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OREX-J: towards a universal software framework for the experimental analysis of optimization algorithms

OR SPECTRUM 2013年第3期35卷 735-769页

作者： Lang, Jan Christian Widjaja, Thomas Tech Univ Darmstadt Chair Operat Res Dept Law Business & Econ D-64289 Darmstadt Germany Tech Univ Darmstadt Chair Informat Syst Dept Law Business & Econ D-64289 Darmstadt Germany

The Operations Research EXperiment Framework for Java (OREX-J) is an object-oriented software framework that helps users to design, implement and conduct computational experiments for the analysis of optimization algorithms. As it was designed in a generic way using object-oriented programming and design patterns, it is not limited to a specific class of optimization problems and algorithms. The purpose of the framework is to reduce the amount of manual labor required for conducting and evaluating computational experiments: OREX-J provides a generic, extensible data model for storing detailed data on an experimental design and its results. Those data can include algorithm parameters, test instance generator settings, the instances themselves, run-times, algorithm logs, solution properties, etc. All data are automatically saved in a relational database (MySQL, http://***/) by means of the object-relational mapping library Hibernate (http://***/). This simplifies the task of analyzing computational results, as even complex analyses can be performed using comparatively simple Structured Query Language (SQL) queries. Also, OREX-J simplifies the comparison of algorithms developed by different researchers: Instead of integrating other researchers' algorithms into proprietary test beds, researchers could use OREX-J as a common experiment framework. This paper describes the architecture and features of OREX-J and exemplifies its usage in a case study. OREX-J has already been used for experiments in three different areas: algorithms and reformulations for mixed-integer programming models for dynamic lot-sizing with substitutions, a simulation-based optimization approach for a stochastic multi-location inventory control model, and an optimization model for software supplier selection and product portfolio planning.

关键词： Operations research methodology experimental analysis of algorithms Test bed Software framework Object-oriented design Design patterns

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experimental analysis of Dynamic algorithms for the Single Source Shortest Paths Problem

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ACM Journal of experimental Algorithmics 1998年 3卷 5-5页

作者： Frigioni, Daniele loffreda, Mario Nanni, Umberto Pasqualone, Giulio Univ. di Roma “La Sapienza”

In this paper we propose the first experimental study of the fully dynamic single-source shortest-paths problem on directed graphs with positive real edge weights. In particular, we perform an experimental analysis of three different algorithms: Dijkstra's algorithm, and the two output bounded algorithms proposed by Ramalingam and Reps in [30] and by Frigioni, Marchetti-Spaccamela and Nanni in [18], respectively. The main goal of this paper is to provide a first experimental evidence for: (a) the effectiveness of dynamic algorithms for shortest paths with respect to a traditional static approach to this problem;(b) the validity of the theoretical model of output boundedness to analyze dynamic graph algorithms. Beside random generated graphs, useful to capture the “asymptotic” behavior of the algorithms, we also developed experiments by considering a widely used graph from the real world, i.e., the Internet graph. © 1998, ACM. All rights reserved.

关键词： dynamic algorithms experimental analysis of algorithms shortest paths

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EXACT AND APPROXIMATION algorithms FOR SORTING BY REVERSALS, WITH APPLICATION TO GENOME REARRANGEMENT

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ALGORITHMICA 1995年第1-2期13卷 180-210页

作者： KECECIOGLU, J SANKOFF, D UNIV MONTREAL CTR RECH MATHMONTREAL H3C 3J7PQCANADA

Motivated by the problem in computational biology of reconstructing the series of chromosome inversions by which one organism evolved from another, we consider the problem of computing the shortest series of reversals that transform one permutation to another. The permutations describe the order of genes on corresponding chromosomes, and a reversal takes an arbitrary substring of elements, and reverses their order. For this problem, we develop two algorithms: a greedy approximation algorithm, that finds a solution provably close to optimal in O(n(2)) time and O(n) space for n-element permutations, and a branch-and-bound exact algorithm, that finds an optimal solution in O(mL(n, n)) time and O(n(2)) space, where m is the size of the branch-and-bound search tree, and L(n, n) is the time tc, solve a linear program of n variables and n constraints. The greedy algorithm is the first to come within a constant factor of the optimum;it guarantees a solution that uses no more than twice the minimum number of reversals. The lower and upper bounds of the branch-and-bound algorithm are a novel application of maximum-weight matchings, shortest paths, and linear programming. In a series of experiments, we study the performance of an implementation on random permutations, and permutations generated by random reversals. For permutations differing by k random reversals, we find that the average upper bound on reversal distance estimates k to within one reversal for k < 1/2n and n less than or equal to 100. For the difficult case of random permutations, we find that the average difference between the upper and lower bounds is less than three reversals for n less than or equal to 50. Due to the tightness of these bounds, we can solve, to optimality, problems on 30 elements in a few minutes of computer time. This approaches the scale of mitochondrial genomes.

