Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature

Finding regions of local repair in hierarchical constraint satisfaction

Algorithms for solving constraint satisfaction problems (CSP) have been successfully applied to several fields including scheduling, design, and planning. Latest extensions of the standard CSP to constraint optimization problems (COP) additionally provided new opportunities for solving several problems of combinatorial optimization more efficiently. Basically, two classes of algorithms have been used for searching constraint satisfaction problems (CSP): local search methods and systematic tree search extended by the classical constraint-processing techniques like e.g. forward checking and backmarking. Both classes exhibit characteristic advantages and drawbacks. This report presents a novel approach for solving constraint optimization problems that combines the advantages of local search and tree search algorithms which have been extended by constraint-processing techniques. This method proved applicability in a commercial nurse scheduling system as well as on randomly generated problems

Robustness and stability in dynamic constraint satisfaction problems

Constraint programming is a paradigm wherein relations between variables are stated in the form of constraints. It is well-known that many real life problems can be modeled as Constraint Satisfaction Problems (CSPs). Much effort has been spent to increase the efficiency of algorithms for solving CSPs. However, many of these techniques assume that the set of variables, domains and constraints involved in the CSP are known and fixed when the problem is modeled. This is a strong limitation because many problems come from uncertain and dynamic environments, where both the original problem may evolve because of the environment, the user or other agents. In such situations, a solution that holds for the original problem can become invalid after changes. There are two main approaches for dealing with these situations: reactive and proactive approaches. Using reactive approaches entails re-solving the CSP after each solution loss, which is a time consuming. That is a clear disadvantage, especially when we deal with short-term changes, where solution loss is frequent. In addition, in many applications, such as on-line planning and scheduling, the delivery time of a new solution may be too long for actions to be taken on time, so a solution loss can produce several negative effects in the modeled problem. For a task assignment production system with several machines, it could cause the shutdown of the production system, the breakage of machines, the loss of the material/object in production, etc. In a transport timetabling problem, the solution loss, due to some disruption at a point, may produce a delay that propagates through the entire schedule. In addition, all the negative effects stated above will probably entail an economic loss. In this thesis we develop several proactive approaches. Proactive approaches use knowledge about possible future changes in order to avoid or minimize their effects. These approaches are applied before the changes occur. Thus, our approaches search for robust solutions, which have a high probability to remain valid after changes. Furthermore, some of our approaches also consider that the solutions can be easily adapted when they did not resist the changes in the original problem. Thus, these approaches search for stable solutions, which have an alternative solution that is similar to the previous one and therefore can be used in case of a value breakage. In this context, sometimes there exists knowledge about the uncertain and dynamic environment. However in many cases, this information is unknown or hard to obtain. For this reason, for the majority of our approaches (specifically 3 of the 4 developed approaches), the only assumptions made about changes are those inherent in the structure of problems with ordered domains. Given this framework and therefore the existence of a significant order over domain values, it is reasonable to assume that the original bounds of the solution space may undergo restrictive or relaxed modifications. Note that the possibility of solution loss only exists when changes over the original bounds of the solution space are restrictive. Therefore, the main objective for searching robust solutions in this framework is to find solutions located as far away as possible from the bounds of the solution space. In order to meet this criterion, we propose several approaches that can be divided in enumeration-based techniques and a search algorithm.Climent Aunés, LI. (2013). Robustness and stability in dynamic constraint satisfaction problems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34785TESI

Choice functions for autonomous search in constraint programming: GA vs. PSO

Heurističke metode nizanja vrijednosti i varijabli su ključni element u ograničenom programiranju. Poznate su kao strategija nabrajanja i mogu značajno utjecati na postupak rješavanja problema. Međutim, prilično je teško izabrati odgovarajući heuristički postupak jer je komplicirano predvidjeti njihovo ponašanje. U zadnje je vrijeme za tu svrhu predloženo samostalno (autonomno) pretraživanje. Ideja je da se strategije koje su se pokazale lošima tijekom postupka rješavanja dinamički zamijene onima koje više obećavaju. Ta se zamjena izvodi korištenjem funkcije izbora, koja u zadanom vremenu procijenjuje ponuđenu strategiju preko indikatora kvalitete. Važnu ulogu u tom procesu ima optimizator kojemu je cilj fino podešavanje funkcije izbora kako bi se garantirala precizna procjena strategija. U ovom radu evaluiramo karakteristike dviju jakih funkcija izbora: prvu podržava genetski algoritam, a drugu optimizator roja čestica. Dajemo interesantne rezultate i demonstriramo mogućnost korištenja tih metoda optimiziranja za samostalno pretraživanje u kontekstu ograničenog programiranja.The variable and value ordering heuristics are a key element in Constraint Programming. Known together as the enumeration strategy they may have important consequences on the solving process. However, a suitable selection of heuristics is quite hard as their behaviour is complicated to predict. Autonomous search has been recently proposed to handle this concern. The idea is to dynamically replace strategies that exhibit poor performances by more promising ones during the solving process. This replacement is carried out by a choice function, which evaluates a given strategy in a given amount of time via quality indicators. An important phase of this process is performed by an optimizer, which aims at finely tuning the choice function in order to guarantee a precise evaluation of strategies. In this paper we evaluate the performance of two powerful choice functions: the first one supported by a genetic algorithm and the second one by a particle swarm optimizer. We present interesting results and we demonstrate the feasibility of using those optimization techniques for Autonomous Search in a Constraint Programming context

Competent genetic-evolutionary optimization of water distribution systems

A genetic algorithm has been applied to the optimal design and rehabilitation of a water distribution system. Many of the previous applications have been limited to small water distribution systems, where the computer time used for solving the problem has been relatively small. In order to apply genetic and evolutionary optimization technique to a large-scale water distribution system, this paper employs one of competent genetic-evolutionary algorithms - a messy genetic algorithm to enhance the efficiency of an optimization procedure. A maximum flexibility is ensured by the formulation of a string and solution representation scheme, a fitness definition, and the integration of a well-developed hydraulic network solver that facilitate the application of a genetic algorithm to the optimization of a water distribution system. Two benchmark problems of water pipeline design and a real water distribution system are presented to demonstrate the application of the improved technique. The results obtained show that the number of the design trials required by the messy genetic algorithm is consistently fewer than the other genetic algorithms

An Overview of Backtrack Search Satisfiability Algorithms

Propositional Satisfiability (SAT) is often used as the underlying model for a significan