Stephan Westphal - Academia.edu (original) (raw)
Papers by Stephan Westphal
An Auction-based Mechanism for the Formation and Scheduling of Heterogeneous Human-machine Teams
2021 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)
Human-machine teams are a key component of future production systems, but formation of the teams ... more Human-machine teams are a key component of future production systems, but formation of the teams is challenging due to uncertain and evolving skills and preferences. We propose a decentralized multi-round auction approach, where job agents specify processing times and workers bid their preferred job execution modes representing possible human-machine teams. The factory assigns jobs to teams while maximizing the number of jobs assigned within the specified planning period. Afterwards, a post-auction mechanism improves the assignment in a fair way without worsening the goal achievement of any party involved. We evaluate our auction and post-auction mechanisms by analyzing the workers' social welfare and the factory's objective for different bidding strategies. It turns out that our mechanism yields efficient assignments and provides incentives for the workers to share true estimations about their capabilities.
Journal of Cleaner Production, 2016
In light of various environmental problems and challenges concerning resource allocation, the uti... more In light of various environmental problems and challenges concerning resource allocation, the utilisation of renewable resources is increasingly important for the efficient use of raw materials. Therefore, cascading utilisation (i.e., the multiple material utilisations of renewable resources prior to their conversion into energy) and approaches that aim to further increase resource efficiency (e.g., the utilisation of by-products) can be considered guiding principles. This paper therefore introduces the Special Volume "Improved Resource Efficiency and Cascading Utilisation of Renewable Materials". Because both research aspects, resource efficiency and cascading utilisation, belong to several disciplines, the Special Volume adopts an interdisciplinary perspective and presents 16 articles, which can be divided into four subjects: Innovative Materials based on Renewable Resources and their Impact on Sustainability and Resource Efficiency, Quantitative Models for the Integrated Optimisation of Production and Distribution in Networks for Renewable Resources, Information Technology-based Collaboration in Value Generating Networks for Renewable Resources, and Consumer Behaviour towards Eco-friendly Products. The interdisciplinary perspective allows a comprehensive overview of current research on resource efficiency , which is supplemented with 15 book reviews showing the extent to which textbooks of selected disciplines already refer to resource efficiency. This introductory article highlights the relevance of the four subjects, presents summaries of all papers, and discusses future research directions. The overall contribution of the Special Volume is that it bridges the resource efficiency research of selected disciplines and that it presents several approaches for more environmentally sound production and consumption.
A column generation approach for optimized routing and coordination of a UAV fleet
2016 IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), 2016
Unmanned Aerial Vecicles (UAVs) in civil and military applications are becoming increasingly popu... more Unmanned Aerial Vecicles (UAVs) in civil and military applications are becoming increasingly popular. Various platform types have already shown their great potential in missions that require rapid surveillance capabilities or logistic support. Large scale incidents require the deployment of several platforms with various capabilities. In this case, coordinated use will lead to more efficient use of the given resources. Problems to resolve resemble known optimization problems from the field of vehicle routing or scheduling. The problem considered in this work includes a given team of homogenous UAVs and a set of target locations with certain requests that need to be served. It is modeled as a variant of the Vehicle Routing Problem (VRP) that is known to be NP hard, i.e. until now no algorithm is known that can solve the problem in polynomial run-time. In this paper, the problem is formulated using a path flow formulation and a column generation algorithm has been implemented and tested to solve simulated realtime instances of the problem in suitable time∗.
A Multi-Round Auction for Staff to Job Assignment Under Myopic Best Response Dynamics
2020 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), 2020
Many production systems still rely on human workers, who—unlike machines—have individual preferen... more Many production systems still rely on human workers, who—unlike machines—have individual preferences and private information to be taken into account when assigning staff to jobs. We propose a multi-round auction where workers bid their work rate on jobs trying to receive the jobs they prefer. The workers use a bidding strategy based on the myopic best response rule. The factory assigns the jobs to the workers while trying to maximize its production rate. To cope with the multiplicity of optimal assignments, the workers apply the Hurwicz criterion combining the best and worst possible outcomes. We evaluate our auction mechanism by examining the workers’ utilities and the factory’s production rate on generated problem instances and compare the results to a similar smart market mechanism for procurement and to the well-known Vickrey-Clarke-Groves auction. Our auction allows the factory to receive information about the maximum work rate of the workers. In return, the workers participat...
