Alejandro Arbelaez

A GPU Implementation of Parallel Constraint-Based Local Search

In this paper we study the performance of constraint-based local search solvers on a GPU. The massively parallel architecture of the GPU makes it possible to explore parallelism at two different levels inside the local search algorithm. First, by executing multiple copies of the algorithm in a multi-walk manner and, second, by evaluating large neighborhoods in parallel in a single-walk manner. Experiments on three well-known problem benchmarks indicate that the current GPU implementation is up to 17 times faster than a well-tuned sequential algorithm implemented on a desktop computer.

From sequential to parallel local search for SAT

In the domain of propositional Satisfiability Problem (SAT), parallel portfolio-based algorithms have become a standard methodology for both complete and incomplete solvers. In this methodology several algorithms explore the search space in parallel, either independently or cooperatively with some communication between the solvers. We conducted a study of the scalability of several SAT solvers in different application domains (crafted, verification, quasigroups and random instances) when drastically increasing the number of cores in the portfolio, up to 512 cores. Our experiments show that on different problem families the behaviors of different solvers vary greatly. We present an empirical study that suggests that the best sequential solver is not necessary the one with the overall best parallel speedup.

A Constraint-Based Local Search for Edge Disjoint Rooted Distance-Constrained Minimum Spanning Tree Problem

Many network design problems arising in areas as diverse as VLSI circuit design, QoS routing, traffic engineering, and computational sustainability require clients to be connected to a facility under path-length constraints and budget limits. These problems can be modelled as Rooted Distance-Constrained Minimum Spanning-Tree Problem (RDCMST), which is NP-hard. An inherent feature of these networks is that they are vulnerable to a failure. Therefore, it is often important to ensure that all clients are connected to two or more facilities via edge-disjoint paths. We call this problem the Edge-disjoint RDCMST (ERDCMST). Previous works on RDCMST have focused on dedicated algorithms which are hard to extend with side constraints, and therefore these algorithms cannot be extended for solving ERDCMST. We present a constraint-based local search algorithm for which we present two efficient local move operators and an incremental way of maintaining objective function. Our local search algorithm can easily be extended and it is able to solve both problems. The effectiveness of our approach is demonstrated by experimenting with a set of problem instances taken from real-world passive optical network deployments in Ireland, the UK, and Italy. We compare our approach with existing exact and heuristic approaches. Results show that our approach is superior to both of the latter in terms of scalability and its anytime behaviour.

Constraint-Based Local Search for the Distance- and Capacity-Bounded Network Design Problem

Many network design problems arising in the fields of transportation, distribution and logistics require clients to be connected to facilities through a set of carriers subject to distance and capacity constraints. Here a carrier could be a cable, vehicle, salesman etc. The distance from a facility to client using a carrier could be expressed as signal loss, time spent, path length, etc. The capacity of a carrier could be interpreted as the maximum number of commodities that a carrier can carry, the maximum number of clients or links that a single carrier can visit, etc. The main decisions are to determine the number of carriers, assign clients to carriers, and design a network for each carrier subject to distance, capacity and some side constraints. In this paper, we focus on the Cable Routing Problem (CRP), which is NP-hard. We present a constraint-based local search algorithm and two efficient local move operators. The effectiveness of our approach is demonstrated by experimenting with 300 instances of the CRP taken from real-world passive optical network deployments in Ireland. The results show that our algorithm can scale to very large problem instances and it can compute good quality solutions in a very limited time.

Using sequential runtime distributions for the parallel speedup prediction of SAT local search

This paper presents a detailed analysis of the scalability and parallelization of local search algorithms for the Satisfiability problem. We propose a framework to estimate the parallel performance of a given algorithm by analyzing the runtime behavior of its sequential version. Indeed, by approximating the runtime distribution of the sequential process with statistical methods, the runtime behavior of the parallel process can be predicted by a model based on order statistics. We apply this approach to study the parallel performance of two SAT local search solvers, namely Sparrow and CCASAT, and compare the predicted performances to the results of an actual experimentation on parallel hardware up to 384 cores. We show that the model is accurate and predicts performance close to the empirical data. Moreover, as we study different types of instances (random and crafted), we observe that the local search solvers exhibit different behaviors and that their runtime distributions can be approximated by two types of distributions: exponential (shifted and non-shifted) and lognormal.

