Replicable parallel branch and bound search

Combinatorial branch and bound searches are a common technique for solving global optimisation and decision problems. Their performance often depends on good search order heuristics, refined over decades of algorithms research. Parallel search necessarily deviates from the sequential search order, sometimes dramatically and unpredictably, e.g. by distributing work at random. This can disrupt effective search order heuristics and lead to unexpected and highly variable parallel performance. The variability makes it hard to reason about the parallel performance of combinatorial searches. This paper presents a generic parallel branch and bound skeleton, implemented in Haskell, with replicable parallel performance. The skeleton aims to preserve the search order heuristic by distributing work in an ordered fashion, closely following the sequential search order. We demonstrate the generality of the approach by applying the skeleton to 40 instances of three combinatorial problems: Maximum Clique, 0/1 Knapsack and Travelling Salesperson. The overheads of our Haskell skeleton are reasonable: giving slowdown factors of between 1.9 and 6.2 compared with a class-leading, dedicated, and highly optimised C++ Maximum Clique solver. We demonstrate scaling up to 200 cores of a Beowulf cluster, achieving speedups of 100x for several Maximum Clique instances. We demonstrate low variance of parallel performance across all instances of the three combinatorial problems and at all scales up to 200 cores, with median Relative Standard Deviation (RSD) below 2%. Parallel solvers that do not follow the sequential search order exhibit far higher variance, with median RSD exceeding 85% for Knapsack

Generation of the exact Pareto set in multi-objective traveling salesman and set covering problems

The calculation of the exact set in Multi-Objective Combinatorial Optimization (MOCO) problems is one of the most computationally demanding tasks as most of the problems are NP-hard. In the present work we use AUGMECON2 a Multi-Objective Mathematical Programming (MOMP) method which is capable of generating the exact Pareto set in Multi-Objective Integer Programming (MOIP) problems for producing all the Pareto optimal solutions in two popular MOCO problems: The Multi-Objective Traveling Salesman Problem (MOTSP) and the Multi-Objective Set Covering problem (MOSCP). The computational experiment is confined to two-objective problems that are found in the literature. The performance of the algorithm is slightly better to what is already found from previous works and it goes one step further generating the exact Pareto set to till now unsolved problems. The results are provided in a dedicated site and can be useful for benchmarking with other MOMP methods or even Multi-Objective Meta-Heuristics (MOMH) that can check the performance of their approximate solution against the exact solution in MOTSP and MOSCP problems

Generation of the exact Pareto set in multi-objective traveling salesman and set covering problems

The calculation of the exact set in Multi-Objective Combinatorial Optimization (MOCO) problems is one of the most computationally demanding tasks as most of the problems are NP-hard. In the present work we use AUGMECON2 a Multi-Objective Mathematical Programming (MOMP) method which is capable of generating the exact Pareto set in Multi-Objective Integer Programming (MOIP) problems for producing all the Pareto optimal solutions in two popular MOCO problems: The Multi-Objective Traveling Salesman Problem (MOTSP) and the Multi-Objective Set Covering problem (MOSCP). The computational experiment is confined to two-objective problems that are found in the literature. The performance of the algorithm is slightly better to what is already found from previous works and it goes one step further generating the exact Pareto set to till now unsolved problems. The results are provided in a dedicated site and can be useful for benchmarking with other MOMP methods or even Multi-Objective Meta-Heuristics (MOMH) that can check the performance of their approximate solution against the exact solution in MOTSP and MOSCP problems

Recent Advances on GPU Computing in Operations Research

Abstract-In the last decade, Graphics Processing Units (GPUs) have gained an increasing popularity as accelerators for High Performance Computing (HPC) applications. Recent GPUs are not only powerful graphics engines but also highly threaded parallel computing processors that can achieve sustainable speedup as compared with CPUs. In this context, researchers try to exploit the capability of this architecture to solve difficult problems in many domains in science and engineering. In this article, we present recent advances on GPU Computing in Operations Research. We focus in particular on Integer Programming and Linear Programming

Recent Advances on GPU Computing in Operations Research

In the last decade, Graphics Processing Units (GPUs) have gained an increasing popularity as accelerators for High Performance Computing (HPC) applications. Recent GPUs are not only powerful graphics engines but also highly threaded parallel computing processors that can achieve sustainable speedup as compared with CPUs. In this context, researchers try to exploit the capability of this architecture to solve difficult problems in many domains in science and engineering. In this article, we present recent advances on GPU Computing in Operations Research. We focus in particular on Integer Programming and Linear Programming

Improved Peel-and-Bound: Methods for Generating Dual Bounds with Multivalued Decision Diagrams

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. In the original version of this paper, we presented 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 tested 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. In this extended version of the paper, we also propose new methods for using relaxed decision diagrams to improve the solutions found using restricted decision diagrams, discuss the heuristic decisions involved with the parallelization of peel-and-bound, and discuss how peel-and-bound can be hyper-optimized for sequencing problems. Furthermore, we test the new methods on the sequence ordering problem and the traveling salesman problem with time-windows (TSPTW), and include an updated and generalized implementation of the algorithm capable of handling any discrete optimization problem. The new results show that peel-and-bound outperforms ddo (a decision diagram based branch-and-bound solver) on the TSPTW. We also close 15 open benchmark instances of the TSPTW.Comment: 50 pages, 31 figures, published by JAIR, supplementary materials at https://github.com/IsaacRudich/ImprovedPnB. arXiv admin note: substantial text overlap with arXiv:2205.0521

An efficient evolutionary algorithm for the orienteering problem

This paper deals with the Orienteering Problem, which is a routing problem. In the Orienteering Problem, each node has a profit assigned and the goal is to find the route that maximizes the total collected profit subject to a limitation on the total route distance. To solve this problem, we propose an evolutionary algorithm, whose key characteristic is to maintain unfeasible solutions during the search. Furthermore, it includes a novel solution codification for the Orienteering Problem, a novel heuristic for node inclusion in the route, an adaptation of the Edge Recombination crossover developed for the Travelling Salesperson Problem, specific operators to recover the feasibility of solutions when required, and the use of the Lin-Kernighan heuristic to improve the route lengths. We compare our algorithm with three state-of-the-art algorithms for the problem on 344 benchmark instances, with up to 7397 nodes. The results show a competitive behavior of our approach in instances of low-medium dimensionality, and outstanding results in the large dimensionality instances reaching new best known solutions with lower computational time than the state-of-the-art algorithms.MTM2015-65317-P, TIN2016-78365-R, IT-609-13, IT-928-16, UFI BETS 201