Proceedings of the 5th International Conference on Vehicle Technology and Intelligent Transport Systems, 2019
Platooning-vehicles travelling close together behaving as a unit-aims to improve network throughp... more Platooning-vehicles travelling close together behaving as a unit-aims to improve network throughput both on highways and in urban traffic. We study the problem of platoon formation in an urban environment using the scenario of logistic service providers equipped with fleets of autonomously driving pods to carry out same-day delivery tasks by creating cross-provider platoons. The novelty of our work is that we investigate the problem of cross-provider platoons, i.e., platoons with members from different self-interested logistic service providers. Our aim is to study platoon formation mechanisms and possible benefits of cross-provider platooning using simulation. We formulate optimal platoon formation as an integer linear optimisation problem (ILP), aiming to find the longest sub-routes to be shared between vehicles by platooning. The proposed method was implemented and tested on a mesoscopic model to simulate platoon formation and operation, on real network data with realistic background traffic models. Comparing our method to a simpler route matching algorithm reveals comparable system level performance; however, our method performs better with respect to local participant utility, i.e.appears more suited to take vehicle/provider preferences into account.
International Journal of Game Theory, 2018
We consider the classical mechanism design problem of fully implementing social choice functions ... more We consider the classical mechanism design problem of fully implementing social choice functions in dominant strategies in settings where monetary payments are allowed and the utility functions are quasi-linear. We consider both the general question of full implementation by indirect mechanisms and the special case of full implementation by incentive compatible direct revelation mechanisms. For the general case of full implementation by indirect mechanisms, we prove that one can restrict attention to incentive compatible augmented revelation mechanisms, in which the type space of each agent is a subset of the set of her possible bids and truthful reporting is a dominant strategy equilibrium. When the type spaces of the agents are finite, we give a complete characterization of the set of social choice functions that can be fully implemented in dominant strategies. For the case that one restricts to incentive compatible direct revelation mechanisms, we show that an adaption of the well-known negative cycle criterion for partial implementability also characterizes the social choice functions that are fully implementable.
Mathematical Methods of Operations Research, 2015
We consider an online knapsack problem with incremental capacity. In each time period, a set of i... more We consider an online knapsack problem with incremental capacity. In each time period, a set of items, each with a specific weight and value, is revealed and, without knowledge of future items, it has to be decided which of these items to accept. Additionally, the knapsack capacity is not fully available from the start but increases by a constant amount in each time period. The goal is to maximize the overall value of the accepted items. This setting extends the basic online knapsack problem by introducing a dynamic instead of a static knapsack capacity and is applicable to classic problems such as resource allocation or one-way trading. In contrast to the basic online knapsack problem, for which no competitive algorithms exist, the setting of incremental capacity facilitates the development of competitive algorithms for a bounded time horizon. We provide a competitive analysis of deterministic and randomized online algorithms for the online knapsack problem with incremental capacity and present lower bounds on
Journal of Scheduling
We consider the problem of scheduling intervals on m identical machines where each interval can b... more We consider the problem of scheduling intervals on m identical machines where each interval can be seen as a job with fixed start and end time. The goal is to accept a maximum cardinality subset of the given intervals and assign these intervals to the machines subject to the constraint that no two intervals assigned to the same machine overlap. We analyze an online version of this problem where, initially, a set of n potential intervals and an upper bound k on the number of failing intervals is given. If an interval fails, it can be accepted neither by the online algorithm nor by the adversary. An online algorithm learns that an interval fails at the time when it is supposed to be started. If a non-failing interval is accepted, it cannot be aborted and must be processed nonpreemptively until completion. For different settings of this problem, we present deterministic and randomized online algorithms and prove lower bounds on the competitive ratio.
