## Exploring bounded optimal coordination for heterogeneous teams with cross-schedule dependencies (2011)

Citations: | 3 - 2 self |

### BibTeX

@TECHREPORT{Korsah11exploringbounded,

author = {G. Ayorkor Korsah},

title = {Exploring bounded optimal coordination for heterogeneous teams with cross-schedule dependencies},

institution = {},

year = {2011}

}

### OpenURL

### Abstract

### Citations

1313 |
Combinatorial Optimization: Algorithms and Complexity
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Citation Context ...he form of the pricing subproblem to be solved can be understood in the context of the theory underlying the simplex algorithm for solving linear programs. As described by Papadimitriou and Steiglitz =-=[89]-=-, suppose we have a linear program in standard-form: min c ′ x Ax = b (5.1) x ≥ 0 The dual of this linear program can be written in terms of dual variables, u, as: max u ′ b u ′ A ≤ c ′ (5.2) u ≷ 0 As... |

968 | Temporal constraint networks
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Citation Context ...0)* !"#$+,(-./0)* !"#$+,(-./0)* 3040/*5* 3040/*6* 3040/*'% Figure 7.3: Play-based architecture of the flexible execution module of xBots. 123It is useful to note that Simple Temporal Networks (STNs) =-=[31]-=- are often used to represent flexible time plans. These networks, instead of representing the start time of tasks as fixed time points, represent them as a time window, or a range of feasible times. A... |

807 | The Hungarian method for the assignment problem
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Citation Context ...1 ∀j ∈ M j∈M xij ∈ {0, 1} (2.7) where N is the set of agents, and M is the set of tasks. The linear assignment problem can be solved in polynomial time with algorithms such as the Hungarian algorithm =-=[68]-=-. For a feasible solution to this problem, the number of agents, |N| must be equal to the number of tasks, |M|. An imbalance in the number of robots and tasks can be fixed by including “dummy” agents ... |

416 | Alliance: An architecture for faulttolerant multi-robot cooperation
- Parker
- 1998
(Show Context)
Citation Context ...as a result of local interactions between members of a team and with the environment. This is referred to as implicit or emergent [45] coordination. We are concerned here with explicit or intentional =-=[91]-=- cooperation in which tasks are explicitly assigned to an agent or sub-team of agents. In robotics, this problem is described as multi-robot task allocation (MRTA). Multi-robot task allocation problem... |

296 |
Integer Programming
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Citation Context ...ming problems (ILP) or mixed integer linear programming problems (MILP), via a branchand-bound process. Details are described in numerous combinatorial optimization references, such as that by Wolsey =-=[117]-=- or by Papadimitriou and Steiglitz [89]. Consider an integer programming problem: ILP0 : min c ′ x Ax ≤ b (A.1) x ≥ 0, integer We obtain the linear programming relaxation of this problem by relaxing t... |

260 |
Computer solutions to the travelling salesman problem
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- 1965
(Show Context)
Citation Context ...sical heuristic methods. Single-route improvements involve reordering some requests within a given vehicle’s route. Techniques developed for the traveling salesman problem, notably Lin’s λ-opt method =-=[78]-=-, are applicable here. In this method, the tour is broken up into λ segments by removing λ edges, and the segments are then reconnected in all possible ways, in a search for a more profitable tour. Th... |

254 |
Scheduling algorithm
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Citation Context ...imization criterion is the weighted sum of execution costs ( ∑ wjCj).” In the scheduling literature, the objective function ∑ wjCj is actually the weighted sum of task completion (or finishing) times =-=[17]-=-. Since the completion time of a task depends on what tasks are scheduled earlier on the same machine, the fact that the objective or utility function depends on task completion times implies that thi... |

