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12
Coalition Structure Generation with Worst Case Guarantees
, 1999
"... Coalition formation is a key topic in multiagent systems. One may prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. Furthermore, finding the optimal coalition ..."
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Cited by 266 (10 self)
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Coalition formation is a key topic in multiagent systems. One may prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. Furthermore, finding the optimal coalition structure is NPcomplete. But then, can the coalition structure found via a partial search be guaranteed to be within a bound from optimum? We show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time remains, our anytime algorithm searches further, and establishes a progressively lower tight bound. Surprisingly, just searching one more node drops the bound in half. As desired, our algorithm lowers the bound rapidly early on, and exhibits diminishing returns to computation. It also significantly outperforms its obvious contenders. Finally, we show how to distribute the desired
Coalitions Among Computationally Bounded Agents
 Artificial Intelligence
, 1997
"... This paper analyzes coalitions among selfinterested agents that need to solve combinatorial optimization problems to operate e ciently in the world. By colluding (coordinating their actions by solving a joint optimization problem) the agents can sometimes save costs compared to operating individua ..."
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Cited by 202 (26 self)
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This paper analyzes coalitions among selfinterested agents that need to solve combinatorial optimization problems to operate e ciently in the world. By colluding (coordinating their actions by solving a joint optimization problem) the agents can sometimes save costs compared to operating individually. A model of bounded rationality is adopted where computation resources are costly. It is not worthwhile solving the problems optimally: solution quality is decisiontheoretically traded o against computation cost. A normative, application and protocolindependent theory of coalitions among boundedrational agents is devised. The optimal coalition structure and its stability are signi cantly a ected by the agents ' algorithms ' performance pro les and the cost of computation. This relationship is rst analyzed theoretically. Then a domain classi cation including rational and boundedrational agents is introduced. Experimental results are presented in vehicle routing with real data from ve dispatch centers. This problem is NPcomplete and the instances are so large thatwith current technologyany agent's rationality is bounded by computational complexity. 1
Negotiation Among Selfinterested Computationally Limited Agents
, 1996
"... A Dissertation Presented by TUOMAS W. SANDHOLM ..."
Coalition formation among bounded rational agents
, 1995
"... This paper analyzes coalitions among selfinterested agents that need to solve combinatorial optimization problems to operate efficiently in the world. By colluding (coordinating their actions by solving a joint optimization problem), the agents can sometimes save costs compared to operating individ ..."
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Cited by 85 (14 self)
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This paper analyzes coalitions among selfinterested agents that need to solve combinatorial optimization problems to operate efficiently in the world. By colluding (coordinating their actions by solving a joint optimization problem), the agents can sometimes save costs compared to operating individually. A model of bounded rationality is adopted, where computation resources are costly. It is not worth solving the problems optimally: solution quality is decisiontheoretically traded off against computation cost. A normative, protocolindependent theory of coalitions among bounded rational (BR) agents is devised. The optimal coalition structure and its stability are significantly affected by the agents' algorithms' performance profiles (PPs) and the unit cost of computation. This relationship is first analyzed theoretically. A domain classification including rational and BR agents is introduced. Experimental results are presented in the distributed vehicle routing domain using real data from 5 dispatch centers; the optimal coalition structure for BR agents differs significantly from the one for rational agents. These problems are NPcomplete and the instances are so large that, with current technology, any agent's rationality is bounded by computational complexity.
Traveling Salesman Problems With Profits: An Overview
 Transportation Science
, 2001
"... Traveling Salesman Problems with Profits (TSPs with Profits) are a generalization of the Traveling Salesman Problem (TSP) where it is not necessary to visit all vertices. With each vertex is associated a profit. The objective is to find a route with a satisfying collected profit (maximized) and trav ..."
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Cited by 74 (2 self)
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Traveling Salesman Problems with Profits (TSPs with Profits) are a generalization of the Traveling Salesman Problem (TSP) where it is not necessary to visit all vertices. With each vertex is associated a profit. The objective is to find a route with a satisfying collected profit (maximized) and travel cost (minimized). Applications of these problems arise in contexts such as traveling salesman problems, job scheduling or carrier transportation. In this paper, the existing literature about TSPs with Profits is surveyed.
Anytime Coalition Structure Generation: An Average Case Study
 Journal of Experimental and Theoretical AI
, 2000
"... Abstract. Coalition formation is a key topic in multiagent systems. One would prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow for exhaustive search for the optimal one. We present experimental res ..."