Solving the traveling tournament problem by packing three-vertex paths
The Traveling Tournament Problem (TTP) is a complex problem in sports scheduling whose solution i... more The Traveling Tournament Problem (TTP) is a complex problem in sports scheduling whose solution is a schedule of home and away games meeting specific feasibility requirements, while minimizing the total distance traveled by all the teams. A recently-developed "hybrid" algorithm, combining local search and integer programming, has resulted in best-known solutions for many TTP instances. In this paper, we tackle the TTP from a graph-theoretic perspective, by generating a new "canonical" schedule in which each team's three-game road trips match up with the underlying graph's minimum-weight P3-packing. By using this new schedule as the initial input for the hybrid algorithm, we develop tournament schedules for five benchmark TTP instances that beat all previously-known solutions.
Computational Statistics
Oblique decision trees recursively divide the feature space by using splits based on linear combi... more Oblique decision trees recursively divide the feature space by using splits based on linear combinations of attributes. Compared to their univariate counterparts, which only use a single attribute per split, they are often smaller and more accurate. A common approach to learn decision trees is by iteratively introducing splits on a training set in a top–down manner, yet determining a single optimal oblique split is in general computationally intractable. Therefore, one has to rely on heuristics to find near-optimal splits. In this paper, we adapt the cross-entropy optimization method to tackle this problem. The approach is motivated geometrically by the observation that equivalent oblique splits can be interpreted as connected regions on a unit hypersphere which are defined by the samples in the training data. In each iteration, the algorithm samples multiple candidate solutions from this hypersphere using the von Mises–Fisher distribution which is parameterized by a mean direction ...
Big Data and Cognitive Computing
The way humans and artificially intelligent machines interact is undergoing a dramatic change. Th... more The way humans and artificially intelligent machines interact is undergoing a dramatic change. This change becomes particularly apparent in domains where humans and machines collaboratively work on joint tasks or objects in teams, such as in industrial assembly or disassembly processes. While there is intensive research work on human–machine collaboration in different research disciplines, systematic and interdisciplinary approaches towards engineering systems that consist of or comprise human–machine teams are still rare. In this paper, we review and analyze the state of the art, and derive and discuss core requirements and concepts by means of an illustrating scenario. In terms of methods, we focus on how reciprocal trust between humans and intelligent machines is defined, built, measured, and maintained from a systems engineering and planning perspective in literature. Based on our analysis, we propose and outline three important areas of future research on engineering and operat...
A branch bound algorithm to determine optimal cross-splits for decision tree induction
Annals of Mathematics and Artificial Intelligence
A combined approximation for the traveling tournament problem and the traveling umpire problem
Journal of Quantitative Analysis in Sports, 2016
We consider the traveling tournament problem (TTP) and the traveling umpire problem (TUP). In TTP... more We consider the traveling tournament problem (TTP) and the traveling umpire problem (TUP). In TTP, the task is to design a double round-robin schedule, where no two teams play against each other in two consecutive rounds, and the total travel distance is minimized. In TUP, the task is to find an assignment of umpires for a given tournament such that every umpire handles at least one game at every team’s home venue and an umpire neither visits a venue nor sees a team (home or away) too often. The task is to minimize the total distance traveled by the umpires. We present a combined approximation for this problem, when the number of umpires is odd. We therefore first design an approximation algorithm for TTP and then show how to define an umpire assignment for this tournament such that a constant-factor approximation for TUP is guaranteed.
