Jimmy Ho-Man Lee

A fuzzy constraint based model for bilateral, multi-issue negotiations in semi-competitive environments

This paper develops a fuzzy constraint based model for bilateral multi-issue negotiation in trading environments. In particular, we are concerned with the principled negotiation approach in which agents seek to strike a fair deal for both parties, but which, nevertheless, maximises their own payoff. Thus, there are elements of both competition and cooperation in the negotiation (hence semi-competitive environments). One of the key intuitions of the approach is that there is often more than one option that can satisfy the interests of both parties. So, if the opponent cannot accept an offer then the proponent should endeavour to find an alternative that is equally acceptable to it, but more acceptable to the opponent. That is, the agent should make a trade-off. Only if such a trade-off is not possible should the agent make a concession. Against this background, our model ensures the agents reach a deal that is fair (Pareto-optimal) for both parties if such a solution exists. Moreover, this is achieved by minimising the amount of private information that is revealed. The model uses prioritised fuzzy constraints to represent trade-offs between the different possible values of the negotiation issues and to indicate how concessions should be made when they are necessary. Also by using constraints to express negotiation proposals, the model can cover the negotiation space more efficiently since each exchange covers a region rather than a single point (which is what most existing models deal with). In addition, by incorporating the notion of a reward into our negotiation model, the agents can sometimes reach agreements that would not otherwise be possible.

Principles and Practice of Constraint Programming – CP 2011

Recently, a variety of constraint programming and Boolean satisfiability approaches to scheduling problems have been introduced. They have in common the use of relatively simple propagation mechanisms and an adaptive way to focus on the most constrained part of the problem. In some cases, these methods compare favorably to more classical constraint programming methods relying on propagation algorithms for global unary or cumulative resource constraints and dedicated search heuristics. In particular, we described an approach that combines restarting, with a generic adaptive heuristic and solution guided branching on a simple model based on a decomposition of disjunctive constraints. In this paper, we introduce an adaptation of this technique for an important subclass of job shop scheduling problems (JSPs), where the objective function involves minimization of earliness/tardiness costs. We further show that our technique can be improved by adding domain specific information for one variant of the JSP (involving time lag constraints). In particular we introduce a dedicated greedy heuristic, and an improved model for the case where the maximal time lag is 0 (also referred to as no-wait JSPs).

Increasing Constraint Propagation by Redundant Modeling: \an Experience Report

This paper describes our experience with a simple modeling and programming approach for increasing the amount of constraint propagation in the constraint solving process. The idea, although similar to redundant constraints, is based on the concept of redundant modeling. We introduce the notions of CSP model and model redundancy, and show how mutually redundant models can be combined and connected using channeling constraints. The combined model contains the mutually redundant models as sub-models. Channeling constraints allow the sub-models to cooperate during constraint solving by propagating constraints freely amongst the sub-models. This extra level of pruning and propagation activities becomes the source of execution speedup. real-life nurse rostering system. We perform two case studies to evaluate the effectiveness and efficiency of our method. The first case study is based on the simple and well-known n-queens problem, while the second case study applies our method in the design and construction of a real-life nurse rostering system. Experimental results provide empirical evidence in line with our prediction.

Prioritised fuzzy constraint satisfaction problems: axioms, instantiation and validation

This paper identifies a generic axiom framework for prioritised fuzzy constraint satisfaction problems (PFCSPs), and proposes methods to instantiate it (i.e., to construct specific schemes which obey the generic axiom framework). In particular, we give five methods to construct the priority operators that are used for calculating the local satisfaction degree of a prioritised fuzzy constraint, and identify priority T-norm operators that can be used for calculating the global satisfaction degree of a prioritised fuzzy constraint problem. Moreover, a number of numerical examples and real examples are used to validate our system, and thus we further obtain some insights into our system. In addition, we explore the relationship between weight schemes and prioritised FCSP schemes, and reveal that the weighted FCSP schemes are the dual of prioritised FCSP schemes, which can, correspondingly, be called posterioritised FCSP schemes.