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Cited by 44 (4 self)
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Abstract. Coalition formation is a key topic in multiagent systems. One would prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow for exhaustive search for the optimal one. We present experimental results for three anytime algorithms that search the space of coalition structures. We show that, in the average case, all three algorithms do much better than the recently established theoretical worst case results in Sandholm et al. (1999a). We also show that no one algorithm is dominant. Each algorithm’s performance is in¯uenced by the particular instance distribution, with each algorithm outperforming the others for diŒerent instances. We present a possible explanation for the behaviour of the algorithms and support our hypothesis with data collected from a controlled experimental run. K eywords: coalition structure, algorithm, multiagent systems 1.
A pricedirected approach to stochastic inventory/routing
 Operations Research
, 2002
"... informs ® doi 10.1287/opre.1040.0114 © 2004 INFORMS We consider a new approach to stochastic inventory/routing that approximates the future costs of current actions using optimal dual prices of a linear program. We obtain two such linear programs by formulating the control problem as a Markov decisi ..."
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Cited by 44 (2 self)
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informs ® doi 10.1287/opre.1040.0114 © 2004 INFORMS We consider a new approach to stochastic inventory/routing that approximates the future costs of current actions using optimal dual prices of a linear program. We obtain two such linear programs by formulating the control problem as a Markov decision process and then replacing the optimal value function with the sum of singlecustomer inventory value functions. The resulting approximation yields statewise lower bounds on optimal infinitehorizon discounted costs. We present a linear program that takes into account inventory dynamics and economics in allocating transportation costs for stochastic inventory routing. On test instances we find that these allocations do not introduce any error in the value function approximations relative to the best approximations that can be achieved without them. Also, unlike other approaches, we do not restrict the set of allowable vehicle itineraries in any way. Instead, we develop an efficient algorithm to both generate and eliminate itineraries during solution of the linear programs and control policy. In simulation experiments, the pricedirected policy outperforms other policies from the literature. Subject classifications: dynamic programming/optimal control, discounted infinitehorizon: separable functional
Network Design and Allocation Mechanisms for Carrier Alliances in Liner Shipping
, 2007
"... When cargo carriers form an alliance, a key issue to resolve is how to provide incentive for carriers to make decisions that are optimal for the alliance as a whole. We propose a mechanism that utilizes capacity exchange prices to influence carrier behavior, and analyze two approaches to modeling th ..."
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Cited by 6 (1 self)
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When cargo carriers form an alliance, a key issue to resolve is how to provide incentive for carriers to make decisions that are optimal for the alliance as a whole. We propose a mechanism that utilizes capacity exchange prices to influence carrier behavior, and analyze two approaches to modeling the impact of these prices on the behavior of an individual carrier. We find that the model used can significantly impact alliance recommendations; one proposed model always finds capacity exchange prices that yield an allocation that is budgetbalanced and stable, yet cannot guarantee centralized feasibility. The second model uses more realistic control parameters and does in fact guarantee centralized feasibility. Finally, experimental results for two and threecarrier alliances are analyzed; it is determined that the benefit associated with collaborating increases with network size and fleet capacity, and depending on the characteristics of demand, fleet capacity is a more important factor. 1
T.: A study of proxies for Shapley allocation of transport costs
 Journal of Artificial Intelligence Research
, 2014
"... We propose and evaluate a number of solutions to the problem of calculating the cost to serve each location in a singlevehicle transport setting. Such cost to serve analysis has application both strategically and operationally in transportation. The problem is formally given by the traveling sal ..."
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Cited by 2 (1 self)
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We propose and evaluate a number of solutions to the problem of calculating the cost to serve each location in a singlevehicle transport setting. Such cost to serve analysis has application both strategically and operationally in transportation. The problem is formally given by the traveling salesperson game (TSG), a cooperative total utility game in which agents correspond to locations in a travelling salesperson problem (TSP). The cost to serve a location is an allocated portion of the cost of an optimal tour. The Shapley value is one of the most important normative division schemes in cooperative games, giving a principled and fair allocation both for the TSG and more generally. We consider a number of direct and samplingbased procedures for calculating the Shapley value, and present the first proof that approximating the Shapley value of the TSG within a constant factor is NPhard. Treating the Shapley value as an ideal baseline allocation, we then develop six proxies for that value which are relatively easy to compute. We perform an experimental evaluation using Synthetic Euclidean games as well as games derived from realworld tours calculated for fastmoving consumer goods scenarios. Our experiments show that several computationally tractable allocation techniques correspond to good proxies for the Shapley value.