Exploiting the Power of Local Search in a Branch and Bound Algorithm for Job Shop Scheduling Matthew J
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A Combined Simulated Annealing and Tabu Search Strategy to Solve a Network Design Problem with Two Classes of Users
Copyright Warning & Restrictions The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted material. Under certain conditions specified in the law, libraries and archives are authorized to furnish a photocopy or other reproduction. One of these specified conditions is that the photocopy or reproduction is not to be “used for any purpose other than private study, scholarship, or research.” If a, user makes a request for, or later uses, a photocopy or reproduction for purposes in excess of “fair use” that user may be liable for copyright infringement, This institution reserves the right to refuse to accept a copying order if, in its judgment, fulfillment of the order would involve violation of copyright law. Please Note: The author retains the copyright while the New Jersey Institute of Technology reserves the right to distribute this thesis or dissertation Printing note: If you do not wish to print this page, then select “Pages from: first page # to: last page #” on the print dialog screen The Van Houten library has removed some of the personal information and all signatures from the approval page and biographical sketches of theses and dissertations in order to protect the identity of NJIT graduates and faculty. ASAC A COMIE SIMUAE AEAIG A AU SEAC SAEGY O SOE A EWOK ESIG OEM WI WO CASSES O USES y Qieg e g A methodology to solve a transportation network design problem (TCNDP) with two classes of users (passenger cars and trucks) is developed. Given an existing highway system, with a capital investment budget constraint, the methodology selects the best links to be expanded by an extra lane by considering one of three types of traffic operations: exclusive for passenger cars, exclusive for trucks, and for both passenger cars and trucks such that the network total user equilibrium (UE) travel time is minimized. -
A Branch-And-Price Approach with Milp Formulation to Modularity Density Maximization on Graphs
A BRANCH-AND-PRICE APPROACH WITH MILP FORMULATION TO MODULARITY DENSITY MAXIMIZATION ON GRAPHS KEISUKE SATO Signalling and Transport Information Technology Division, Railway Technical Research Institute. 2-8-38 Hikari-cho, Kokubunji-shi, Tokyo 185-8540, Japan YOICHI IZUNAGA Information Systems Research Division, The Institute of Behavioral Sciences. 2-9 Ichigayahonmura-cho, Shinjyuku-ku, Tokyo 162-0845, Japan Abstract. For clustering of an undirected graph, this paper presents an exact algorithm for the maximization of modularity density, a more complicated criterion to overcome drawbacks of the well-known modularity. The problem can be interpreted as the set-partitioning problem, which reminds us of its integer linear programming (ILP) formulation. We provide a branch-and-price framework for solving this ILP, or column generation combined with branch-and-bound. Above all, we formulate the column gen- eration subproblem to be solved repeatedly as a simpler mixed integer linear programming (MILP) problem. Acceleration tech- niques called the set-packing relaxation and the multiple-cutting- planes-at-a-time combined with the MILP formulation enable us to optimize the modularity density for famous test instances in- cluding ones with over 100 vertices in around four minutes by a PC. Our solution method is deterministic and the computation time is not affected by any stochastic behavior. For one of them, column generation at the root node of the branch-and-bound tree arXiv:1705.02961v3 [cs.SI] 27 Jun 2017 provides a fractional upper bound solution and our algorithm finds an integral optimal solution after branching. E-mail addresses: (Keisuke Sato) [email protected], (Yoichi Izunaga) [email protected]. -
An Improved Tabu Search Algorithm for the Fixed-Spectrum Frequency-Assignment Problem Roberto Montemanni, Jim N
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 52, NO. 3, MAY 2003 891 An Improved Tabu Search Algorithm for the Fixed-Spectrum Frequency-Assignment Problem Roberto Montemanni, Jim N. J. Moon, and Derek H. Smith Abstract—A tabu search algorithm with a dynamic tabu list for this meant that several or many pairs of transmitters had the fixed-spectrum frequency-assignment problem is presented. inadequate frequency separation. It is now recognized that For cellular problems, the algorithm can be combined with an the pattern of interference obtained when this approach is efficient cell reoptimization step. The algorithm is tested on several sets of test problems and compared with existing algorithms of used may be quite unsatisfactory. One way to overcome the established performance. In particular, it is used to improve problem is to minimize a measure of interference based on some of the best existing assignments for COST 259 benchmarks. the signal-to-interference ratio (SIR) at specified reception These results add support to the claim that the algorithm is the points [10], [11]. This approach is conceptually attractive as most effective available, at least when solution quality is a more interference is directly minimized and it can take account of important criterion than solution speed. The algorithm is robust and easy to tune. multiple interference. However, it is computationally demanding and may restrict the size of the problems that can be handled. Index Terms—Fixed-spectrum problems, radio-frequency Our recent experiences with this approach suggest that, if data assignment, tabu search algorithm. structures of similar efficiency are used, run times are increased by a factor of about 20. -
