Despite more than a decade of experimental work in multi-robot systems, important theoretical aspects of multi-robot coordination mechanisms have, to date, been largely untreated. To address this issue, we focus on the problem of multi-robot task allocation (MRTA). Most work on MRTA has been ad hoc and empirical, with many coordination architectures having been proposed and validated in a proof-of-concept fashion, but infrequently analyzed. With the goal of bringing objective grounding to this important area of research, we present a formal study of MRTA problems. A domain-independent taxonomy of MRTA problems is given, and it is shown how many such problems can be viewed as instances of other, well-studied, optimization problems. We demonstrate how relevant theory from operations research and combinatorial optimization can be used for analysis and greater understanding of existing approaches to task allocation, and show how the same theory can be used in the synthesis of new approaches.

/pdf/a-formal-analysis-and-taxonomy-of-task-allocation-in-multi-37udlnz144.pdf

A Formal Analysis and Taxonomy of Task Allocation in Multi-Robot Systems

Mixed-integer programs (MIPs) involving logical implications modeled through big-M coefficients are notoriously among the hardest to solve. In this paper, we propose and analyze computationally an automatic problem reformulation of quite general applicability, aimed at removing the model dependency on the big-M coefficients. Our solution scheme defines a master integer linear problem (ILP) with no continuous variables, which contains combinatorial information on the feasible integer variable combinations that can be “distilled” from the original MIP model. The master solutions are sent to a slave linear program (LP), which validates them and possibly returns combinatorial inequalities to be added to the current master ILP. The inequalities are associated to minimal (or irreducible) infeasible subsystems of a certain linear system, and can be separated efficiently in case the master solution is integer. The overall solution mechanism closely resembles the Benders' one, but the cuts we produce are purely co...

/pdf/combinatorial-benders-cuts-for-mixed-integer-linear-4mpxfss209.pdf

Combinatorial Benders' Cuts for Mixed-Integer Linear Programming

Scheduling and routing of automated guided vehicles : A hybrid approach

ion, Reformulation and Approximation, 6th International Symposium, Proceedings SARA 2005, LNCS 3607, pages 76–91. Springer, 2005. [17] A. M. Frisch, C. Jefferson, B. Martinez Hernandez, and I. Miguel. The Rules of Constraint Modelling. In Proceedings IJCAI05, pages 311–318, 2005. [18] A. M. Frisch, I. Miguel, and T. Walsh. Extensions to proof planning for generating implied constraints. In Proceedings of Calculemus-01, pages 130–141, 2001. [19] P. A. Geelen. Dual Viewpoint Heuristics for Binary Constraint Satisfaction Problems. In B. Neumann, editor, Proceedings ECAI’92, pages 31–35, 1992. [20] I. Gent, C. Jefferson, I. Lynce, I. Miguel, P. Nightingale, B. Smith, and A. Tarim. Search in the Patience Game ‘Black Hole’. Technical Report CPPod-10-2005, CPPod Research Group, 2005. Available from http://www.dcs.stand.ac.uk/s ̃cppod/publications/reports/. [21] L. Getoor, G. Ottosson, M. Fromherz, and B. Carlson. Effective Redundant Constraints for Online Scheduling. In Proceedings of AAAI’97, pages 302–307, 1997. [22] W. Harvey and P. J. Stuckey. Improving Linear Constraint Propagation by Changing Constraint Representation. Constraints, 8:173 – 207, 2003.

Chapter 11 - Modelling

We combine mixed integer linear programming (MILP) and constraint programming (CP) to solve planning and scheduling problems. Tasks are allocated to facilities using MILP and scheduled using CP, and the two are linked via logic-based Benders decomposition. Tasks assigned to a facility may run in parallel subject to resource constraints (cumulative scheduling). We solve minimum cost problems, as well as minimum makespan problems in which all tasks have the same release date and deadline. We obtain computational speedups of several orders of magnitude relative to the state of the art in both MILP and CP.