Applied Intelligence
Univariate decision tree induction methods for multiclass classification problems such as CART, C... more Univariate decision tree induction methods for multiclass classification problems such as CART, C4.5 and ID3 continue to be very popular in the context of machine learning due to their major benefit of being easy to interpret. However, as these trees only consider a single attribute per node, they often get quite large which lowers their explanatory value. Oblique decision tree building algorithms, which divide the feature space by multidimensional hyperplanes, often produce much smaller trees but the individual splits are hard to interpret. Moreover, the effort of finding optimal oblique splits is very high such that heuristics have to be applied to determine local optimal solutions. In this work, we introduce an effective branch and bound procedure to determine global optimal bivariate oblique splits for concave impurity measures. Decision trees based on these bivariate oblique splits remain fairly interpretable due to the restriction to two attributes per split. The resulting tre...
Approximating the Traveling Tournament Problem with Maximum Tour Length 2
Algorithms and Computation, 2010
Page 1. Approximating the Traveling Tournament Problem with Maximum Tour Length 2 Clemens Thielen... more Page 1. Approximating the Traveling Tournament Problem with Maximum Tour Length 2 Clemens Thielen and Stephan Westphal ... Abstract. We consider the traveling tournament problem, which is a well-known benchmark problem in tournament timetabling. ...
Information Processing Letters, Apr 1, 2008
We consider the online problem k-CTP, which is the problem to guide a vehicle from some site s to... more We consider the online problem k-CTP, which is the problem to guide a vehicle from some site s to some site t on a road map given by a graph G = (V, E) in which up to k (unknown) edges are blocked by avalanches. An online algorithm learns from a blocked edge when reaching one of its endpoints. Thus, it might have to change its route to the target t up to k times. We show that no deterministic online algorithm can achieve a competitive ratio smaller than 2k + 1 and give an easy algorithm which matches this lower bound. Furthermore, we show that randomization can not improve the competitive ratio substantially, by establishing a lower bound of k + 1 for the competitivity of randomized online algorithms against an oblivious adversary.
Scheduling the German Basketball League
Interfaces, Oct 13, 2014
Scheduling the German Basketball League
Interfaces, 2014
Algorithmic Approaches to Flexible Job Shop Scheduling
Aspects of Online Routing and Scheduling
An Auction-based Mechanism for the Formation and Scheduling of Heterogeneous Human-machine Teams
2021 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)
Human-machine teams are a key component of future production systems, but formation of the teams ... more Human-machine teams are a key component of future production systems, but formation of the teams is challenging due to uncertain and evolving skills and preferences. We propose a decentralized multi-round auction approach, where job agents specify processing times and workers bid their preferred job execution modes representing possible human-machine teams. The factory assigns jobs to teams while maximizing the number of jobs assigned within the specified planning period. Afterwards, a post-auction mechanism improves the assignment in a fair way without worsening the goal achievement of any party involved. We evaluate our auction and post-auction mechanisms by analyzing the workers' social welfare and the factory's objective for different bidding strategies. It turns out that our mechanism yields efficient assignments and provides incentives for the workers to share true estimations about their capabilities.
Journal of Cleaner Production, 2016
In light of various environmental problems and challenges concerning resource allocation, the uti... more In light of various environmental problems and challenges concerning resource allocation, the utilisation of renewable resources is increasingly important for the efficient use of raw materials. Therefore, cascading utilisation (i.e., the multiple material utilisations of renewable resources prior to their conversion into energy) and approaches that aim to further increase resource efficiency (e.g., the utilisation of by-products) can be considered guiding principles. This paper therefore introduces the Special Volume "Improved Resource Efficiency and Cascading Utilisation of Renewable Materials". Because both research aspects, resource efficiency and cascading utilisation, belong to several disciplines, the Special Volume adopts an interdisciplinary perspective and presents 16 articles, which can be divided into four subjects: Innovative Materials based on Renewable Resources and their Impact on Sustainability and Resource Efficiency, Quantitative Models for the Integrated Optimisation of Production and Distribution in Networks for Renewable Resources, Information Technology-based Collaboration in Value Generating Networks for Renewable Resources, and Consumer Behaviour towards Eco-friendly Products. The interdisciplinary perspective allows a comprehensive overview of current research on resource efficiency , which is supplemented with 15 book reviews showing the extent to which textbooks of selected disciplines already refer to resource efficiency. This introductory article highlights the relevance of the four subjects, presents summaries of all papers, and discusses future research directions. The overall contribution of the Special Volume is that it bridges the resource efficiency research of selected disciplines and that it presents several approaches for more environmentally sound production and consumption.
