Portfolio Approaches in Constraint Programming

Recent research has shown that the performance of a single, arbitrarily efficient algorithm can be significantly outperformed by using a portfolio of —possibly on-average slower— algorithms. Within the Constraint Programming (CP) context, a portfolio solver can be seen as a particular constraint solver that exploits the synergy between the constituent solvers of its portfolio for predicting which is (or which are) the best solver(s) to run for solving a new, unseen instance. In this thesis we examine the benefits of portfolio solvers in CP. Despite portfolio approaches have been extensively studied for Boolean Satisfiability (SAT) problems, in the more general CP field these techniques have been only marginally studied and used. We conducted this work through the investigation, the analysis and the construction of several portfolio approaches for solving both satisfaction and optimization problems. We focused in particular on sequential approaches, i.e., single-threaded portfolio solvers always running on the same core. We started from a first empirical evaluation on portfolio approaches for solving Constraint Satisfaction Problems (CSPs), and then we improved on it by introducing new data, solvers, features, algorithms, and tools. Afterwards, we addressed the more general Constraint Optimization Problems (COPs) by implementing and testing a number of models for dealing with COP portfolio solvers. Finally, we have come full circle by developing sunny-cp: a sequential CP portfolio solver that turned out to be competitive also in the MiniZinc Challenge, the reference competition for CP solvers.

Hybrid constraint programming and metaheuristic methods for large scale optimization problems

This work presents hybrid Constraint Programming (CP) and metaheuristic methods for the solution of Large Scale Optimization Problems; it aims at integrating concepts and mechanisms from the metaheuristic methods to a CP-based tree search environment in order to exploit the advantages of both approaches. The modeling and solution of large scale combinatorial optimization problem is a topic which has arisen the interest of many researcherers in the Operations Research field; combinatorial optimization problems are widely spread in everyday life and the need of solving difficult problems is more and more urgent. Metaheuristic techniques have been developed in the last decades to effectively handle the approximate solution of combinatorial optimization problems; we will examine metaheuristics in detail, focusing on the common aspects of different techniques. Each metaheuristic approach possesses its own peculiarities in designing and guiding the solution process; our work aims at recognizing components which can be extracted from metaheuristic methods and re-used in different contexts. In particular we focus on the possibility of porting metaheuristic elements to constraint programming based environments, as constraint programming is able to deal with feasibility issues of optimization problems in a very effective manner. Moreover, CP offers a general paradigm which allows to easily model any type of problem and solve it with a problem-independent framework, differently from local search and metaheuristic methods which are highly problem specific. In this work we describe the implementation of the Local Branching framework, originally developed for Mixed Integer Programming, in a CP-based environment. Constraint programming specific features are used to ease the search process, still mantaining an absolute generality of the approach. We also propose a search strategy called Sliced Neighborhood Search, SNS, that iteratively explores slices of large neighborhoods of an incumbent solution by performing CP-based tree search and encloses concepts from metaheuristic techniques. SNS can be used as a stand alone search strategy, but it can alternatively be embedded in existing strategies as intensification and diversification mechanism. In particular we show its integration within the CP-based local branching. We provide an extensive experimental evaluation of the proposed approaches on instances of the Asymmetric Traveling Salesman Problem and of the Asymmetric Traveling Salesman Problem with Time Windows. The proposed approaches achieve good results on practical size problem, thus demonstrating the benefit of integrating metaheuristic concepts in CP-based frameworks.

Structural analysis of combinatorial optimization problem characteristics and their resolution using hybrid approaches

Many combinatorial problems coming from the real world may not have a clear and well defined structure, typically being dirtied by side constraints, or being composed of two or more sub-problems, usually not disjoint. Such problems are not suitable to be solved with pure approaches based on a single programming paradigm, because a paradigm that can effectively face a problem characteristic may behave inefficiently when facing other characteristics. In these cases, modelling the problem using different programming techniques, trying to ”take the best” from each technique, can produce solvers that largely dominate pure approaches. We demonstrate the effectiveness of hybridization and we discuss about different hybridization techniques by analyzing two classes of problems with particular structures, exploiting Constraint Programming and Integer Linear Programming solving tools and Algorithm Portfolios and Logic Based Benders Decomposition as integration and hybridization frameworks.

Constraint Programming-based Job Dispatching for Modern HPC Applications

A High-Performance Computing job dispatcher is a critical software that assigns the finite computing resources to submitted jobs. This resource assignment over time is known as the on-line job dispatching problem in HPC systems. The fact the problem is on-line means that solutions must be computed in real-time, and their required time cannot exceed some threshold to do not affect the normal system functioning. In addition, a job dispatcher must deal with a lot of uncertainty: submission times, the number of requested resources, and duration of jobs. Heuristic-based techniques have been broadly used in HPC systems, at the cost of achieving (sub-)optimal solutions in a short time. However, the scheduling and resource allocation components are separated, thus generates a decoupled decision that may cause a performance loss. Optimization-based techniques are less used for this problem, although they can significantly improve the performance of HPC systems at the expense of higher computation time. Nowadays, HPC systems are being used for modern applications, such as big data analytics and predictive model building, that employ, in general, many short jobs. However, this information is unknown at dispatching time, and job dispatchers need to process large numbers of them quickly while ensuring high Quality-of-Service (QoS) levels. Constraint Programming (CP) has been shown to be an effective approach to tackle job dispatching problems. However, state-of-the-art CP-based job dispatchers are unable to satisfy the challenges of on-line dispatching, such as generate dispatching decisions in a brief period and integrate current and past information of the housing system. Given the previous reasons, we propose CP-based dispatchers that are more suitable for HPC systems running modern applications, generating on-line dispatching decisions in a proper time and are able to make effective use of job duration predictions to improve QoS levels, especially for workloads dominated by short jobs.

Distributed Large-scale Mixed-Integer Optimization with Application to Energy and Multi-robot Networks

Several decision and control tasks in cyber-physical networks can be formulated as large- scale optimization problems with coupling constraints. In these "constraint-coupled" problems, each agent is associated to a local decision variable, subject to individual constraints. This thesis explores the use of primal decomposition techniques to develop tailored distributed algorithms for this challenging set-up over graphs. We first develop a distributed scheme for convex problems over random time-varying graphs with non-uniform edge probabilities. The approach is then extended to unknown cost functions estimated online. Subsequently, we consider Mixed-Integer Linear Programs (MILPs), which are of great interest in smart grid control and cooperative robotics. We propose a distributed methodological framework to compute a feasible solution to the original MILP, with guaranteed suboptimality bounds, and extend it to general nonconvex problems. Monte Carlo simulations highlight that the approach represents a substantial breakthrough with respect to the state of the art, thus representing a valuable solution for new toolboxes addressing large-scale MILPs. We then propose a distributed Benders decomposition algorithm for asynchronous unreliable networks. The framework has been then used as starting point to develop distributed methodologies for a microgrid optimal control scenario. We develop an ad-hoc distributed strategy for a stochastic set-up with renewable energy sources, and show a case study with samples generated using Generative Adversarial Networks (GANs). We then introduce a software toolbox named ChoiRbot, based on the novel Robot Operating System 2, and show how it facilitates simulations and experiments in distributed multi-robot scenarios. Finally, we consider a Pickup-and-Delivery Vehicle Routing Problem for which we design a distributed method inspired to the approach of general MILPs, and show the efficacy through simulations and experiments in ChoiRbot with ground and aerial robots.