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2013

Selected Works

Operations Research, Systems Engineering and Industrial Engineering

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Articles 1 - 30 of 71

Full-Text Articles in Engineering

Hybrid Agent Based Simulation With Adaptive Learning Of Travel Mode Choices For University Commuters, Nagesh Shukla, Albert Munoz, Jun Ma, Nam Huynh Feb 2014

Hybrid Agent Based Simulation With Adaptive Learning Of Travel Mode Choices For University Commuters, Nagesh Shukla, Albert Munoz, Jun Ma, Nam Huynh

Albert Munoz

This paper presents a methodology for developing a hybrid agent-based micro-simulation model to capture the impacts of commuter travel mode choices on a University campus transport network. The proposed methodology involves: (i) developing realistic population of commuter agents (students and staff); (ii) assigning activity lists and travel mode choices to agents using machine learning method; and, (iii) traffic micro-simulation of the study area transport network. This furthers the understanding of current transport modal distributions, factors affecting the travel mode choice decisions, and, network performance through a number of hypothetical travel scenarios.


Biofuel Production In Ireland—An Approach To 2020 Targets With A Focus On Algal Biomass, Fionnuala Murphy Dec 2013

Biofuel Production In Ireland—An Approach To 2020 Targets With A Focus On Algal Biomass, Fionnuala Murphy

Fionnuala Murphy

Under the Biofuels Obligation Scheme in Ireland, the biofuels penetration rate target for 2013 was set at 6% by volume from a previous 4% from 2010. In 2012 the fuel blend reached 3%, with approximately 70 million L of biodiesel and 56 million L of ethanol blended with diesel and gasoline, respectively. Up to and including April 2013, the current blend rate in Ireland for biodiesel was 2.3% and for bioethanol was 3.7% which equates to approximately 37.5 million L of biofuel for the first four months of 2013. The target of 10% by 2020 remains, which equates to approximately …


Experimental Evaluation Of A Joint Cognitive System For 4d Trajectory Management, Rolf Klomp, Clark Borst, Max Mulder, Gesa Praetorius, Martijn Moij Nov 2013

Experimental Evaluation Of A Joint Cognitive System For 4d Trajectory Management, Rolf Klomp, Clark Borst, Max Mulder, Gesa Praetorius, Martijn Moij

Gesa Praetorius

Effective joint human-automation coordination is essential in order to support the central role of the human operator in foreseen future trajectory-based air traffic operations. The SESAR WP-E project C-SHARE aims to achieve this by taking a Cognitive Systems Engineering approach, based upon accomplishing joint human and automation cognition through a shared representation of 4D-trajectory management. In foregoing research, a work domain model and a joint human-machine interface has been developed to support the human operator in the task of en-route 4D trajectory re-planning. This paper presents the findings of two experiments that aimed to determine the effect of both the …


In Situ Performance Of A Complex Urban Turnout Grillage System Using Fibre-Reinforced Foamed Urethane (Ffu) Bearers, Sakdirat Kaewunruen Nov 2013

In Situ Performance Of A Complex Urban Turnout Grillage System Using Fibre-Reinforced Foamed Urethane (Ffu) Bearers, Sakdirat Kaewunruen

Sakdirat Kaewunruen

A full-scale trial to investigate in-situ behaviours of a turnout grillage system using an alternative material, ‘fibre-reinforced foamed urethane (FFU)’ bearers, has been carried out at a complex turnout junction under heavy mixed traffics at Hornsby, New South Wales, Australia. The turnout junction was renewed using the FFU bearers altogether with new special track components. Influences of the FFU bearers on track geometry (recorded by track inspection vehicle ‘AK Car’ and based on survey data), track settlement, track dynamics and acoustic characteristics have been measured. Operational train pass-by measurements have been analysed to evaluate the effectiveness of the replacement methodology. …


Communicating Intended Routes In Ecdis: Evaluating Technological Change, Thomas Porathe, Margareta Lützhöft, Gesa Praetorius Oct 2013

Communicating Intended Routes In Ecdis: Evaluating Technological Change, Thomas Porathe, Margareta Lützhöft, Gesa Praetorius