A column generation approach for optimized routing and coordination of a UAV fleet
2016 IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), 2016
Unmanned Aerial Vecicles (UAVs) in civil and military applications are becoming increasingly popu... more Unmanned Aerial Vecicles (UAVs) in civil and military applications are becoming increasingly popular. Various platform types have already shown their great potential in missions that require rapid surveillance capabilities or logistic support. Large scale incidents require the deployment of several platforms with various capabilities. In this case, coordinated use will lead to more efficient use of the given resources. Problems to resolve resemble known optimization problems from the field of vehicle routing or scheduling. The problem considered in this work includes a given team of homogenous UAVs and a set of target locations with certain requests that need to be served. It is modeled as a variant of the Vehicle Routing Problem (VRP) that is known to be NP hard, i.e. until now no algorithm is known that can solve the problem in polynomial run-time. In this paper, the problem is formulated using a path flow formulation and a column generation algorithm has been implemented and tested to solve simulated realtime instances of the problem in suitable time∗.
A Multi-Round Auction for Staff to Job Assignment Under Myopic Best Response Dynamics
2020 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), 2020
Many production systems still rely on human workers, who—unlike machines—have individual preferen... more Many production systems still rely on human workers, who—unlike machines—have individual preferences and private information to be taken into account when assigning staff to jobs. We propose a multi-round auction where workers bid their work rate on jobs trying to receive the jobs they prefer. The workers use a bidding strategy based on the myopic best response rule. The factory assigns the jobs to the workers while trying to maximize its production rate. To cope with the multiplicity of optimal assignments, the workers apply the Hurwicz criterion combining the best and worst possible outcomes. We evaluate our auction mechanism by examining the workers’ utilities and the factory’s production rate on generated problem instances and compare the results to a similar smart market mechanism for procurement and to the well-known Vickrey-Clarke-Groves auction. Our auction allows the factory to receive information about the maximum work rate of the workers. In return, the workers participat...
Proceedings of the 5th International Conference on Vehicle Technology and Intelligent Transport Systems, 2019
Platooning-vehicles travelling close together behaving as a unit-aims to improve network throughp... more Platooning-vehicles travelling close together behaving as a unit-aims to improve network throughput both on highways and in urban traffic. We study the problem of platoon formation in an urban environment using the scenario of logistic service providers equipped with fleets of autonomously driving pods to carry out same-day delivery tasks by creating cross-provider platoons. The novelty of our work is that we investigate the problem of cross-provider platoons, i.e., platoons with members from different self-interested logistic service providers. Our aim is to study platoon formation mechanisms and possible benefits of cross-provider platooning using simulation. We formulate optimal platoon formation as an integer linear optimisation problem (ILP), aiming to find the longest sub-routes to be shared between vehicles by platooning. The proposed method was implemented and tested on a mesoscopic model to simulate platoon formation and operation, on real network data with realistic background traffic models. Comparing our method to a simpler route matching algorithm reveals comparable system level performance; however, our method performs better with respect to local participant utility, i.e.appears more suited to take vehicle/provider preferences into account.