/pdf/a-hybrid-method-for-planning-and-scheduling-4yug8hvg4c.pdf

A hybrid method for planning and scheduling

Hybrid Benders Decomposition Algorithms in Constraint Logic Programming.- Branch-and-Check: A Hybrid Framework Integrating Mixed Integer Programming and Constraint Logic Programming.- Towards Inductive Constraint Solving.- Collaborative Learning for Constraint Solving.- Towards Stochastic Constraint Programming: A Study of Onine Multi-Choice Knapsack with Deadlines.- Global Cut Framework for Removing Symmetries.- Symmetry Breaking.- The Non-existence of (3,1,2)-Conjugate Orthogonal Idempotent Latin Square of Order 10.- Random 3-SAT and BDDs: The Plot Thickens Further.- Capturing Structure with Satisfiability.- Phase Transitions and Backbones of 3-SAT and Maximum 3-SAT.- Solving Non-binary CSPs Using the Hidden Variable Encoding.- A Filtering Algorithm for the Stretch Constraint.- Network Flow Problems in Constraint Programming.- Pruning for the Minimum Constraint Family and for the Number of Distinct Values Constraint Family.- A Constraint Programming Approach to the Stable Marriage Problem.- Components for State Restoration in Tree Search.- Adaptive Constraint Handling with CHR in Java.- Consistency Maintenance for ABT.- Constraint-Based Verification of Client-Server Protocols.- A Temporal Concurrent Constraint Programming Calculus.- Lower Bounds for Non-binary Constraint Optimization Problems.- New Lower Bounds of Constraint Violations for Over-Constrained Problems.- A General Scheme for Multiple Lower Bound Computation in Constraint Optimization.- Solving Disjunctive Constraints for Interactive Graphical Applications.- Sweep as a Generic Pruning Technique Applied to the Non-overlapping Rectangles Constraint.- Non-overlapping Constraints between Convex Polytopes.- Formal Models of Heavy-Tailed Behavior in Combinatorial Search.- The Phase Transition of the Linear Inequalities Problem.- In Search of a Phase Transition in the AC-Matching Problem.- Specific Filtering Algorithms for Over-Constrained Problems.- Specializing Russian Doll Search.- A CLP Approach to the Protein Side-Chain Placement Problem.- Fast, Constraint-Based Threading of HP-Sequences to Hydrophobic Cores.- One Flip per Clock Cycle.- Solving Constraints over Floating-Point Numbers.- Optimal Pruning in Parametric Differential Equations.- Interaction of Constraint Programming and Local Search for Optimisation Problems.- Partition-k-AC: An Efficient Filtering Technique Combining Domain Partition and Arc Consistency.- Neighborhood-Based Variable Ordering Heuristics for the Constraint Satisfaction Problem.- The Expressive Power of Binary Linear Programming.- Constraint Generation via Automated Theory Formation.- The Traveling Tournament Problem Description and Benchmarks.- Deriving Explanations and Implications for Constraint Satisfaction Problems.- Generating Tradeoffs for Interactive Constraint-Based Configuration.- Structural Constraint-Based Modeling and Reasoning with Basic Configuration Cells.- Composition Operators for Constraint Propagation:An Application to Choco.- Solving Boolean Satisfiability Using Local Search Guided by Unit Clause Elimination.- GAC on Conjunctions of Constraints.- Dual Models of Permutation Problems.- Boosting Local Search with Artificial Ants.- Fast Optimal Instruction Scheduling for Single-Issue Processors with Arbitrary Latencies.- Evaluation of Search Heuristics for Embedded System Scheduling Problems.- Interpreting Sloppy Stick Figures with Constraint-Based Subgraph Matching.- Selecting and Scheduling Observations for Agile Satellites: Some Lessons from the Constraint Reasoning Community Point of View.- A Dynamic Distributed Constraint Satisfaction Approach to Resource Allocation.- A Constraint Optimization Framework for Mapping a Digital Signal Processing Application onto a Parallel Architecture.- iOpt: A Software Toolkit for Heuristic Search Methods.- AbsCon: A Prototype to Solve CSPs with Abstraction.- A Constraint Engine for Manufacturing Process Planning.- On the Dynamic Detection of Interchangeability in Finite Constraint Satisfaction Problems.- Automatic Generation of Implied Clauses for SAT.- Verification of Infinite-State Systems by Specialization of CLP Programs.- Partially Ordered Constraint Optimization Problems.- Translations for Comparing Soft Frameworks.- Counting Satisfiable k-CNF Formulas.- High-Level Modelling and Reformulation of Constraint Satisfaction Problems.- Distributed Constraint Satisfaction as a Computational Model of Negotiation via Argumentation.- Aircraft Assignment Using Constraint Programming.- Labelling Heuristics for CSP Application Domains.- Improving SAT Algorithms by Using Search Pruning Techniques.- Optimum Symmetry Breaking in CSPs Using Group Theory.- Distributed Dynamic Backtracking.- Constraint Programming for Distributed Resource Allocation.- Exploiting the CSP Structure by Interchangeability.- Constraint Processing Techniques for Model-Based Reasoning about Dynamic Systems.- Distributed Constraint Satisfaction with Cooperating Asynchronous Solvers.- Building Negative Reduced Cost Paths Using Constraint Programming.- An Incremental and Non-binary CSP Solver: The Hyperpolyhedron Search Algorithm.- Partial Stable Generated Models of Generalized Logic Programs with Constraints.- Heterogeneous Constraint Problems An Outline of the Field of Work.- Comparing SAT Encodings for Model Checking.- Asynchronous Search for Numeric DisCSPs.- Temporal Concurrent Constraint Programming.

Principles and practice of constraint programming - CP 2001 : 7th International Conference, CP 2001, Paphos, Cyprus, November 26-December 1, 2001 : proceedings

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Principles and practice of constraint programming - CP 2001 : 7th International Conference, CP 2001, Paphos, Cyprus, November 26-December 1, 2001 : proceedings