ABSTRACT. ZOOM link: https://technion.zoom.us/j/97111314813

During the past two years, the speaker has been drafting Section 7.2.2.3 of The Art of Computer Programming, which is intended to be a solid introduction to techniques for solving Constraint Satisfaction Problems. The CP 2022 conference is an excellent opportunity for him to get feedback from the leading experts on the subject, and so he was delighted to learn that the organizers were also interested in hearing a few words from him. Rather than giving a canned lecture, he much prefers to let the audience choose the topics, and for all questions to be kept a secret from him until the lecture is actually in progress. (He believes that people often learn more from answers that are spontaneously fumbled than from responses that are carefully preplanned.) Questions related to constraints will naturally be quite welcome, but questions on any subject whatsoever will not be ducked! He'll try to answer them all as best he can, without spending a great deal of time on any one topic, unless there is special interest to go into more depth. Meanwhile he hopes to have drafted some notes for circulation before the conference begins, in case some attendees might wish to focus some of their questions on expository material related to his forthcoming book, either during this session or informally afterwards. Warning: His least favorite questions have the form "What is your favorite X?" If you want to ask such questions, please try to do it cleverly so that he doesn't have to choose between different things that he loves in different ways.

How to download the current draft of Section 7.2.2.3?

You may have a look at the current draft at http://cs.stanford.edu/~knuth/fasc7a.ps.gz. Please note that this draft will hopefully be extended by a dozen or more pages by the time CP begins (the same link will be used). Don also points out that a reward of $2.56 per bug detected will be given to first responders, plus 32 cents per excellent suggestion for improvement.

How to ask questions?

If you wish to ask a question, please send it by e-mail to christine.solnon@insa-lyon.fr before July 31, 2022.

ABSTRACT. Constraint programming has proven to be a successful framework for determining whether a given instance of the three-dimensional stable matching problem with cyclic preferences (3DSM-CYC) admits a solution. If such an instance is satisfiable, constraint models can even compute its optimal solution for several different objective functions. On the other hand, the only existing output for unsatisfiable 3DSM-CYC instances is a simple declaration of impossibility.

In this paper, we explore four ways to adapt constraint models designed for 3DSM-CYC to the maximum relaxation version of the problem, that is, the computation of the smallest part of an instance whose modification leads to satisfiability. We also extend our models to support the presence of costs on elements in the instance, and to return the relaxation with lowest total cost for each of the four types of relaxation. Empirical results reveal that our relaxation models are efficient, as in most cases, they show little overhead compared to the satisfaction version.

ABSTRACT. Research in constraint programming typically focuses on problem solving efficiency. However, the way users conceptualise problems and communicate with constraint programming tools is often sidelined. How humans think about constraint problems can be important for the development of efficient tools that are useful to a broader audience. For example, a system incorporating knowledge on how people think about constraint problems can provide explanations to users and improve the communication between the human and the solver.

We present an initial step towards better understanding of the human side of the constraint solving process. To our knowledge, this is the first human-centred study addressing how people approach constraint modelling and solving. We observed three sets of ten users each (constraint programmers, computer scientists and non-computer scientists) and analysed how they find solutions for well-known constraint problems. We found regularities offering clues about how to design systems that are more intelligible to humans.

ABSTRACT. In real applications, typically, there is a lack of information about the uncertainty/dynamismassociated with them. An effort has been done in the literature for finding robust solutions for their associated Constraint Satisfaction Problems (CSPs). Here, we analyze a previous exact/complete approach from the state-of-the-art that focuses on CSPs with ordered domains and dynamic bounds. However, this approach has low performance in large-scale CSPs. For this reason, in this paper, we present an inexact/incomplete approach that is faster at finding robust solutions for large-scale CSPs. This is specially handy when the computation time available for finding a solution is limited and/or a new solution must be re-computed on-line (because the original one is lost due to the dynamism). Specifically, we present a Large Neighbourhood Search (LNS) algorithm combined with Constraint Programming(CP) and Branch-and-bound (B&B) that searches for robust solutions. Furthermore, we also present a robust-value selection heuristic that guides the search towards more promising branches. We evaluate our approach with large-scale CSPs instances. Including the case study of scheduling problems. The evaluation shows a considerable improvement in the robustness of the solutions achieved by our algorithm for large-scale CSPs.