International Journal of Game Theory, 2018
We consider the classical mechanism design problem of fully implementing social choice functions ... more We consider the classical mechanism design problem of fully implementing social choice functions in dominant strategies in settings where monetary payments are allowed and the utility functions are quasi-linear. We consider both the general question of full implementation by indirect mechanisms and the special case of full implementation by incentive compatible direct revelation mechanisms. For the general case of full implementation by indirect mechanisms, we prove that one can restrict attention to incentive compatible augmented revelation mechanisms, in which the type space of each agent is a subset of the set of her possible bids and truthful reporting is a dominant strategy equilibrium. When the type spaces of the agents are finite, we give a complete characterization of the set of social choice functions that can be fully implemented in dominant strategies. For the case that one restricts to incentive compatible direct revelation mechanisms, we show that an adaption of the well-known negative cycle criterion for partial implementability also characterizes the social choice functions that are fully implementable.
Mathematical Methods of Operations Research, 2015
We consider an online knapsack problem with incremental capacity. In each time period, a set of i... more We consider an online knapsack problem with incremental capacity. In each time period, a set of items, each with a specific weight and value, is revealed and, without knowledge of future items, it has to be decided which of these items to accept. Additionally, the knapsack capacity is not fully available from the start but increases by a constant amount in each time period. The goal is to maximize the overall value of the accepted items. This setting extends the basic online knapsack problem by introducing a dynamic instead of a static knapsack capacity and is applicable to classic problems such as resource allocation or one-way trading. In contrast to the basic online knapsack problem, for which no competitive algorithms exist, the setting of incremental capacity facilitates the development of competitive algorithms for a bounded time horizon. We provide a competitive analysis of deterministic and randomized online algorithms for the online knapsack problem with incremental capacity and present lower bounds on
Journal of Scheduling
We consider the problem of scheduling intervals on m identical machines where each interval can b... more We consider the problem of scheduling intervals on m identical machines where each interval can be seen as a job with fixed start and end time. The goal is to accept a maximum cardinality subset of the given intervals and assign these intervals to the machines subject to the constraint that no two intervals assigned to the same machine overlap. We analyze an online version of this problem where, initially, a set of n potential intervals and an upper bound k on the number of failing intervals is given. If an interval fails, it can be accepted neither by the online algorithm nor by the adversary. An online algorithm learns that an interval fails at the time when it is supposed to be started. If a non-failing interval is accepted, it cannot be aborted and must be processed nonpreemptively until completion. For different settings of this problem, we present deterministic and randomized online algorithms and prove lower bounds on the competitive ratio.
Solving the traveling tournament problem by packing three-vertex paths
The Traveling Tournament Problem (TTP) is a complex problem in sports scheduling whose solution i... more The Traveling Tournament Problem (TTP) is a complex problem in sports scheduling whose solution is a schedule of home and away games meeting specific feasibility requirements, while minimizing the total distance traveled by all the teams. A recently-developed "hybrid" algorithm, combining local search and integer programming, has resulted in best-known solutions for many TTP instances. In this paper, we tackle the TTP from a graph-theoretic perspective, by generating a new "canonical" schedule in which each team's three-game road trips match up with the underlying graph's minimum-weight P3-packing. By using this new schedule as the initial input for the hybrid algorithm, we develop tournament schedules for five benchmark TTP instances that beat all previously-known solutions.
Computational Statistics
Oblique decision trees recursively divide the feature space by using splits based on linear combi... more Oblique decision trees recursively divide the feature space by using splits based on linear combinations of attributes. Compared to their univariate counterparts, which only use a single attribute per split, they are often smaller and more accurate. A common approach to learn decision trees is by iteratively introducing splits on a training set in a top–down manner, yet determining a single optimal oblique split is in general computationally intractable. Therefore, one has to rely on heuristics to find near-optimal splits. In this paper, we adapt the cross-entropy optimization method to tackle this problem. The approach is motivated geometrically by the observation that equivalent oblique splits can be interpreted as connected regions on a unit hypersphere which are defined by the samples in the training data. In each iteration, the algorithm samples multiple candidate solutions from this hypersphere using the von Mises–Fisher distribution which is parameterized by a mean direction ...