A nurse rostering system using constraint programming and redundant modeling

The paper describes the design and implementation of a constraint-based nurse rostering system using a redundant modeling approach. Nurse rostering is defined as the process of generating timetables for specifying the work shifts of nurses over a given period of time. This process is difficult because the human roster planner has to ensure that every rostering decision made complies with a mixture of hard hospital rules and soft nurse preference rules. Moreover, some nurse shift pre-assignments often break the regularity of wanted (or unwanted) shifts and reduce the choices for other unfilled slots. Soft constraints amount to disjunction, which can be modeled as choices in the search space. This approach, although straightforward, incurs overhead in the search of solution. To reduce search time, the authors propose redundant modeling, an effective way to increase constraint propagation through cooperation among different models for the same problem. The problem domain involves around 25 to 28 nurses and 11 shift types. Experiments and pilot testing of the system confirm the effectiveness and efficiency of the method.

A Constraint-Based Interactive Train Rescheduling Tool

In this paper, we report the design and implementation of a constraint-based interactive train rescheduling tool, a project in collaboration with the International Institute for Software Technology, United Nations University (UNU/IIST), Macau. We formulate train rescheduling as constraint satisfaction and describe a constraint propagation approach for tackling the problem. Algorithms for timetable verification and train rescheduling are designed under a coherent framework. Formal correctness properties of the rescheduling algorithm are established. We define two optimality criteria for rescheduling that correspond to minimizing the number of station visits affected and passenger delay respectively. Two heuristics are then proposed to speed up and direct the search towards optimal solutions. The feasibility of our proposed algorithms and heuristics are confirmed with experimentation using real-life data.

Finite domain bounds consistency revisited

A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with constraint propagation for pruning the search space. Constraint propagation is performed by propagators implementing a certain notion of consistency. Bounds consistency is the method of choice for building propagators for arithmetic constraints and several global constraints in the finite integer domain. However, there has been some confusion in the definition of bounds consistency and of bounds propagators. We clarify the differences among the three commonly used notions of bounds consistency in the literature. This serves as a reference for implementations of bounds propagators by defining (for the first time) the a priori behavior of bounds propagators on arbitrary constraints.

Symmetry Breaking Constraints for Value Symmetries in Constraint Satisfaction

Constraint satisfaction problems (CSPs) sometimes contain both variable symmetries and value symmetries, causing adverse effects on CSP solvers based on tree search. As a remedy, symmetry breaking constraints are commonly used. While variable symmetry breaking constraints can be expressed easily and propagated efficiently using lexicographic ordering, value symmetry breaking constraints are often difficult to formulate. In this paper, we propose two methods of using symmetry breaking constraints to tackle value symmetries. First, we show theoretically when value symmetries in one CSP correspond to variable symmetries in another CSP of the same problem. We also show when variable symmetry breaking constraints in the two CSPs, combined using channeling constraints, are consistent. Such results allow us to tackle value symmetries efficiently using additional CSP variables and channeling constraints. Second, we introduce value precedence, a notion which can be used to break a common class of value symmetries, namely symmetries of indistinguishable values. While value precedence can be expressed using inefficient if-then constraints in existing CSP solvers, we propose efficient propagation algorithms for implementing global value precedence constraints. We also characterize several theoretical properties of the value precedence constraints. Extensive experiments are conducted to verify the feasibility and efficiency of the two proposals.

A constraint-based nurse rostering system using a redundant modeling approach

This paper describes the design and implementation of a nurse rostering system using a redundant modeling approach. Nurse rostering is defined as a process of generating timetables for specifying the work shifts of nurses over a given period of time. This process is difficult because the human roster planner has to ensure that every rostering decision made complies with a mixture of hard hospital rules and soft nurse preference rules. Moreover, some nurse shift pre-assignments often break the regularity of wanted (or unwanted) shifts and reduce the choices for other unfilled slots. Soft constraints amount to disjunction, which can be modeled as choices in the search tree. This approach, although straightforward, incurs overhead in the search of solution. We propose redundant modeling, an effective way to speed up constraint propagation through cooperations among different models for the same problem, as a means to reduce search time. Experiments and pilot testing of the system confirm the feasibility of our method.

Speeding up constraint propagation by redundant modeling

The paper describes a simple modeling and programming approach for speeding up constraint propagation. The idea, although similar to redundant constraints, is based on the concept of redundant modeling. We define CSP model and model redundancy formally, and show how mutually redundant models can be combined and connected using channeling constraints. The combined model contains the original but redundant models as sub-models. Channeling constraints allow the sub-models to cooperate during constraint-solving by propagating constraints freely amongst the sub-models. This extra level of pruning and propagation activities becomes the source of execution speedup. We apply our method to the design and construction of a real-life nurse rostering system. Experimental results provide empirical evidence in line with our prediction.