Massively Parallel Local Search for SAT

Parallel portfolio-based algorithms have become a standard methodology for both complete and incomplete solvers for SAT solving. In this methodology several algorithms explore the search space in parallel, either independently or cooperatively with some communication between the solvers. Unlike previous work where parallel algorithms are limited to few cores (usually up to 16 cores), this work studies the performance of parallel local search for SAT with a large degree of parallelism, up to 256 cores, and compares various cooperation strategies. The strategy with the best performance consists in considering small groups of solvers (e.g. 4 or 8) sharing information and performing no inter-group communication.

Learning Sequential and Parallel Runtime Distributions for Randomized Algorithms

In cloud systems, computation time can be rented by the hour and for a given number of processors. Thus, accurate predictions of the behaviour of both sequential and parallel algorithms has become an important issue, in particular in the case of costly methods such as randomized combinatorial optimization tools. In this work, our objective is to use machine learning to predict performance of sequential and parallel local search algorithms. In addition to classical features of the instances used by other machine learning tools, we consider data on the sequential runtime distributions of a local search method. This allows us to predict with a high accuracy the parallel computation time of a large class of instances, by learning the behaviour of the sequential version of the algorithm on a small number of instances. Experiments with three solvers on SAT and TSP instances indicate that our method works well, with a correlation coefficient of up to 0.85 for SAT instances and up to 0.95 for TSP instances.

Constraint-Based Local Search for Finding Node-Disjoint Bounded-Paths in Optical Access Networks

Mass deployment of fibre access networks is without doubt one of the goals of many network operators around the globe. The Passive Optical Network has been proposed as a solution to help deliver mass deployment of fibre-to-the-home FTTH, by reducing the cost per customer compared to current commercially available technologies. A major failure in the access network e.g., fibre cut, amplifier failure, or other equipment can fail might affect tens of thousands of customers. Therefore, protecting the network from such failures is one of the most important requirements in the deployment of FTTH solutions. In this paper we use a constraint-based local search approach to design reliable passive optical networks via node-disjoint paths whereby each customer is protected against any one node or link failure. We experiment with a set of very large size real-world networks corresponding to Ireland, Italy and the UK and demonstrate the tradeoff between cost and resiliency.

A constraint-based parallel local search for the edge-disjoint rooted distance-constrained minimum spanning tree problem

Many network design problems arising in areas as diverse as VLSI circuit design, QoS routing, traffic engineering, and computational sustainability require clients to be connected to a facility under path-length constraints and budget limits. These problems can be seen as instances of the rooted distance-constrained minimum spanning-tree problem (RDCMST), which is NP-hard. An inherent feature of these networks is that they are vulnerable to a failure. Therefore, it is often important to ensure that all clients are connected to two or more facilities via edge-disjoint paths. We call this problem the edge-disjoint RDCMST (ERDCMST). Previous work on the RDCMST has focused on dedicated algorithms and therefore it is difficult to use these algorithms to tackle the ERDCMST. We present a constraint-based parallel local search algorithm for solving the ERDCMST. Traditional ways of extending a sequential algorithm to run in parallel perform either portfolio-based search in parallel or parallel neighbourhood search. Instead, we exploit the semantics of the constraints of the problem to perform multiple moves in parallel by ensuring that they are mutually independent. The ideas presented in this paper are general and can be adapted to other problems as well. The effectiveness of our approach is demonstrated by experimenting with a set of problem instances taken from real-world passive optical network deployments in Ireland, Italy, and the UK. Our results show that performing moves in parallel can significantly reduce the elapsed time and improve the quality of the solutions of our local search approach.

Constraint Programming and Machine Learning for Interactive Soccer Analysis

A soccer competition consists of n teams playing against each other in a league or tournament system, according to a single or double round-robin schedule. These competitions offer an excellent opportunity to model interesting problems related to questions that soccer fans frequently ask about their favourite teams. For instance, at some stage of the competition, fans might be interested in determining whether a given team still has chances of winning the competition (i.e., finishing first in a league or being within the first k teams in a tournament to qualify to the playoff). This problem relates to the elimination problem, which is NP-complete for the actual FIFA pointing rule system (0, 1, 3), zero point to a loss, one point to a tie, and three points to a win. In this paper, we combine constraint programming with machine learning to model a general soccer scenario in a real-time application.