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Uncertainty and change
 Handbook of Constraint Programming, chapter 21
, 2006
"... Constraint Programming (CP) has proven to be a very successful technique for reasoning about assignment problems, as evidenced by the many applications described elsewhere in this book. Much of its success is due to the simple and elegant underlying formulation: describe the world in terms of decisi ..."
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Cited by 27 (4 self)
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Constraint Programming (CP) has proven to be a very successful technique for reasoning about assignment problems, as evidenced by the many applications described elsewhere in this book. Much of its success is due to the simple and elegant underlying formulation: describe the world in terms of decision variables that must be assigned values, place clear and explicit restrictions on the values that may be assigned simultaneously, and then find a set of assignments to all the variables that obeys those restrictions. Thus, CP makes two assumptions about the problems it tackles: 1. There is no uncertainty in the problem definition: each problem has a crisp and complete description. 2. Problems are not dynamic: they do not change between the initial description and the final execution of the solution. Unfortunately, these two assumptions do not hold for many practical and important applications. For example, scheduling production in a factory is, in practice, fundamentally dynamic and uncertain: the full set of jobs to be scheduled is not known in advance, and continues to grow as existing jobs are being completed; machines break down; raw material
Robust solutions for combinatorial auctions
 In Proceedings of the 6th ACM Conference on Electronic Commerce
, 2005
"... Bids submitted in auctions are usually treated as enforceable commitments in most bidding and auction theory literature. In reality bidders often withdraw winning bids before the transaction when it is in their best interests to do so. Given a bidwithdrawal in a combinatorial auction, finding an al ..."
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Cited by 21 (2 self)
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Bids submitted in auctions are usually treated as enforceable commitments in most bidding and auction theory literature. In reality bidders often withdraw winning bids before the transaction when it is in their best interests to do so. Given a bidwithdrawal in a combinatorial auction, finding an alternative repair solution of adequate revenue without causing undue disturbance to the remaining winning bids in the original solution may be difficult or even impossible. We have called this the “Bidtaker’s Exposure Problem”. When faced with such unreliable bidders, it is preferable for the bidtaker to preempt such uncertainty by having a solution that is robust to bidwithdrawal and provides a guarantee that possible withdrawals may be repaired easily with a bounded loss in revenue. Firstly, we use the Weighted Super Solutions framework [13], from the field of Constraint Programming, to solve the problem of finding a robust solution of maximum revenue. A weighted super solution guarantees that any subset of bids likely to be withdrawn can be repaired to form a new solution of at least a given revenue by making a limited number of changes. Secondly, we introduce an auction model that uses a form of leveled commitment contract [27, 28], which we have called mutual bid bonds, to improve solution reparability by facilitating backtracking on winning bids by the bidtaker. We then examine the tradeoff between robustness and revenue in different economically motivated auction scenarios for different constraints on the revenue of repair solutions. We also demonstrate experimentally that fewer winning bids partake in robust solutions, thereby reducing any associated overhead in dealing with extra bidders.
A declarative approach to robust weighted MaxSAT
 IN: PROCEEDINGS OF THE 12TH INTERNATIONAL ACM SIGPLAN SYMPOSIUM ON PRINCIPLES AND PRACTICE OF DECLARATIVE PROGRAMMING (PPDP 2010
, 2010
"... The presence of uncertainty in the real world makes robustness to be a desired property of solutions to constraint satisfaction problems. Roughly speaking, a solution is robust if it can be easily repaired when unexpected events happen. This issue has already been addressed in the frameworks of Boo ..."
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Cited by 3 (1 self)
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The presence of uncertainty in the real world makes robustness to be a desired property of solutions to constraint satisfaction problems. Roughly speaking, a solution is robust if it can be easily repaired when unexpected events happen. This issue has already been addressed in the frameworks of Boolean satisfiability (SAT) and Constraint Programming (CP). Most works on robustness implement search algorithms to look for such solutions instead of taking the declarative approach of reformulation, since reformulation tends to generate prohibitively large formulas, especially in the CP setting. On the other hand, recent works suggest the use of SAT and MaxSAT encodings for solving CP instances. In this paper we present how robust solutions to weighted MaxSAT problems can be effectively obtained via reformulation into pseudoBoolean formulae, thus providing a much flexible approach to robustness. We illustrate the use of our approach in the robust combinatorial auctions setting and provide some promising experimental results.