Heuristic Search Viewed As Path Finding in a Graph
ARTIFICIAL INTELLIGENCE 193 Heuristic Search Viewed as Path Finding in a Graph Ira Pohl IBM Thomas J. Watson Research Center, Yorktown Heights, New York Recommended by E. J. Sandewall ABSTRACT This paper presents a particular model of heuristic search as a path-finding problem in a directed graph. A class of graph-searching procedures is described which uses a heuristic function to guide search. Heuristic functions are estimates of the number of edges that remain to be traversed in reaching a goal node. A number of theoretical results for this model, and the intuition for these results, are presented. They relate the e])~ciency of search to the accuracy of the heuristic function. The results also explore efficiency as a consequence of the reliance or weight placed on the heuristics used. I. Introduction Heuristic search has been one of the important ideas to grow out of artificial intelligence research. It is an ill-defined concept, and has been used as an umbrella for many computational techniques which are hard to classify or analyze. This is beneficial in that it leaves the imagination unfettered to try any technique that works on a complex problem. However, leaving the con. cept vague has meant that the same ideas are rediscovered, often cloaked in other terminology rather than abstracting their essence and understanding the procedure more deeply. Often, analytical results lead to more emcient procedures. Such has been the case in sorting [I] and matrix multiplication [2], and the same is hoped for this development of heuristic search. This paper attempts to present an overview of recent developments in formally characterizing heuristic search. -
Cooperative and Adaptive Algorithms Lecture 6 Allaa (Ella) Hilal, Spring 2017 May, 2017 1 Minute Quiz (Ungraded)
Cooperative and Adaptive Algorithms Lecture 6 Allaa (Ella) Hilal, Spring 2017 May, 2017 1 Minute Quiz (Ungraded) • Select if these statement are true (T) or false (F): Statement T/F Reason Uniform-cost search is a special case of Breadth- first search Breadth-first search, depth- first search and uniform- cost search are special cases of best- first search. A* is a special case of uniform-cost search. ECE457A, Dr. Allaa Hilal, Spring 2017 2 1 Minute Quiz (Ungraded) • Select if these statement are true (T) or false (F): Statement T/F Reason Uniform-cost search is a special case of Breadth- first F • Breadth- first search is a special case of Uniform- search cost search when all step costs are equal. Breadth-first search, depth- first search and uniform- T • Breadth-first search is best-first search with f(n) = cost search are special cases of best- first search. depth(n); • depth-first search is best-first search with f(n) = - depth(n); • uniform-cost search is best-first search with • f(n) = g(n). A* is a special case of uniform-cost search. F • Uniform-cost search is A* search with h(n) = 0. ECE457A, Dr. Allaa Hilal, Spring 2017 3 Informed Search Strategies Hill Climbing Search ECE457A, Dr. Allaa Hilal, Spring 2017 4 Hill Climbing Search • Tries to improve the efficiency of depth-first. • Informed depth-first algorithm. • An iterative algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by incrementally changing a single element of the solution. • It sorts the successors of a node (according to their heuristic values) before adding them to the list to be expanded. -
Backtracking / Branch-And-Bound
Backtracking / Branch-and-Bound Optimisation problems are problems that have several valid solutions; the challenge is to find an optimal solution. How optimal is defined, depends on the particular problem. Examples of optimisation problems are: Traveling Salesman Problem (TSP). We are given a set of n cities, with the distances between all cities. A traveling salesman, who is currently staying in one of the cities, wants to visit all other cities and then return to his starting point, and he is wondering how to do this. Any tour of all cities would be a valid solution to his problem, but our traveling salesman does not want to waste time: he wants to find a tour that visits all cities and has the smallest possible length of all such tours. So in this case, optimal means: having the smallest possible length. 1-Dimensional Clustering. We are given a sorted list x1; : : : ; xn of n numbers, and an integer k between 1 and n. The problem is to divide the numbers into k subsets of consecutive numbers (clusters) in the best possible way. A valid solution is now a division into k clusters, and an optimal solution is one that has the nicest clusters. We will define this problem more precisely later. Set Partition. We are given a set V of n objects, each having a certain cost, and we want to divide these objects among two people in the fairest possible way. In other words, we are looking for a subdivision of V into two subsets V1 and V2 such that X X cost(v) − cost(v) v2V1 v2V2 is as small as possible. -
Module 5: Backtracking
