Distributed Domain Propagation

This is the final version. Available on open access from the publisher via the DOI in this record16th International Symposium on Experimental Algorithms (SEA 2017), 21-23 June 2017, London, UKPortfolio parallelization is an approach that runs several solver instances in parallel and terminates when one of them succeeds in solving the problem. Despite it’s simplicity portfolio parallelization has been shown to perform well for modern mixed-integer programming (MIP) and boolean satisfiability problem (SAT) solvers. Domain propagation has also been shown to be a simple technique in modern MIP and SAT solvers that effectively finds additional domain reductions after a variables domain has been reduced. This paper investigates the impact of distributed domain propagation in modern MIP solvers that employ portfolio parallelization. Computational experiments were conducted for two implementations of this parallelization approach. While both share global variable bounds and solutions they communicate differently. In one implementation the communication is performed only at designated points in the solving process and in the other it is performed completely asynchronously. Computational experiments show a positive performance impact of communicating global variable bounds and provide valuable insights in communication strategies for parallel solvers.German Federal Ministry of Education and Researc

Evaluating and Tuning n-fold Integer Programming

In recent years, algorithmic breakthroughs in stringology, computational social choice, scheduling, etc., were achieved by applying the theory of so-called n-fold integer programming. An n-fold integer program (IP) has a highly uniform block structured constraint matrix. Hemmecke, Onn, and Romanchuk [Math. Programming, 2013] showed an algorithm with runtime a^{O(rst + r^2s)} n^3, where a is the largest coefficient, r,s, and t are dimensions of blocks of the constraint matrix and n is the total dimension of the IP; thus, an algorithm efficient if the blocks are of small size and with small coefficients. The algorithm works by iteratively improving a feasible solution with augmenting steps, and n-fold IPs have the special property that augmenting steps are guaranteed to exist in a not-too-large neighborhood. However, this algorithm has never been implemented and evaluated. We have implemented the algorithm and learned the following along the way. The original algorithm is practically unusable, but we discover a series of improvements which make its evaluation possible. Crucially, we observe that a certain constant in the algorithm can be treated as a tuning parameter, which yields an efficient heuristic (essentially searching in a smaller-than-guaranteed neighborhood). Furthermore, the algorithm uses an overly expensive strategy to find a "best" step, while finding only an "approximatelly best" step is much cheaper, yet sufficient for quick convergence. Using this insight, we improve the asymptotic dependence on n from n^3 to n^2 log n which yields the currently asymptotically fastest algorithm for n-fold IP. Finally, we tested the behavior of the algorithm with various values of the tuning parameter and different strategies of finding improving steps. First, we show that decreasing the tuning parameter initially leads to an increased number of iterations needed for convergence and eventually to getting stuck in local optima, as expected. However, surprisingly small values of the parameter already exhibit good behavior. Second, our new strategy for finding "approximatelly best" steps wildly outperforms the original construction

Combining hybrid genetic search with ruin-and-recreate for solving the capacitated vehicle routing problem

The Capacitated Vehicle Routing Problem (CVRP) has been subject to intense research efforts for more than sixty years. Yet, significant algorithmic improvements are still being made. The most competitive heuristic solution algorithms of today utilize, and often combine, strategies and elements from evolutionary algorithms, local search, and ruin-and-recreate based large neighborhood search. In this paper we propose a new hybrid metaheuristic for the CVRP, where the education phase of the hybrid genetic search (HGS) algorithm proposed by (Vidal Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhood 2020) is extended by applying large neighborhood search (LNS). By performing a series of computational experiments, we attempt to answer the following research questions: 1) Is it possible to gain performance by adding LNS as a component in the education phase of HGS? 2) How does the addition of LNS change the relative importance of the local search neighborhoods of HGS? 3) What is the effect of devoting computational efforts to the creation of an elite solution in the initial population of HGS? Through a set of computational experiments we answer these research questions, while at the same time obtaining a good configuration of global parameter settings for the proposed heuristic. Testing the heuristic on benchmark instances from the literature with limited computing time, it outperforms existing algorithms, both in terms of the final gap and the primal integral.publishedVersio

Routing Arena: A Benchmark Suite for Neural Routing Solvers

Neural Combinatorial Optimization has been researched actively in the last eight years. Even though many of the proposed Machine Learning based approaches are compared on the same datasets, the evaluation protocol exhibits essential flaws and the selection of baselines often neglects State-of-the-Art Operations Research approaches. To improve on both of these shortcomings, we propose the Routing Arena, a benchmark suite for Routing Problems that provides a seamless integration of consistent evaluation and the provision of baselines and benchmarks prevalent in the Machine Learning- and Operations Research field. The proposed evaluation protocol considers the two most important evaluation cases for different applications: First, the solution quality for an a priori fixed time budget and secondly the anytime performance of the respective methods. By setting the solution trajectory in perspective to a Best Known Solution and a Base Solver's solutions trajectory, we furthermore propose the Weighted Relative Average Performance (WRAP), a novel evaluation metric that quantifies the often claimed runtime efficiency of Neural Routing Solvers. A comprehensive first experimental evaluation demonstrates that the most recent Operations Research solvers generate state-of-the-art results in terms of solution quality and runtime efficiency when it comes to the vehicle routing problem. Nevertheless, some findings highlight the advantages of neural approaches and motivate a shift in how neural solvers should be conceptualized

The effect of different mathematical formulations on a matheuristic algorithm for the production routing problem

We perform an experimental study to evaluate the performance of a matheuristic for the production routing problem (PRP). First, we develop a basic matheuristic that prescribes starting from a partial initial solution, completing it using a sequence of constructive heuristics, and improving it using a general-purpose mixed-integer programming heuristic. Next, we investigate the effect of three state-of-the-art mathematical formulations on the proposed matheuristic convergence. The formulations are implemented and tested with and without the use of valid inequalities. In addition, by suggesting different techniques to generate a feasible starting solution for our matheuristic, we assess the contribution of an initial solution to the matheuristic’s overall performance. We conduct extensive computational experiments on benchmark data instances for the PRP. The results show that a proper choice of an embedded mathematical formulation depends on the data instances’ features, such as the number of customers and the length of the planning horizon. The comparisons undertaken in this study indicate that having a better initial solution does not necessarily lead to finding a better final solution.publishe