250 |
The Decomposition Principle for Linear Programming
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- 1960
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Citation Context ...on is too large for its LP relaxation to be solved by any approach involving exhaustive column enumeration. In the column generation approach, which is a generalization of Dantzig-Wolfe decomposition =-=[30]-=-, the algorithm starts out by considering only a subset of columns, and new columns are added as needed. The columns to be added are determined by solving, often by dynamic programming, a subproblem c... |

245 | Algorithms for the vehicle routing and scheduling problems with time window constraints
- Solomon
- 1987
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Citation Context ...nt insertion algorithms have been proposed for the various variants of the VRP. 42These include insertion heuristics for the basic capacitated VRP [21, 84], for the capacitated VRP with time windows =-=[92, 106]-=- as well as for the PDP and the DARP [54, 80, 96, 97]. The key questions addressed in the design of these insertion heuristics are: Which request should be selected next for insertion? and Where will ... |

220 | Branch-and-price: column generation for solving huge integer programs
- Barnhart, Johnson, et al.
- 1998
(Show Context)
Citation Context ...tion, we adopt a mathematical programming approach. We first express the problem with a set-partitioning formulation with side constraints, and then, in the next chapter, we devise a branch-and-price =-=[6]-=- (branchand-bound with column generation) algorithm to solve the formulated problem. The choice of a mathematical programming approach solved in a branch-and-bound framework is motivated by the goal o... |

205 | A formal analysis and taxonomy of task allocation in multi-robot systems
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- 2004
(Show Context)
Citation Context ...organize this work and identify the theoretical foundations of what they describe as largely ad-hoc approaches to multi-robot task allocation, Gerkey and Matarić proposed a taxonomy for MRTA problems =-=[47]-=-. This taxonomy, which is now widely used, provides a common vocabulary for describing MRTA problems. It is, however, limited in scope. It is described by its authors as restricted to systems with ind... |

182 |
Scheduling of vehicles from a central depot to a number of delivery points
- Clarke, JW
- 1964
(Show Context)
Citation Context ...sidering solution cost. They can be broadly classified into savings algorithms, and insertion heuristics. Savings algorithms, the most widely known of which is the Clarke and Wright Savings Algorithm =-=[23]-=- for the capacitated VRP, are based on the notion of generating cost savings by merging existing routes. The algorithm involves repeatedly computing savings for possible merges, and selecting the best... |

153 | A Tabu Search Heuristics for Vehicle Routing Problem
- Gendrearu, Hertz, et al.
- 1991
(Show Context)
Citation Context .... As in the previous two algorithms, a key design feature is how neighborhoods are defined, and some fairly involved schemes have been derived. Tabu search algorithms have been developed for the CVRP =-=[44, 87, 107, 119]-=-, the VRPTW [3, 108], the PDP and DARP [2, 27, 72]. 3.1.3 Problems with Cross-Schedule Dependencies Recent work in the vehicle routing literature has considered cross-schedule precedence constraints a... |

151 | Market-based multirobot coordination: A survey and analysis - Dias, Zlot, et al. - 2005 |

144 | Multi-robot exploration controlled by a market economy
- Zlot, Stentz, et al.
(Show Context)
Citation Context ... the resource, increases the efficiency of the team as a whole. Market based approaches have been applied to problems in the no dependencies class [46, 104], problems with 45in-schedule dependencies =-=[8, 36, 57, 69, 122]-=-, instantaneous assignment problems with crossschedule dependencies [11, 56, 77, 79] and time-extended assignment problems with limited forms of cross-schedule dependencies [24, 75]. In their survey o... |

141 | at al. Coordination for multi-robot exploration and mapping
- Simmons
(Show Context)
Citation Context ...cation address the ND [ST-SR-IA] problem. A few examples are work by Vail and Veloso using potential fields [114], Gerkey and Matarić using auction methods [46], and Simmons et al also using acutions =-=[104]-=-. Gerkey and Matarić [47] present a detailed discussion of ST-SR-IA problems with no dependencies, so we will not elaborate further on this class. 18ND [ST-SR-TA] In the time extended version of the ... |