Gesa Praetorius

Misunderstanding each other's intentions is one of the most common causes of shipping accidents. By sending out a number of waypoints ahead and displaying them on the Electronic Chart Display and Information System (ECDIS) a ship's intentions would be clearly visible for other ships. Displaying ships’ intentions would be a major change compared to navigation today. It could be very beneficial but it could also have unintended consequences. This paper reports on findings from an evaluation looking for unintended consequences of change using system simulation. During the simulation an unanticipated behavior was observed. Bridge crews started to click and drag …


Parcel-Level Redevelopment Strategies For Distressed Neighborhoods, Michael P. Johnson Jr., Justin Hollander Oct 2013

Parcel-Level Redevelopment Strategies For Distressed Neighborhoods, Michael P. Johnson Jr., Justin Hollander

Michael P. Johnson

Certain distressed neighborhoods cannot support traditional residential-focused development. For these communities, we develop decision models for acquisition and redevelopment of chronically vacant lands and structures for primarily non-residential and greening uses. We address social benefits and costs of redevelopment strategies, parcel clustering to exploit economies of scale, and conflicting values among stakeholders. We illustrate our models using data from Baltimore, MD.


Joint User Grouping And Linear Virtual Beamforming: Complexity, Algorithms And Approximation Bounds, Mingyi Hong, Zi Xu, Meisam Razaviyayn, Zhi-Quan Luo Oct 2013

Joint User Grouping And Linear Virtual Beamforming: Complexity, Algorithms And Approximation Bounds, Mingyi Hong, Zi Xu, Meisam Razaviyayn, Zhi-Quan Luo

Mingyi Hong

In a wireless system with a large number of distributed nodes, the quality of communication can be greatly improved by pooling the nodes to perform joint transmission/reception. In this paper, we consider the problem of optimally selecting a subset of nodes from potentially a large number of candidates to form a virtual multi-antenna system, while at the same time designing their joint linear transmission strategies. We focus on two specific application scenarios: 1) multiple single antenna transmitters cooperatively transmit to a receiver; 2) a single transmitter transmits to a receiver with the help of a number of cooperative relays. We …


Enhanced Adaptive Management: Integrating Decision Analysis, Scenario Analysis And Environmental Modeling For The Everglades, Matteo Convertino, Christy Foran, Jeffrey Keisler, Lynn Scarlett, Andrew Loschiavo, Greg Kiker, Igor Linkov Sep 2013

Enhanced Adaptive Management: Integrating Decision Analysis, Scenario Analysis And Environmental Modeling For The Everglades, Matteo Convertino, Christy Foran, Jeffrey Keisler, Lynn Scarlett, Andrew Loschiavo, Greg Kiker, Igor Linkov

Jeffrey Keisler

We propose to enhance existing adaptive management efforts with a decision-analytical approach that can
guide the initial selection of robust restoration alternative plans and inform the need to adjust these
alternatives in the course of action based on continuously acquired monitoring information and changing
stakeholder values. We demonstrate an application of enhanced adaptive management for a wetland
restoration case study inspired by the Florida Everglades restoration effort. We find that alternatives
designed to reconstruct the pre-drainage flow may have a positive ecological impact, but may also have high
operational costs and only marginally contribute to meeting other objectives such as …


A Study On Correlation Between Consciousness Level And Performance Of The Worker, Devendra Kumar Chaturvedi Dr., Manish Kumar Arya Aug 2013

A Study On Correlation Between Consciousness Level And Performance Of The Worker, Devendra Kumar Chaturvedi Dr., Manish Kumar Arya

Manish Kumar Arya

Consciousness is significantly related to workplace performance among managers and workers. A considerable amount of research indicates that consciousness is one of the best predictors of performance in the workplace. Conscious employees are generally more reliable, more motivated, and harder working. They have also lower rate of absenteeism and counterproductive work behaviours such as stealing and fighting with other employees. Furthermore, consciousness is the only personality trait that correlates with performance across all categories of jobs. This is a pilot study to determine the workers performance related with consciousness. The consciousness will be experimentally measured using the self developed sensor …


Innovation And Learning Through Knowledge Gatekeepers:A Critical Examination Of The Relationship Betweentrust, Openness, And The Use Of Gatekeepers, Deogratias Harorimana Dr Aug 2013

Innovation And Learning Through Knowledge Gatekeepers:A Critical Examination Of The Relationship Betweentrust, Openness, And The Use Of Gatekeepers, Deogratias Harorimana Dr

Dr Deogratias Harorimana

The term ‘gatekeeper’ is widely used to represent a class of those who collect information, knowledge and contextualise this before they can share with the rest of the members of the organisation knowledge networks-both formal and informal organisations. In this study, it was found:

1 that there is a strong relationship between the openness of a given firm, as regards its knowledge sharing culture and level trust, and that firm’s use of knowledge gatekeepers

2 that the stage of a given firm’s growth corresponds to its strategic use of different types of gatekeeping.