关键词： COMPUTATIONAL BIOLOGY APPROXIMATION algorithms BRANCH-AND-BOUND algorithms experimental analysis of algorithms EDIT DISTANCE PERMUTATIONS SORTING BY REVERSALS CHROMOSOME INVERSIONS GENOME REARRANGEMENTS

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Standardized validation of vehicle routing algorithms

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APPLIED INTELLIGENCE 2024年第2期54卷 1335-1364页

作者： Jastrzab, Tomasz Myller, Michal Tulczyjew, Lukasz Blocho, Miroslaw Kawulok, Michal Czornik, Adam Nalepa, Jakub Silesian Tech Univ Akad 16 PL-44100 Gliwice Poland Blees Spoo Z Starego 27A Gliwice Poland

Designing routing schedules is a pivotal aspect of smart delivery systems. Therefore, the field has been blooming for decades, and numerous algorithms for this task have been proposed for various formulations of rich vehicle routing problems. There is, however, an important gap in the state of the art that concerns the lack of an established and widely-adopted approach toward thorough verification and validation of such algorithms in practical scenarios. We tackle this issue and propose a comprehensive validation approach that can shed more light on functional and non-functional abilities of the solvers. Additionally, we propose novel similarity metrics to measure the distance between the routing schedules that can be used in verifying the convergence abilities of randomized techniques. To reflect practical aspects of intelligent transportation systems, we introduce an algorithm for elaborating solvable benchmark instances for any vehicle routing formulation, alongside the set of quality metrics that help quantify the real-life characteristics of the delivery systems, such as their profitability. The experiments prove the flexibility of our approach through utilizing it to the NP-hard pickup and delivery problem with time windows, and present the qualitative, quantitative, and statistical analysis scenarios which help understand the capabilities of the investigated techniques. We believe that our efforts will be a step toward the more critical and consistent evaluation of emerging vehicle routing (and other) solvers, and will allow the community to easier confront them, thus ultimately focus on the most promising research avenues that are determined in the quantifiable and traceable manner.

关键词： Benchmark Vehicle routing Verification and validation experimental analysis of algorithms

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Probability distribution of solution time in GRASP: An experimental investigation

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JOURNAL OF HEURISTICS 2002年第3期8卷 343-373页

作者： Aiex, RM Resende, MGC Ribeiro, CC Catholic Univ Rio de Janeiro Dept Comp Sci BR-22453900 Rio De Janeiro Brazil AT&T Labs Res Informat Sci Res Ctr Florham Pk NJ 07932 USA

A GRASP (greedy randomized adaptive search procedure) is a multi-start metaheuristic for combinatorial optimization. We study the probability distributions of solution time to a sub-optimal target value in five GRASPs that have appeared in the literature and for which source code is available. The distributions are estimated by running 12,000 independent runs of the heuristic. Standard methodology for graphical analysis is used to compare the empirical and theoretical distributions and estimate the parameters of the distributions. We conclude that the solution time to a sub-optimal target value fits a two-parameter exponential distribution. Hence, it is possible to approximately achieve linear speed-up by implementing GRASP in parallel.

关键词： combinatorial optimization meta-heuristic GRASP experimental analysis of algorithms probability distribution parallel algorithm

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New benchmark instances for the Capacitated Vehicle Routing Problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第3期257卷 845-858页

作者： Uchoa, Eduardo Pecin, Diego Pessoa, Artur Poggi, Marcus Vidal, Thibaut Subramanian, Anand Univ Fed Fluminense Dept Engn Prod Rua Passo da Patria156 Sao DomingosBloco E BR-24210240 Niteroi RJ Brazil Pontificia Univ Catolica Rio de Janeiro Dept Informat Rua Marques Sao Vicente 225 BR-22451900 Rio De Janeiro RJ Brazil Univ Fed Paraiba Ctr Informat Dept Sistemas Comp Rua Escoteiros BR-58058600 Joao Pessoa Paraiba Brazil

The recent research on the CVRP is being slowed down by the lack of a good set of benchmark instances. The existing, sets suffer from at least one of the following drawbacks: (i) became too easy for current algorithms;(ii) are too artificial;(iii) are too homogeneous, not covering the wide range of characteristics found in real applications. We propose a new set of 100 instances ranging from 100 to 1000 customers, designed in order to provide a more comprehensive and balanced experimental setting. Moreover, the same generating scheme was also used to provide an extended benchmark of 600 instances. In addition to having a greater discriminating ability to identify "which algorithm is better", these new benchmarks should also allow for a deeper statistical analysis of the performance of an algorithm. In particular, they will enable one to investigate how the characteristics of an instance affect its performance. We report such an analysis on state-of-the-art exact and heuristic methods. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Routing Benchmark instances experimental analysis of algorithms

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A comparison of sequential Delaunay triangulation algorithms

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COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS 1997年第5-6期7卷 361-385页

作者： Su, P Drysdale, RLS JUSTSYST PITTSBURGH RES CTR PITTSBURGHPA 15213 DARTMOUTH COLL DEPT COMP SCISUDIKOFF LAB 6211HANOVERNH 03755

This paper presents an experimental comparison of a number of different algorithms for computing the Delaunay triangulation. The algorithms examined are: Dwyer's divide and conquer algorithm, Fortune's sweepline algorithm, several versions of the incremental algorithm (including one by Ohya, Iri and Murota, a new bucketing-based algorithm described in this paper, and Devillers's version of a Delaunay-tree based algorithm that appears in LEDA), an algorithm that incrementally adds a correct Delaunay triangle adjacent to a current triangle in a manner similar to gift wrapping algorithms for convex hulls, and Barber's convex hull based algorithm. Most of the algorithms examined are designed for good performance on uniformly distributed sites. However, we also test implementations of these algorithms on a number of non-uniform distributions. The experiments go beyond measuring total running time, which tends to be machine-dependent. We also analyze the major high-level primitives that algorithms use and do an experimental analysis of how often implementations of these algorithms perform each operation. (C) 1997 Elsevier Science B.V.