Reformulation based MaxSAT robustness
"... The use of SAT and MaxSAT encodings for solving constraint satisfaction problems (CSP) has been gaining wide acceptance in the last years. On the other hand, the presence of uncertainty in the real world makes robustness to be a desired property of solutions to CSPs. Roughly speaking, a solution is ..."
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Cited by 1 (0 self)
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The use of SAT and MaxSAT encodings for solving constraint satisfaction problems (CSP) has been gaining wide acceptance in the last years. On the other hand, the presence of uncertainty in the real world makes robustness to be a desired property of solutions to CSPs. Roughly speaking, a solution is robust if it can be easily repaired when unexpected events happen. In fact, this issue has already been addressed in the frameworks of Boolean satisfiability (SAT) and constraint programming (CP). Most works on robustness implement search algorithms to look for such solutions instead of taking a reformulation approach, since reformulation tends to generate prohibitively large formulas, especially in the CP setting. In this paper we consider the unaddressed problem of robustness in weighted MaxSAT, by showing how robust solutions to weighted MaxSAT instances can be effectively obtained via reformulation into pseudoBoolean formulae. Our encoding provides a reasonable balance between increase in size and performance, as shown by our experiments in the robust resource allocation framework. We also address the problem of flexible robustness, where some of the breakages may be left unrepaired if a totally robust solution does not exist. In conclusion, we provide an easytoimplement new method for achieving robustness in combinatorial optimization problems.
Reformulation based MaxSAT robustness (Extended abstract) ∗
"... Abstract. The presence of uncertainty in the real world makes robustness a desirable property of solutions to Constraint Satisfaction Problems (CSP). A solution is said to be robust if it can be easily repaired when unexpected events happen. This has already been addressed in the frameworks of Boo ..."
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Abstract. The presence of uncertainty in the real world makes robustness a desirable property of solutions to Constraint Satisfaction Problems (CSP). A solution is said to be robust if it can be easily repaired when unexpected events happen. This has already been addressed in the frameworks of Boolean satisfiability (SAT) and Constraint Programming (CP). In this paper we consider the unaddressed problem of robustness in weighted MaxSAT, by showing how robust solutions to weighted MaxSAT instances can be effectively obtained via reformulation into pseudoBoolean formulae. Our encoding provides a reasonable balance between increase in size and performance. We also consider flexible robustness for problems having some unrepairable breakage, in other words, problems for which there does not exist a robust solution. 1
Incremental DCOP Search Algorithms for Solving Dynamic DCOP Problems
"... Abstract—Distributed constraint optimization (DCOP) problems are wellsuited for modeling multiagent coordination problems. However, it only models static problems, which do not change over time. Consequently, researchers have introduced the Dynamic DCOP (DDCOP) model to model dynamic problems. I ..."
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Abstract—Distributed constraint optimization (DCOP) problems are wellsuited for modeling multiagent coordination problems. However, it only models static problems, which do not change over time. Consequently, researchers have introduced the Dynamic DCOP (DDCOP) model to model dynamic problems. In this paper, we make two key contributions: (a) a procedure to reason with the incremental changes in DDCOPs and (b) an incremental pseudotree construction algorithm that can be used by DCOP algorithms such as anyspace ADOPT and anyspace BnBADOPT to solve DDCOPs. Due to the incremental reasoning employed, our experimental results show that anyspace ADOPT and anyspace BnBADOPT are up to 42 % and 38 % faster, respectively, with the incremental procedure and the incremental pseudotree reconstruction algorithm than without them. I.