In early and decline (renewal) stages, for …


The Evaluation Of Flash Point And Cold Filter Plugging Point With Blends Of Diesel And Cyn-Diesel Pyrolysis Fuel For Automotive Engines, Fionnuala Murphy Jul 2013

The Evaluation Of Flash Point And Cold Filter Plugging Point With Blends Of Diesel And Cyn-Diesel Pyrolysis Fuel For Automotive Engines, Fionnuala Murphy

Fionnuala Murphy

The production of synthetic fuels from alternative sources has increased in recent years as a cleaner, more sustainable source of transport fuel is now required. The European Commission has outlined renewable energy targets pertaining to transport fuel which must be met by 2020. In response to these targets Ireland has committed, through the Biofuels Obligation Scheme of 2008, to producing 3% of transport fuels from biofuels by 2010 and 10% by 2020. In order to be suitable for sale in Europe, diesel fuels and biodiesels must meet certain European fuel specifications outlined in the EN 590:2009 standard. The aim of …


Miscanthus Production And Processing In Ireland: An Analysis Of Energy Requirements And Environmental Impacts, Fionnuala Murphy Jul 2013

Miscanthus Production And Processing In Ireland: An Analysis Of Energy Requirements And Environmental Impacts, Fionnuala Murphy

Fionnuala Murphy

The environmental impact of bioenergy supply systems can be determined using life cycle assessment methodologies. This study focuses on the impact of production of Miscanthus pellets and briquettes, potentially used to satisfy renewable energy requirements in Ireland. The impact categories considered are particularly important when assessing bioenergy systems; global warming potential, acidification potential, eutrophication potential, and energy demand. The scope of the study incorporates Miscanthus cultivation, harvest, processing and transport to a biomass distributor. The aim of the research is to evaluate the effects of changes in keys variables on the overall environmental impacts of the system. The scenarios examined …


Joint Access Point Selection And Power Allocation For Uplink Wireless Networks, Mingyi Hong, Alfredo Garcia, Jorge Barrera, Stephen G. Wilson Jul 2013

Joint Access Point Selection And Power Allocation For Uplink Wireless Networks, Mingyi Hong, Alfredo Garcia, Jorge Barrera, Stephen G. Wilson

Mingyi Hong

We consider the distributed uplink resource allocation problem in a multi-carrier wireless network with multiple access points (APs). Each mobile user can optimize its own transmission rate by selecting a suitable AP and by controlling its transmit power. Our objective is to devise suitable algorithms by which mobile users can jointly perform these tasks in a distributed manner. Our approach relies on a game theoretic formulation of the joint power control and AP selection problem. In the proposed game, each user is a player with an associated strategy containing a discrete variable (the AP selection decision) and a continuous vector …


Distributed Linear Precoder Optimization And Base Station Selection For An Uplink Heterogeneous Network, Mingyi Hong, Zhi-Quan Luo Jun 2013

Distributed Linear Precoder Optimization And Base Station Selection For An Uplink Heterogeneous Network, Mingyi Hong, Zhi-Quan Luo

Mingyi Hong

In a heterogeneous wireless cellular network, each user may be covered by multiple access points such as macro/pico/relay/femto base stations (BS). An effective approach to maximize the sum utility (e.g., system throughput) in such a network is to jointly optimize users' linear procoders as well as their BS associations. In this paper, we first show that this joint optimization problem is NP-hard and thus is difficult to solve to global optimality. To find a locally optimal solution, we formulate the problem as a noncooperative game in which the users and the BSs both act as players. We introduce a set …


“Under Dangerous Conditions” – Safety Construction And Safety-Related Work Onboard Of Merchant Vessels, Gesa Praetorius, Monica Lundh May 2013

“Under Dangerous Conditions” – Safety Construction And Safety-Related Work Onboard Of Merchant Vessels, Gesa Praetorius, Monica Lundh