ABSTRACT. Modern electrical power utilities must maintain their electrical equipment and replace them as they reach the end of their useful life. The Transmission Maintenance Scheduling (TMS) problem consists in generating an annual maintenance plan for electric power transportation equipment while maintaining the stability of the network and ensuring a continuous power flow for customers. Each year, a list of equipment that needs to be maintained or replaced is available and the goal is to generate an optimal maintenance plan. This paper proposes a constraint-based scheduling approach to solve the TMS problem. The model considers two types of constraints: (1) constraints that can be naturally formalized inside a constraint programming model, and (2) complex constraints that do not have a proper formalization from the field specialists. The latter cannot be integrated inside the model due to their complexity. Their satisfaction is thus verified by a black box tool, which is a simulator mimicking the impact of a maintenance schedule on the real power network. The simulator is based on complex differential power-flow equations. Experiments are carried out at five strategic points of Hydro-Québec power grid infrastructure, which involves more than 200 electrical equipment and 300 withdrawal requests. Results show that our model is able to comply with most of the formalized and unformalized constraints. It also generates maintenance schedules within an execution time of few minutes. The generated schedules are similar to the ones proposed by a field specialist and can be used to simulate maintenance programs for the next 10 years.

ABSTRACT. The Single-Row Facility Layout Problem is an NP-hard problem dealing with the ordering of departments with given lengths and pairwise traffic intensities in a facility. In this context, one seeks to minimize the sum of the distances between department pairs, weighted by the corresponding traffic intensities. Practical applications of this problem include the arrangement of rooms on a corridor in hospitals or offices, airplanes and gates in an airport or machines in a manufacture. This paper presents two novel exact models for the Constrained Single-Row Facility Layout Problem, a recent variant of the problem including positioning, ordering and adjacency constraints. On the one hand, the state-of-the-art mixed-integer programming model for the unconstrained problem is extended to incorporate the constraints. On the other hand, a decision diagram-based approach is described, based on an existing dynamic programming model for the unconstrained problem. Computational experiments show that both models outperform the only mixed-integer programming model in the literature, to the best of our knowledge. While the two models have execution times of the same order of magnitude, the decision diagram-based approach handles positioning constraints much better but the mixed-integer programming model has the advantage for ordering constraints.

ABSTRACT. Modern-day factories of the agricultural industry need to produce and distribute large amounts of compound feed to handle the daily demands of livestock farming. As a highly-automated production process is utilized to fulfill the large-scale requirements in this domain, finding efficient machine schedules is a challenging task which requires the consideration of complex constraints and the execution of optional cleaning jobs to prevent a contamination of the final products. Furthermore, it is critical to minimize job tardiness in the schedule, since the truck routes which are used to distribute the products to customers are sensitive to delays. Thus, there is a strong need for efficient automated methods which are able to produce optimized schedules in this domain.

This paper formally introduces a novel real-life problem in this area and investigates constraint-modeling techniques as well as a metaheuristic approach to efficiently solve practical scenarios. In particular, we investigate two innovative constraint programming model variants as well as an integer programming formulation to model the contamination constraints which require an efficient utilization of variables with a real valued domain. To tackle large-scale instances, we additionally provide a local search approach based on simulated annealing that utilizes problem-specific neighborhood operators.

We provide a set of new real-life problem instances that we use in an extensive experimental evaluation of all proposed approaches. Computational results show that our models can be successfully used together with state-of-the-art constraint solvers to provide several optimal results as well as high-quality bounds for many real-life instances. Additionally, the proposed metaheuristic approach could reach many optimal results and delivers the best upper bounds on many of the large practical instances in our experiments.

ABSTRACT. Decision diagrams are an increasingly important tool in cutting-edge solvers for discrete optimization. However, the field of decision diagrams is relatively new, and is still incorporating the library of techniques that conventional solvers have had decades to build. We drew inspiration from the warm-start technique used in conventional solvers to address one of the major challenges faced by decision diagram based methods. Decision diagrams become more useful the wider they are allowed to be, but also become more costly to generate, especially with large numbers of variables. We present a method of peeling off a sub-graph of previously constructed diagrams and using it as the initial diagram for subsequent iterations that we call peel-and-bound. We test the method on the sequence ordering problem, and our results indicate that our peel-and-bound scheme generates stronger bounds than a branch-and-bound scheme using the same propagators, and at significantly less computational cost.

ABSTRACT. Dominance breaking is an effective technique to reduce the time for solving constraint optimization problems. Lee and Zhong propose an automated dominance breaking framework for a class of constraint optimization problems based on specific forms of objectives and constraints. In this paper, we propose to enhance the framework for problems with nested function calls which can be flattened to functional constraints. In particular, we focus on aggregation functions and exploit such properties as monotonicity, commutativity and associativity to give an efficient procedure for generating effective dominance breaking nogoods. Experimentation also shows orders-of-magnitude runtime speedup using the generated dominance breaking nogoods and demonstrates the ability to discover new dominance relations on problems with ineffective or no known dominance breaking constraints in the literature.