关键词： Voronoi diagram Delaunay triangulation experimental analysis of algorithms practical algorithms

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Core instances for testing: A case study

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2005年第1期166卷 51-62页

作者： Mastrolilli, M Bianchi, L IDSIA CH-6928 Manno Switzerland

Data generation for computational testing of optimization algorithms is a key topic in experimental algorithmics. Recently, concern has arisen that many published computational experiments are inadequate with respect to the way test instances are generated. In this paper we suggest a new research direction that might be useful to cope with the possible limitations of data generation. The basic idea is to select a finite set of instances which `represent' the whole set of instances. We propose a measure of the representativeness of an instance, which we call e-representativeness: for a minimization problem, an instance x(epsilon) is epsilon-representative of another instance x if a (1 + epsilon)-approximate solution to x can be obtained by solving x(epsilon). Focusing on a strongly NP-hard single machine scheduling problem, we show how to map the infinite set of all instances into a finite set of epsilon-representative core instances. We propose to use this finite set of epsilon-representative core instances to test heuristics. (c) 2004 Elsevier B.V. All rights reserved.

关键词： testing methodology experimental analysis of algorithms approximation algorithms scheduling optimization problems

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Bounds for parametric sequence comparison

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DISCRETE APPLIED MATHEMATICS 2002年第3期118卷 181-198页

作者： Fernández-Baca, D Seppäläinen, T Slutzki, G Iowa State Univ Sci & Technol Dept Comp Sci Ames IA 50011 USA Iowa State Univ Sci & Technol Dept Math Ames IA 50011 USA

We consider the problem of computing a global alignment between two or more sequences subject to varying mismatch and indel penalties. We prove a tight 3(n/2pi)(2/3) + O(n(1/3)log n) bound on the worst-case number of distinct optimum alignments for two sequences of length n as the parameters are varied. This refines a O(n(2/3)) upper bound by Gusfield et al., answering a question posed by Pevzner and Waterman. Our lower bound requires an unbounded alphabet. For strings over a binary alphabet, we prove a Q(n 1 :2) lower bound. For the parametric global alignment of k greater than or equal to 2 sequences under sum-of-pairs scoring we prove a 3(((k)(2))n/2pi)(2/3) + O(k(2/3)n(1/3) log n) upper bound on the number of distinct optimality regions and a Q(n 23) lower bound, partially answering a problem of Pevzner. Based on experimental evidence, we conjecture that for two random sequences, the number of optimality regions is approximately rootn with high probability. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： sequence alignment multiple alignment parametric analysis computational biology experimental analysis of algorithms

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Paging Multiple Users in Cellular Network: Yellow Page and Conference Call Problems

Paging Multiple Users in Cellular Network: Yellow Page and C...

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9th International Symposium on experimental algorithms

作者： Bar-Noy, Amotz Cheilaris, Panagiotis Feng, Yi CUNY Grad Ctr Dept Comp Sci 365 5th Ave New York NY 10016 USA CUNY Brooklyn Coll Dept Comp & Informat Sci Brooklyn NY 11210 USA Ben Gurion Univ Negev Ctr Adv Studies Math Dept Math IL-84105 Beer Sheva Israel

ISBN: (纸本)9783642131929

Mobile users are roaming in a zone of cells in a cellular network system. The probabilities of each user residing in each cell are known, and all probabilities are independent. The task is to find any one, or all, of the users, by paging the cells in a predetermined number of rounds. In each round, any subset of the cells can be paged. When a cell is paged, the list of users in it is returned. The paging process terminates when the required user(s) are found. The objective is to minimize the expected number of paged cells. Finding any one user is known as the yellow page problem, and finding all users is known as the conference call problem. The conference call problem has been proved NP-hard, and a polynomial time approximation scheme exists. We study both problems in a unified framework. We introduce three methods for computing the paging cost. We give a hierarchical classification of users. For certain classes of users, we either provide polynomial time optimal solutions, or provide relatively efficient exponential time solutions. We design a family of twelve fast greedy heuristics that generate competitive paging strategies. We implement optimal algorithms and non-optimal heuristics. We test the performance of our greedy heuristics on many patterns of input data with different parameters. We select the best heuristics for both problems based on our simulation. We evaluate their performances on randomly generated Zipf and uniform data and on real user data.

关键词： cellular networks paging location management experimental analysis of algorithms heuristics

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