127 |
A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows, Operations Research 40
- Desrochers, Desrosiers, et al.
- 1992
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Citation Context ...ime window and capacity constraints. This method has been found to yield excellent lower bounds that are then embedded 41in a branch-and-bound framework to solve the integer set partitioning problem =-=[34]-=-. Column generation is also used by Kohl et al [65] in their solution to the VRPTW problem. When column generation is allowed throughout the branch-and-bound tree (as opposed to just at the root node)... |

115 |
Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem
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- 1993
(Show Context)
Citation Context ...suring that as the algorithm proceeds it becomes less and less likely that a good solution will be replaced by a poorer one. Simulated annealing algorithms have been developed for the capacitated VRP =-=[87]-=- and for the VRPTW [109]. In deterministic annealing, the new solution is accepted according to a deterministic rule, rather than a probabilistic rule. In the threshold-accepting version, the new solu... |

106 |
M+: A scheme for multi-robot cooperation through negotiated task allocation and achievement
- Botelho, Alami
- 1999
(Show Context)
Citation Context ...ls, since routing times and costs are captured in these models. MRTA Solution Approaches There are a few multi-robot task allocation approaches that support cross-schedule dependencies. The M+ system =-=[11]-=- performs task allocation with a market system that does instantaneous assignment. It supports precedence constraints by allowing negotiation only on executable tasks, defined as tasks whose anteceden... |

97 |
A tabu search heuristic for the vehicle routing problem with soft time windows
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(Show Context)
Citation Context ...ithms, a key design feature is how neighborhoods are defined, and some fairly involved schemes have been derived. Tabu search algorithms have been developed for the CVRP [44, 87, 107, 119], the VRPTW =-=[3, 108]-=-, the PDP and DARP [2, 27, 72]. 3.1.3 Problems with Cross-Schedule Dependencies Recent work in the vehicle routing literature has considered cross-schedule precedence constraints and simultaneity cons... |

91 | Task allocation via coalition formation among autonomous agents
- Shehory, Kraus
- 1995
(Show Context)
Citation Context ...le tasks simultaneously (MT). MRTA Solution Approaches There is a lot of work in the multi-robot coordination literature that addresses the coalition formation problem. For example, Shehory and Kraus =-=[100]-=- address an instantaneous assignment problem with multi-agent tasks and single-task agents (XD [ST-MR-IA]) in which goods of various sizes and weights need to be transported. Some goods can be transpo... |

90 |
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Citation Context ... advantage that at any point in time, the consistency of the remainder of the plan can be verified. Simple Temporal Networks have been used to enable flexible scheduling of the plans of single agents =-=[85]-=-, as well as individual agents operating as part of a team [105]. The use of STNs is complementary to our approach which focuses on ensuring satisfaction of cross-schedule dependencies during executio... |

88 |
The period routing problem
- Christofides, Beasley
- 1984
(Show Context)
Citation Context ...erge in each iteration [1, 33, 116]. Several different insertion algorithms have been proposed for the various variants of the VRP. 42These include insertion heuristics for the basic capacitated VRP =-=[21, 84]-=-, for the capacitated VRP with time windows [92, 106] as well as for the PDP and the DARP [54, 80, 96, 97]. The key questions addressed in the design of these insertion heuristics are: Which request s... |

82 | Scheduling Independent Tasks to Reduce Mean Finishing Time - Coffman, Sethi - 1974 |

81 |
Parallel iterative search methods for vehicle routing problems
- Taillard
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(Show Context)
Citation Context .... As in the previous two algorithms, a key design feature is how neighborhoods are defined, and some fairly involved schemes have been derived. Tabu search algorithms have been developed for the CVRP =-=[44, 87, 107, 119]-=-, the VRPTW [3, 108], the PDP and DARP [2, 27, 72]. 3.1.3 Problems with Cross-Schedule Dependencies Recent work in the vehicle routing literature has considered cross-schedule precedence constraints a... |