Incremental DCOP Search Algorithms for Solving Dynamic DCOP Problems
"... Abstract—Distributed constraint optimization (DCOP) problems are wellsuited for modeling multiagent coordination problems. However, it only models static problems, which do not change over time. Consequently, researchers have introduced the Dynamic DCOP (DDCOP) model to model dynamic problems. I ..."
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Abstract—Distributed constraint optimization (DCOP) problems are wellsuited for modeling multiagent coordination problems. However, it only models static problems, which do not change over time. Consequently, researchers have introduced the Dynamic DCOP (DDCOP) model to model dynamic problems. In this paper, we make two key contributions: (a) a procedure to reason with the incremental changes in DDCOP problems and (b) an incremental pseudotree construction algorithm that can be used by DCOP algorithms such as anyspace ADOPT and anyspace BnBADOPT to solve DDCOP problems. Due to the incremental reasoning employed, our experimental results show that anyspace ADOPT and anyspace BnBADOPT are up to 42 % and 38 % faster, respectively, with the incremental procedure and the incremental pseudotree reconstruction algorithm than without them. I.
Head of Department:
, 2007
"... 4.6 Multiple heuristics and timeslicing................ 97 4.6.1 Initial tests on single heuristics............... 98 4.6.2 Using multiple heuristics.................. 98 4.6.3 Properties.......................... 99 4.6.4 MH configuration...................... 104 4.6.5 Evaluation metrics: efficie ..."
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4.6 Multiple heuristics and timeslicing................ 97 4.6.1 Initial tests on single heuristics............... 98 4.6.2 Using multiple heuristics.................. 98 4.6.3 Properties.......................... 99 4.6.4 MH configuration...................... 104 4.6.5 Evaluation metrics: efficiency and robustness....... 106 4.6.6 Experiments........................ 107 4.6.7 Test dimensioned upon the restaurant Eco......... 108 4.6.8 Tests scaled on a restaurant of 100 tables......... 115 4.6.9 Tests on quasigroup with holes (QWH).......... 120 4.6.10 Discussion......................... 125 4.7 Chapter summary.......................... 126 5 Modelling table configurations and seating plan flexibility 127
Auction Robustness through Satisfiability Modulo Theories
, 2003
"... Solution robustness is a desirable feature when dealing with uncertainty. This issue has rarely been taken into account in the field of auctions, where the goal is to obtain optimal solutions (i.e., maximize the auctioneer’s benefit). In this paper we define a notion of robustness for auctions whe ..."
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Solution robustness is a desirable feature when dealing with uncertainty. This issue has rarely been taken into account in the field of auctions, where the goal is to obtain optimal solutions (i.e., maximize the auctioneer’s benefit). In this paper we define a notion of robustness for auctions where some resources may become unavailable once the auction has already been cleared. This notion of robustness balances the number of changes needed for repairing the solution and the possible loss of benefit for the auctioneer. In order to obtain robust solutions for auctions, we provide a mechanism based on transporting the concept of supermodel to the setting of weighted MaxSAT. We show that finding a supermodel of a weighted MaxSAT formula amounts to find a model of an SMT (Satisfiability Modulo Theories) formula.
Reasoning about Optimal Collections of Solutions
"... The problem of finding a collection of solutions to a combinatorial problem that is optimal in terms of an intersolution objective function exists in many application settings. For example, maximizing diversity amongst a set of solutions in a product configuration setting is desirable so that a wi ..."
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The problem of finding a collection of solutions to a combinatorial problem that is optimal in terms of an intersolution objective function exists in many application settings. For example, maximizing diversity amongst a set of solutions in a product configuration setting is desirable so that a wide range of different options is offered to a customer. Given the computationally challenging nature of these multisolution queries, existing algorithmic approaches either apply heuristics or combinatorial search, which does not scale to large solution spaces. However, in many domains compiling the original problem into a compact representation can support computationally efficient query answering. In this paper we present a new approach to find optimal collections of solutions when the problem is compiled into a multivalued decision diagram. We demonstrate empirically that for realworld configuration problems, both exact and approximate versions of our methods are effective and are capable of significantly outperforming stateoftheart searchbased techniques.