Big Data and Cognitive Computing
The way humans and artificially intelligent machines interact is undergoing a dramatic change. Th... more The way humans and artificially intelligent machines interact is undergoing a dramatic change. This change becomes particularly apparent in domains where humans and machines collaboratively work on joint tasks or objects in teams, such as in industrial assembly or disassembly processes. While there is intensive research work on human–machine collaboration in different research disciplines, systematic and interdisciplinary approaches towards engineering systems that consist of or comprise human–machine teams are still rare. In this paper, we review and analyze the state of the art, and derive and discuss core requirements and concepts by means of an illustrating scenario. In terms of methods, we focus on how reciprocal trust between humans and intelligent machines is defined, built, measured, and maintained from a systems engineering and planning perspective in literature. Based on our analysis, we propose and outline three important areas of future research on engineering and operat...
A branch bound algorithm to determine optimal cross-splits for decision tree induction
Annals of Mathematics and Artificial Intelligence
A combined approximation for the traveling tournament problem and the traveling umpire problem
Journal of Quantitative Analysis in Sports, 2016
We consider the traveling tournament problem (TTP) and the traveling umpire problem (TUP). In TTP... more We consider the traveling tournament problem (TTP) and the traveling umpire problem (TUP). In TTP, the task is to design a double round-robin schedule, where no two teams play against each other in two consecutive rounds, and the total travel distance is minimized. In TUP, the task is to find an assignment of umpires for a given tournament such that every umpire handles at least one game at every team’s home venue and an umpire neither visits a venue nor sees a team (home or away) too often. The task is to minimize the total distance traveled by the umpires. We present a combined approximation for this problem, when the number of umpires is odd. We therefore first design an approximation algorithm for TTP and then show how to define an umpire assignment for this tournament such that a constant-factor approximation for TUP is guaranteed.
Applied Intelligence
Univariate decision tree induction methods for multiclass classification problems such as CART, C... more Univariate decision tree induction methods for multiclass classification problems such as CART, C4.5 and ID3 continue to be very popular in the context of machine learning due to their major benefit of being easy to interpret. However, as these trees only consider a single attribute per node, they often get quite large which lowers their explanatory value. Oblique decision tree building algorithms, which divide the feature space by multidimensional hyperplanes, often produce much smaller trees but the individual splits are hard to interpret. Moreover, the effort of finding optimal oblique splits is very high such that heuristics have to be applied to determine local optimal solutions. In this work, we introduce an effective branch and bound procedure to determine global optimal bivariate oblique splits for concave impurity measures. Decision trees based on these bivariate oblique splits remain fairly interpretable due to the restriction to two attributes per split. The resulting tre...
Approximating the Traveling Tournament Problem with Maximum Tour Length 2
Algorithms and Computation, 2010
Page 1. Approximating the Traveling Tournament Problem with Maximum Tour Length 2 Clemens Thielen... more Page 1. Approximating the Traveling Tournament Problem with Maximum Tour Length 2 Clemens Thielen and Stephan Westphal ... Abstract. We consider the traveling tournament problem, which is a well-known benchmark problem in tournament timetabling. ...
Information Processing Letters, Apr 1, 2008
We consider the online problem k-CTP, which is the problem to guide a vehicle from some site s to... more We consider the online problem k-CTP, which is the problem to guide a vehicle from some site s to some site t on a road map given by a graph G = (V, E) in which up to k (unknown) edges are blocked by avalanches. An online algorithm learns from a blocked edge when reaching one of its endpoints. Thus, it might have to change its route to the target t up to k times. We show that no deterministic online algorithm can achieve a competitive ratio smaller than 2k + 1 and give an easy algorithm which matches this lower bound. Furthermore, we show that randomization can not improve the competitive ratio substantially, by establishing a lower bound of k + 1 for the competitivity of randomized online algorithms against an oblivious adversary.
Scheduling the German Basketball League
Interfaces, Oct 13, 2014
Scheduling the German Basketball League
Interfaces, 2014
Algorithmic Approaches to Flexible Job Shop Scheduling
Aspects of Online Routing and Scheduling