79 |
Set partitioning: A survey
- Balas, Padberg
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(Show Context)
Citation Context ... assignment of tasks to coalitions where each robot can only perform one task at a time (i.e. can be a member of only one coalition) (XD [ST-MRIA]), this is equivalent to the set-partitioning problem =-=[4]-=- in combinatorial optimization. When each robot can perform multiple tasks simultaneously (i.e. be a member of multiple coalitions simultaneously) (XD [MT-MR-IA]), it is a set-covering problem [4]. Th... |

64 |
The pickup and delivery problem with time windows
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(Show Context)
Citation Context ...ticular, we will focus on solution methods for DARP and PDP problems. Solution methods generally fall into the broad categories of exact approaches based on variations of the branch-and-bound process =-=[26, 39]-=- and heuristic approaches [53, 111]. Typically, heuristic methods allow the solution of much larger problem instances compared to exact approaches, but at the expense of guarantees on solution quality... |

60 |
A branch-and-price algorithm for the generalized assignment problem
- Savelsbergh
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Citation Context ...istic multi-robot task allocation scenarios. There are several well-known combinatorial optimization problems that exemplify the ID class of problems. These include the generalized assignment problem =-=[98, 103]-=-, several machine scheduling problems [17], the Multiple Traveling Salesman Problem (m-TSP) [7] and several forms of the vehicle routing problem (VRP) [113]. While the linear assignment problem that e... |

58 | DRIVE: Dynamic routing of independent vehicles
- Savelsbergh, Sol
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(Show Context)
Citation Context ...K, (3.13) x k ij ∈ {0, 1} ∀i ∈ N, j ∈ N, k ∈ K, (3.14) Set-partitioning Formulation (Two-index Model) An example of a set partitioning formulation is that proposed by Savelsbergh and Sol for the DARP =-=[99]-=-. In this model, Ωk is the set of feasible routes for vehicle k, and the 2-index variable x k r is a binary decision variable that takes on the value 1 if route r ∈ Ωk is performed by vehicle k and 0 ... |

57 | Auction-based multi-robot routing
- Lagoudakis, Keskinocak, et al.
- 2005
(Show Context)
Citation Context ... tasks have been allocated. The contribution of their approach is a reduction in the complexity of the winner determination algorithm, relative to that 23for combinatorial auctions. Lagoudakis et al =-=[70]-=- also address market-based approaches to multi-robot routing, this time with a focus on contributing a theoretical analysis of the performance of auction methods for solving this problem. They study t... |

55 | Traderbots: A new paradigm for robust and efficient multirobot coordination in dynamic environments
- Dias
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(Show Context)
Citation Context ...ction or market-based approaches have become widely-used for solving multi-robot task allocation problems since their distributed nature are particularly suited to distributed robot teams. TraderBots =-=[36]-=- is a market-based architecture for multi-robot coordination in which agents hold auctions and submit bids to determine task allocation. The system enables computation of a time-extended allocation of... |

54 | A comparison of coordinated planning methods for cooperating rovers
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(Show Context)
Citation Context ...pports only instantaneous assignment of tasks to agents – each agent is assigned only one task to execute, and the method cannot support determining a schedule of tasks for each agent. 26Chien et al =-=[20]-=- address a robot routing problem corresponding to a geological scenario in which a team of rovers must perform a set of distributed science goals. In addition to individual resource constraints for ea... |

46 |
2-Path Cuts for the Vehicle Routing Problem with Time Windows
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(Show Context)
Citation Context ...s been found to yield excellent lower bounds that are then embedded 41in a branch-and-bound framework to solve the integer set partitioning problem [34]. Column generation is also used by Kohl et al =-=[65]-=- in their solution to the VRPTW problem. When column generation is allowed throughout the branch-and-bound tree (as opposed to just at the root node), the resulting algorithm is called branch-and-pric... |