Gesa Praetorius

The following paper presents findings from a qualitative study conducted on board of two merchant vessels. Interviews and observations have been used to obtain insights in how safety is defined and promoted by the personnel working on board. The merchant vessel, the crew and the single mariner are identified to be part of a socio-technical system displaying three levels of system aggregation; person-centred, crew-centred, and vessel-centred. The common ground of a crew, an overlap of the individual mariners’ experience and knowledge, is identified as a basis for trust and predictability of action on board, which is a necessity to be …


A Decision Support Model For The Location Of Hand Sanitizer Dispensers In Hospitals, Laila Cure Ph.D., Richard Van Enk Ph.D., Ewing Tiong Ph.D. May 2013

A Decision Support Model For The Location Of Hand Sanitizer Dispensers In Hospitals, Laila Cure Ph.D., Richard Van Enk Ph.D., Ewing Tiong Ph.D.

Laila Cure

Compliance with hand hygiene practices is directly affected by the accessibility and availability of cleaning agents. Nevertheless, the decision of where to locate these dispensers is often not explicitly or fully addressed in the literature. In this paper, we study the problem of selecting the locations to install alcohol-based hand sanitizer dispensers throughout a hospital unit. We investigate the relevant criteria in selecting dispenser locations that promote compliance with hand hygiene practices, propose metrics for the evaluation of various location configurations, and formulate a dispenser location optimization model that incorporates such criteria. A complete methodology to collect data and obtain …


Virtual Teams And Its Application In New Product Development, R&D And Smes, Nader Ale Ebrahim May 2013

Virtual Teams And Its Application In New Product Development, R&D And Smes, Nader Ale Ebrahim

Nader Ale Ebrahim

A comprehensive definition of virtual teams may be taken as: small temporary groups of geographically, organizationally and/or time dispersed knowledge workers who coordinate their work, predominantly with electronic information and communication technologies in order to accomplish one or more organization tasks (Ale Ebrahim et al., 2009). Nowadays, this definition have gained popularity as found in Wikipedia (wikipedia, 2011). Virtual R&D team is a kind of virtual team that concentrate on the R&D tasks and projects (Ale Ebrahim et al., 2011).


Uncertain Congestion Games With Assorted Human Agent Populations, Asrar Ahmed, Pradeep Reddy Varakantham, Shih-Fen Cheng May 2013

Uncertain Congestion Games With Assorted Human Agent Populations, Asrar Ahmed, Pradeep Reddy Varakantham, Shih-Fen Cheng

Shih-Fen CHENG

Congestion games model a wide variety of real-world resource congestion problems, such as selfish network routing, traffic route guidance in congested areas, taxi fleet optimization and crowd movement in busy areas. However, existing research in congestion games assumes: (a) deterministic movement of agents between resources; and (b) perfect rationality (i.e. maximizing their own expected value) of all agents. Such assumptions are not reasonable in dynamic domains where decision support has to be provided to humans. For instance, in optimizing the performance of a taxi fleet serving a city, movement of taxis can be involuntary or nondeterministic (decided by the specific …


An Analysis Of Extreme Price Shocks And Illiquidity Among Systematic Trend Followers, Bernard Lee, Shih-Fen Cheng, Annie Koh May 2013

An Analysis Of Extreme Price Shocks And Illiquidity Among Systematic Trend Followers, Bernard Lee, Shih-Fen Cheng, Annie Koh

Shih-Fen Cheng

We construct an agent-based model to study the interplay between extreme price shocks and illiquidity in the presence of systematic traders known as trend followers. The agent-based approach is particularly attractive in modeling commodity markets because the approach allows for the explicit modeling of production, capacities, and storage constraints. Our study begins by using the price stream from a market simulation involving human participants and studies the behavior of various trend-following strategies, assuming initially that their participation will not impact the market. We notice an incremental deterioration in strategy performance as and when strategies deviate further and further from the …


Decentralized Decision Support For An Agent Population In Dynamic And Uncertain Domains, Pradeep Reddy Varakantham, Shih-Fen Cheng, Thi Duong Nguyen May 2013

Decentralized Decision Support For An Agent Population In Dynamic And Uncertain Domains, Pradeep Reddy Varakantham, Shih-Fen Cheng, Thi Duong Nguyen

