sequence of cars to be placed on an assembly line. Stations, along the assembly line install options (e.g. air conditioning), but have limited capacities, and hence cars requiring the same options need to be distributed far enough apart. The desired separation is not always feasible, leading to an optimisa...

In this paper we use a divide-and-conquer approach to tackle large-scale optimization problems with overlapping components. Decomposition for an overlapping problem is challenging as its components depend on one another. The existing decomposition methods typically assign all the linked decision variables into one group, thus cannot reduce the orig...

Resource constrained job scheduling problems are ubiquitous in real-world logistics and supply chain management. By solving these optimisation problems, organisations can efficiently utilise logistical resources and improve delivery performance. Because of their complexity, finding optimal solution is challenging. Existing solution methods based on...

This work describes a genetic algorithm based approach for the optimization of the Hunter Valley coal export system in Newcastle, Australia. The Port of Newcastle features three coal export terminals, operating primarily in cargo assembly mode. They share a rail network on their inbound operations and a channel on their outbound operations. Maximiz...

This article considers the high-multiplicity resource-constrained project scheduling problem with generalised precedence constraints (RCPSP/max). Projects, which can be partitioned into relatively few classes, are to be scheduled subject to resource and generalised precedence constraints. We show that there exists symmetry between projects of the s...

A hybrid exact/meta-heuristic algorithm that combines Benders decomposition and a Bees Algorithm inspired approach is presented. The algorithm is tested using a transmission network expansion and energy storage planning model. The Bee-Benders hybrid algorithm (BBHA) is shown to be an effective hybrid matheuristic algorithm that exhibits equivalent...

Given a network with n nodes, the p-hub center problem locates p hubs and allocates the remaining non-hub nodes to the hubs in such a way that the maximum distance (or time) between all pairs of nodes is minimized. Commonly, it is assumed that a vehicle is available to operate between each demand center and hub. Thus traditional p-hub center models...

This article considers transportation disruptions and its detrimental impact on the quality of the enroute shipment. The authors consider a supply chain system of a short life cycle product that has a capacitated supplier, a retailer and multiple routes of transportation under different disruption risks, uncertain cost of transportation, and uncert...

This data article presents a description of a benchmark dataset for the multiple depot vehicle scheduling problem (MDVSP). The MDVSP is to assign vehicles from different depots to timetabled trips to minimize the total cost of empty travel and waiting. The dataset has been developed to evaluate the heuristics of the MDVSP that are presented in “A n...

The multiple depot vehicle scheduling problem (MDVSP) with a single vehicle type considers the assignment of timetabled trips to homogeneous vehicles that are stationed at different depots. The assignment of trips to a vehicle also provides a schedule for a vehicle. The objective is to minimise the total cost due to waiting and travelling empty whi...

We study the uncapacitated 2-allocation p-hub median problem (U2ApHMP), which is a special case of the well-studied hub median problem. The hub median problem designs a hub network in which the location of p hubs needs to be decided (the hubs are fully interconnected). The other nodes (known as access nodes) in the hub median problem are then alloc...

The Port of Newcastle features three coal export terminals, operating primarily in cargo assembly mode, that share a rail network on their inbound side, and a channel on their outbound side. Maximising throughput at a single coal terminal, taking into account its layout, its equipment, and its operating policies, is already challenging, but maximis...

A two-stage flexible flow shop is considered, where first- and second-stage machines form disjoint pairs, each with a buffer. The buffer capacity varies from pair to pair, and the buffer requirement varies from job to job. Each job is to be assigned to a pair of machines for processing and uses the required amount of buffer from the start till the...

In this paper, we extend traditional hub location models for an intermodal network design on a sparse network structure. While traditional hub location problems have been employed for developing network designs for many specific applications, their general assumptions – such as full connectivity, uniform transfer mode, and direct connections betwee...

This study considers a resource constrained job scheduling problem. Jobs need to be scheduled on different machines satisfying a due time. If delayed, the jobs incur a penalty which is measured as a weighted tardiness. Furthermore, the jobs use up some proportion of an available resource and hence there are limits on multiple jobs executing at the...

Many large-scale combinatorial problems contain too many variables and constraints for conventional mixed-integer programming (MIP) solvers to manage. To make the problems easier for the solvers to handle, various meta-heuristic techniques can be applied to reduce the size of the search space, by removing, or aggregating, variables and constraints....