44 | Plays as effective multiagent plans enabling opponentadaptive play selection
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(Show Context)
Citation Context ..., the presented approach also enables graceful degradation by enabling the team to continue execution of the unaffected parts of the plan. To implement our approach, we make use of the plays paradigm =-=[12]-=-, described shortly, to represent and execute the team plan, and extend this paradigm to support intermittent synchronization between agents. This play-based architecture, which will be described in d... |

44 |
Cyclic transfer algorithms for multi-vehicle routing and scheduling problems
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(Show Context)
Citation Context ...segments are then reconnected in all possible ways, in a search for a more profitable tour. There are several variations on this method. There are also a variety of multi-route improvement techniques =-=[16, 61, 110]-=- by which requests or groups of requests are moved between routes. In general, these arc exchange operations define a neighborhood around the current solution, which is searched for a better solution.... |

42 |
Building multi-robot coalitions through automated task solution synthesis
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Citation Context ...ed in the CD [ST-MR-TA] category, described in the next section. Complex Dependencies in Problems with Multi-Robot Tasks: CD [ST-MR-IA], CD [ST-MR-TA], CD [MT-MR-IA] and CD [MT-MR-TA] Parker and Tang =-=[90]-=- present a method for coalition formation through a process they describe as automated task solution synthesis. This work involves building a solution to a task by dynamically connecting a network of ... |

41 |
A distributed tasks allocation scheme in multi-uav context
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Citation Context ...led planning and scheduling by each rover using the ASPEN planner. The third approach is an auction-based approach in which the individual rovers use the ASPEN planner to generate bids. Lemaire et al =-=[75]-=- support simple ordering constraints between tasks in the form of “Task x must take place n seconds before task y”. This is done in a simple way by first auctioning one task to a robot, designated the... |

40 |
Robot exploration with combinatorial auctions
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(Show Context)
Citation Context ...s bid their incremental cost to insert the new task into their current schedule, plus a percentage of their expected profit for executing the task, where that percentage could be zero. Berhault et al =-=[8]-=- address a similar exploration task in which members of the robotic team need to visit a number of predetermined target points in the environment. They also use a market mechanism, and their approach ... |

40 | GRAMMPS: A generalized mission planner for multiple mobile robots
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Citation Context ...Interrelatedness ST-SR-IA ST-SR-TA MT-SR-IA MT-SR-TA ST-MR-IA No Dependencies (ND) Vail & Veloso [114], Gerey & Matarić [46], Simmons et al [104] In-schedule Dependencies (ID) Brummit et al (GRAMMPS) =-=[18]-=-, Melvin et al [82], Dias (TraderBots) [36], Berhault et al [8], , Koenig et al [62] Lagoudakis et al [70] Cross-schedule Dependencies (XD) Botelho & Alami (M+) [11], MacKenzie [79] Chien et al [20], ... |

40 | Multi-robot coalition formation
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(Show Context)
Citation Context ...of the problem with precedence constraints by ensuring that when a task is selected for execution, coalitions are simultaneously formed to perform any pending predecessors of that task. Vig and Adams =-=[115]-=- adapt the Shehory and Kraus’s [101] coalition formation algorithm (developed for disembodied agents) to be more suitable for the multi-robot domain by reducing the required communication, discouragin... |

37 |
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Citation Context ... relaxing selected constraints on appropriately formulated integer programs, resulting in problems for which specialized algorithms can be formulated (e.g. spanning tree and shortest path relaxations =-=[22]-=-, shortest path relaxations with capacity and time window constraints [66], and Lagrangian relaxations [40] [41]). For the DARP and PDP, more sophisticated methods are required. Cordeau [26] presents ... |

37 |
J.-M.: A parallel route building algorithm for the vehicle routing problem with time windows
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Citation Context ...nt insertion algorithms have been proposed for the various variants of the VRP. 42These include insertion heuristics for the basic capacitated VRP [21, 84], for the capacitated VRP with time windows =-=[92, 106]-=- as well as for the PDP and the DARP [54, 80, 96, 97]. The key questions addressed in the design of these insertion heuristics are: Which request should be selected next for insertion? and Where will ... |