Shih-Fen CHENG

This research is motivated by problems in urban transportation and labor mobility, where the agent flow is dynamic, non-deterministic and on a large scale. In such domains, even though the individual agents do not have an identity of their own and do not explicitly impact other agents, they have implicit interactions with other agents. While there has been much research in handling such implicit effects, it has primarily assumed controlled movements of agents in static environments. We address the issue of decision support for individual agents having involuntary movements in dynamic environments . For instance, in a taxi fleet serving …


Lagrangian Relaxation For Large-Scale Multi-Agent Planning, Geoff Gordon, Pradeep Varakantham, William Yeoh, Hoong Chuin Lau, Shih-Fen Cheng May 2013

Lagrangian Relaxation For Large-Scale Multi-Agent Planning, Geoff Gordon, Pradeep Varakantham, William Yeoh, Hoong Chuin Lau, Shih-Fen Cheng

Shih-Fen Cheng

Multi-agent planning is a well-studied problem with various applications including disaster rescue, urban transportation and logistics, both for autonomous agents and for decision support to humans. Due to computational constraints, existing research typically focuses on one of two scenarios: unstructured domains with many agents where we are content with heuristic solutions, or domains with small numbers of agents or special structure where we can provide provably near-optimal solutions. By contrast, in this paper, we focus on providing provably near-optimal solutions for domains with large numbers of agents, by exploiting a common domain-general property: if individual agents each have limited influence …


Lagrangian Relaxation For Large-Scale Multi-Agent Planning, Geoff Gordon, Pradeep Reddy Varakantham, William Yeoh, Ajay Srinivasan, Hoong Chuin Lau, Shih-Fen Cheng May 2013

Lagrangian Relaxation For Large-Scale Multi-Agent Planning, Geoff Gordon, Pradeep Reddy Varakantham, William Yeoh, Ajay Srinivasan, Hoong Chuin Lau, Shih-Fen Cheng

Shih-Fen CHENG

Multi-agent planning is a well-studied problem with applications in various areas. Due to computational constraints, existing research typically focuses either on unstructured domains with many agents, where we are content with heuristic solutions, or domains with small numbers of agents or special structure, where we can find provably near-optimal solutions. In contrast, here we focus on provably near-optimal solutions in domains with many agents, by exploiting influence limits. To that end, we make two key contributions: (a) an algorithm, based on Lagrangian relaxation and randomized rounding, for solving multi-agent planning problems represented as large mixed-integer programs; (b) a proof of …


Notes On Equilibria In Symmetric Games, Shih-Fen Cheng, Daniel M. Reeves, Yevgeniy Vorobeychik, Michael P. Wellman May 2013

Notes On Equilibria In Symmetric Games, Shih-Fen Cheng, Daniel M. Reeves, Yevgeniy Vorobeychik, Michael P. Wellman

Shih-Fen CHENG

In a symmetric game, every player is identical with respect to the game rules. We show that a symmetric 2strategy game must have a pure-strategy Nash equilibrium. We also discuss Nash’s original paper and its generalized notion of symmetry in games. As a special case of Nash’s theorem, any finite symmetric game has a symmetric Nash equilibrium. Furthermore, symmetric infinite games with compact, convex strategy spaces and continuous, quasiconcave utility functions have symmetric pure-strategy Nash equilibria. Finally, we discuss how to exploit symmetry for more efficient methods of finding Nash equilibria.


Distributing Complementary Resources Across Multiple Periods With Stochastic Demand, Shih-Fen Cheng, John Tajan, Hoong Chuin Lau May 2013

Distributing Complementary Resources Across Multiple Periods With Stochastic Demand, Shih-Fen Cheng, John Tajan, Hoong Chuin Lau

Shih-Fen CHENG

In this paper, we evaluate whether the robustness of a market mechanism that allocates complementary resources could be improved through the aggregation of time periods in which resources are consumed. In particular, we study a multi-round combinatorial auction that is built on a general equilibrium framework. We adopt the general equilibrium framework and the particular combinatorial auction design from the literature, and we investigate the benefits and the limitation of time-period aggregation when demand-side uncertainties are introduced. By using simulation experiments, we show that under stochastic conditions the performance variation of the process decreases as the time frame length (time …


Designing The Market Game For A Commodity Trading Simulation, Shih-Fen Cheng May 2013