Medical residents need to successfully undertake a minimum number of surgical procedures across a variety of medical areas in order to complete their training. This paper addresses the problem of determining monthly training schedules for medical residents with the objective of minimizing the tardiness of their training. We develop a mixed integer...

In this paper, we address the problem of vehicle scheduling in a recreational vehicle rental operation. Two mathematical formulations have been employed in the literature to model the recreational vehicle scheduling problem (RVSP): an assignment-problem-based formulation and a network-flow-based formulation. We propose a new formulation motivated b...

The fixed interval scheduling problem—also known as the personnel task scheduling problem—optimizes the allocation of available resources (workers, machines, or shifts) to execute a given set of jobs or tasks. We introduce a new approach to solve this problem by decomposing it into separate subproblems. We establish the mathematical basis for optim...

We study the single allocation hub covering problem, which is a special case of the general hub location problem and an important extension to traditional covering problems. Hubs are located at some nodes in the network and are used to facilitate (consolidate, transfer, distribute) flows. An important feature in hub location is that the transfer co...

Hybrid methods are highly effective means of solving combinatorial optimization problems and have become increasingly popular. In particular, integrations of exact and incomplete methods have proved to be effective where the hybrid takes advantage of the relative performance of each individual method. However, these methods often require significan...

We introduce the single allocation p-hub median location and routing problem with simultaneous pickup and delivery based on observations from real life hub networks. The aim of our problem is to minimize the cost of transferring the flow between hubs and routing the flow in the network. We propose several mixed integer programming formulations and...

Port terminals processing large cargo vessels play an important role in bulk material supply chains. This paper addresses the question of how to allocate vessels to a location on a berth and the sequence in which the vessels should be processed in order to minimize delays. An important consideration in the berth allocation is the presence of tidal...

Pit planning and long-term production scheduling are important tasks within the mining industry. This is a great opportunity for optimisation techniques, as the scale of a lot of mining operations means that a small percentage increase in efficiency can translate to millions of dollars in profit. The precedence constrained production scheduling pro...

In this paper, a novel bi-level grouping optimization model is proposed for solving Storage Location Assignment Problem with Grouping Constraint (SLAP-GC). A major challenge of this problem is the grouping constraint which restricts the number of groups each product can have and the locations of items in the same group. In SLAP-GC, the problem cons...

Abstract We describe an electricity transmission network expansion and energy storage planning model (TESP) that determines the location and capacity of energy storage systems (ESS) in the network for the purposes of demand shifting and transmission upgrade deferral. This problem is significantly harder than the standard network expansion models th...

Whenever sets of objects are piled up in heaps, columns or stacks, any rearrangement of these objects requires substantial amount of time, effort and cost. In this paper, we study the problem of optimizing such “stack-rearrangement operations” when multiple similar objects or blocks need to be rearranged. We discuss the problem in the context of ya...

The Steiner tree problem in graphs (STPG) is a well known NP-hard combinatorial problem with various applications in transport, computational biology, network and VLSI design. Exact methods have been developed to solve this problem to proven optimality, however the exponential nature of these algorithms mean that they become intractable with large-...

Real world combinatorial optimisation problems do not often reduce to neatly delineated theoretical problems. Rather, they combine characteristics of various subproblems which then appear to be strongly intertwined. The present contribution introduces a challenging integration of task and personnel scheduling in which both tasks and shifts must be...

Understanding potential future influence of environmental, economic, and social drivers on land-use and sustainability is critical for guiding strategic decisions that can help nations adapt to change, anticipate opportunities, and cope with surprises. Using the Land-Use Trade-Offs (LUTO) model, we undertook acomprehensive, detailed, integrated, an...

Fires initiated by powerline faults disproportionately are associated with a majority of bushfire fatalities in SouthEastern Australia. Over 150 deaths have occurred since 1977 in SouthEastern Australia. A response from governments and utilities has been to embark on electricity asset improvement and replacement programs where the definition of imp...

In this paper, we extend job scheduling models to include aspects of history-dependent scheduling, where setup times for a job are affected by the aggregate activities of all predecessors of that job. Traditional approaches to machine scheduling typically address objectives and constraints that govern the relative sequence of jobs being executed us...