36 |
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Citation Context ... the various variants of the VRP. 42These include insertion heuristics for the basic capacitated VRP [21, 84], for the capacitated VRP with time windows [92, 106] as well as for the PDP and the DARP =-=[54, 80, 96, 97]-=-. The key questions addressed in the design of these insertion heuristics are: Which request should be selected next for insertion? and Where will it be inserted? Insertions are either performed seque... |

35 | Simple auctions with performance guarantees for multi-robot task allocation
- Lagoudakis, Keskinocak, et al.
- 2004
(Show Context)
Citation Context ... the resource, increases the efficiency of the team as a whole. Market based approaches have been applied to problems in the no dependencies class [46, 104], problems with 45in-schedule dependencies =-=[8, 36, 57, 69, 122]-=-, instantaneous assignment problems with crossschedule dependencies [11, 56, 77, 79] and time-extended assignment problems with limited forms of cross-schedule dependencies [24, 75]. In their survey o... |

32 |
Rinnooy Kan, Complexity of scheduling under precedence constraints
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Citation Context ... 1} ∀i ∈ N, ∀j ∈ M (2.11) For the time-extended case, the problem of machine scheduling with precedence constraints on unrelated machines to minimize weighted sum of completion times (R|prec| ∑ wjCj) =-=[17, 76]-=-, falls into this category. Mathematical models have also been proposed for vehicle routing problems with simultaneity and/or precedence constraints [14, 15, 74, 94], and as discussed earlier, these m... |

32 | Multi-robot dynamic role assignment and coordination through shared potential fields
- Vail, Veloso
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(Show Context)
Citation Context ...iety of approaches, from centralized to distributed, that have been proposed for multi-robot task allocation problems. For example, for a role-assignment problem with no dependencies (ND), Vail et al =-=[114]-=- propose an allocation strategy based on shared potential fields. As mentioned in the previous chapter, some multi-robot task allocation approaches for the in-schedule dependencies class (ID) leverage... |

30 |
On multi-robot task allocation
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(Show Context)
Citation Context ...logically inspired robotic systems, coordinated team behavior emerges as a result of local interactions between members of a team and with the environment. This is referred to as implicit or emergent =-=[45]-=- coordination. We are concerned here with explicit or intentional [91] cooperation in which tasks are explicitly assigned to an agent or sub-team of agents. In robotics, this problem is described as m... |

29 | Distributed management of flexible times schedules
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(Show Context)
Citation Context ... [70] provides theoretical guarantees for various bidding rules under different objective functions. 3.2.2 Other (Non-Market-Based) Approaches to Problems with Cross-Schedule Dependencies Smith et al =-=[105]-=- and Barbulescu et al [5] address a distributed coordination problem in an oversubscribed, dynamic and uncertain environment as defined within the DARPA Coordinators program. Each agent is responsible... |

28 |
Heuristic algorithms for the handicapped persons transportation problem
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Citation Context ... methods for DARP and PDP problems. Solution methods generally fall into the broad categories of exact approaches based on variations of the branch-and-bound process [26, 39] and heuristic approaches =-=[53, 111]-=-. Typically, heuristic methods allow the solution of much larger problem instances compared to exact approaches, but at the expense of guarantees on solution quality. There are also approaches that co... |

27 |
The multiple traveling salesman problem: an overview of formulations and solution procedures
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Citation Context ...problems that exemplify the ID class of problems. These include the generalized assignment problem [98, 103], several machine scheduling problems [17], the Multiple Traveling Salesman Problem (m-TSP) =-=[7]-=- and several forms of the vehicle routing problem (VRP) [113]. While the linear assignment problem that exemplifies the no-dependencies (ND) class could be solved in polynomial time, these exemplifyin... |