Designing The Market Game For A Commodity Trading Simulation, Shih-Fen Cheng

Shih-Fen CHENG

In this paper, we propose to design a market game that (a) can be used in modeling and studying commodity trading scenarios, and (b) can be used in capturing human traders' behaviors. Specifically, we demonstrate the usefulness of this commodity trading game in a single-commodity futures trading scenario. A pilot experiment was run with a mixture of human traders and an autonomous agent that emulates the aggregatedmarket condition, with the assumption that this autonomous agent would hint each of its action through a public announcement. We show that the information collected from this simulation can be used to extract the …


Decision Support For Assorted Populations In Uncertain And Congested Environments, Pradeep Reddy Varakantham, Asrar Ahmed, Shih-Fen Cheng May 2013

Decision Support For Assorted Populations In Uncertain And Congested Environments, Pradeep Reddy Varakantham, Asrar Ahmed, Shih-Fen Cheng

Shih-Fen Cheng

This research is motivated by large scale problems in urban transportation and labor mobility where there is congestion for resources and uncertainty in movement. In such domains, even though the individual agents do not have an identity of their own and do not explicitly interact with other agents, they effect other agents. While there has been much research in handling such implicit effects, it has primarily assumed deterministic movements of agents. We address the issue of decision support for individual agents that are identical and have involuntary movements in dynamic environments. For instance, in a taxi fleet serving a city, …


An Analysis Of Extreme Price Shocks And Illiquidity Among Trend Followers, Bernard Lee, Shih-Fen Cheng, Annie Koh May 2013

An Analysis Of Extreme Price Shocks And Illiquidity Among Trend Followers, Bernard Lee, Shih-Fen Cheng, Annie Koh

Shih-Fen CHENG

We construct an agent-based model to study the interplay between extreme price shocks and illiquidity in the presence of systematic traders known as trend followers. The agent-based approach is particularly attractive in modeling commodity markets because the approach allows for the explicit modeling of production, capacities, and storage constraints. Our study begins by using the price stream from a market simulation involving human participants and studies the behavior of various trend-following strategies, assuming initially that their participation will not impact the market. We notice an incremental deterioration in strategy performance as and when strategies deviate further and further from the …


A Mechanism For Organizing Last-Mile Service Using Non-Dedicated Fleet, Shih-Fen Cheng, Duc Thien Nguyen, Hoong Chuin Lau May 2013

A Mechanism For Organizing Last-Mile Service Using Non-Dedicated Fleet, Shih-Fen Cheng, Duc Thien Nguyen, Hoong Chuin Lau

Shih-Fen CHENG

Unprecedented pace of urbanization and rising income levels have fueled the growth of car ownership in almost all newly formed megacities. Such growth has congested the limited road space and significantly affected the quality of life in these megacities. Convincing residents to give up their cars and use public transport is the most effective way in reducing congestion; however, even with sufficient public transport capacity, the lack of last-mile (from the transport hub to the destination) travel services is the major deterrent for the adoption of public transport. Due to the dynamic nature of such travel demands, fixed-size fleets will …


An Agent-Based Commodity Trading Simulation, Shih-Fen Cheng, Yee Pin Lim May 2013

An Agent-Based Commodity Trading Simulation, Shih-Fen Cheng, Yee Pin Lim

Shih-Fen CHENG

In this paper, an event-centric commodity trading simulation powered by the multiagent framework is presented. The purpose of this simulation platform is for training novice traders. The simulation is progressed by announcing news events that affect various aspects of the commodity supply chain. Upon receiving these events, market agents that play the roles of producers, consumers, and speculators would adjust their views on the market and act accordingly. Their actions would be based on their roles and also their private information, and collectively they shape the market dynamics. This simulation has been effectively deployed for several training sessions. We will …


Iterated Weaker-Than-Weak Dominance, Shih-Fen Cheng, Michael P. Wellman May 2013

Iterated Weaker-Than-Weak Dominance, Shih-Fen Cheng, Michael P. Wellman

Shih-Fen CHENG

We introduce a weakening of standard gametheoretic δ-dominance conditions, called dominance, which enables more aggressive pruning of candidate strategies at the cost of solution accuracy. Equilibria of a game obtained by eliminating a δ-dominated strategy are guaranteed to be approximate equilibria of the original game, with degree of approximation bounded by the dominance parameter. We can apply elimination of δ-dominated strategies iteratively, but the for which a strategy may be eliminated depends on prior eliminations. We discuss implications of this order independence, and propose greedy heuristics for determining a sequence of eliminations to reduce the game as far as possible …