Module-5 : Backtracking Contents 1. Backtracking: 3. 0/1Knapsack problem 1.1. General method 3.1. LC Branch and Bound solution 1.2. N-Queens problem 3.2. FIFO Branch and Bound solution 1.3. Sum of subsets problem 4. NP-Complete and NP-Hard problems 1.4. Graph coloring 4.1. Basic concepts 1.5. Hamiltonian cycles 4.2. Non-deterministic algorithms 2. Branch and Bound: 4.3. P, NP, NP-Complete, and NP-Hard 2.1. Assignment Problem, classes 2.2. Travelling Sales Person problem Module 5: Backtracking 1. Backtracking Some problems can be solved, by exhaustive search. The exhaustive-search technique suggests generating all candidate solutions and then identifying the one (or the ones) with a desired property. Backtracking is a more intelligent variation of this approach. The principal idea is to construct solutions one component at a time and evaluate such partially constructed candidates as follows. If a partially constructed solution can be developed further without violating the problem’s constraints, it is done by taking the first remaining legitimate option for the next component. If there is no legitimate option for the next component, no alternatives for any remaining component need to be considered. In this case, the algorithm backtracks to replace the last component of the partially constructed solution with its next option. It is convenient to implement this kind of processing by constructing a tree of choices being made, called the state-space tree. Its root represents an initial state before the search for a solution begins. The nodes of the first level in the tree represent the choices made for the first component of a solution; the nodes of the second level represent the choices for the second component, and soon. -
A Tabu Search Algorithm with Efficient Diversification Strategy for High School Timetabling Problem
International Journal of Computer Science & Information Technology (IJCSIT) Vol 5, No 4, August 2013 A TABU SEARCH ALGORITHM WITH EFFICIENT DIVERSIFICATION STRATEGY FOR HIGH SCHOOL TIMETABLING PROBLEM Salman Hooshmand1 , Mehdi Behshameh2 and OmidHamidi3 1Department of Computer Engineering, Hamedan University of Technology, Hamedan Iran [email protected] 2Department of Computer Engineering, Islamic Azad University ,Toyserkan Branch, Toyserkan, Iran [email protected] 3Department of Science, Hamedan University of Technology, Hamedan, Iran [email protected] ABSTRACT The school timetabling problem can be described as scheduling a set of lessons (combination of classes, teachers, subjects and rooms) in a weekly timetable. This paper presents a novel way to generate timetables for high schools. The algorithm has three phases. Pre-scheduling, initial phase and optimization through tabu search. In the first phase, a graph based algorithm used to create groups of lessons to be scheduled simultaneously; then an initial solution is built by a sequential greedy heuristic. Finally, the solution is optimized using tabu search algorithm based on frequency based diversification. The algorithm has been tested on a set of real problems gathered from Iranian high schools. Experiments show that the proposed algorithm can effectively build acceptable timetables. KEYWORDS Timetabling. Tabu Search. Diversification .Graph . Scheduling 1. INTRODUCTION Scheduling high school lessons has been considered to be one of the main concerns of schools’ staff before beginning of the term. Manual timetabling is tedious and generally takes several weeks to build an acceptable timetable. The main difficulty is related to the size of the problem; the algorithm should consider several conflicting criteria and conditions often for a large number of classes, teachers and courses. -
Solving Zero-One Mixed Integer Programming Problems Using Tabu Search
Solving Zero-One Mixed Integer Programming Problems Using Tabu Search by Arne Løkketangen * Fred Glover # 20 April 1997 Abstract We describe a tabu search approach for solving general zero- one mixed integer programming problems that exploits the extreme point property of zero-one solutions. Specialized choice rules and aspiration criteria are identified for the problems, expressed as functions of integer infeasibility measures and objective function values. The first-level TS mechanisms are then extended with advanced level strategies and learning. We also look at probabilistic measures in this framework, and examine how the learning tool Target Analysis can be applied to identify better control structures and decision rules. Computational results are reported on a portfolio of multiconstraint knapsack problems. Our approach is designed to solve thoroughly general 0/1 MIP problems and thus contains no problem domain specific knowledge, yet it obtains solutions for the multiconstraint knapsack problem whose quality rivals, and in some cases surpasses, the best solutions obtained by special purpose methods that have been created to exploit the special structure of these problems. Keywords Tabu Search, Heuristics, Integer Programming #* School of Business, CB419 Molde College University of Colorado Britvn. 2 Boulder, CO 80309 6400 Molde USA Norway Email: [email protected] Email: [email protected] 2 Introduction Tabu search (TS) has been applied to solving a variety of zero-one mixed integer programming (MIP) problems with special structures, ranging from scheduling and routing to group technology and probabilistic logic. (See, for example, the volume Annals of Operations Research 41 (1993), and the application surveys in Glover and Laguna (1993), and Glover (1996)). -
Dynamic Temporary Blood Facility Locationallocation During And
Dynamic temporary blood facility location-allocation during and post-disaster periods Article (Accepted Version) Sharma, Bhuvnesh, Ramkumar, M, Subramanian, Nachiappan and Malhotra, Bharat (2017) Dynamic temporary blood facility location-allocation during and post-disaster periods. Annals of Operations Research. ISSN 0254-5330 This version is available from Sussex Research Online: http://sro.sussex.ac.uk/id/eprint/71673/ This document is made available in accordance with publisher policies and may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher’s version. Please see the URL above for details on accessing the published version. Copyright and reuse: Sussex Research Online is a digital repository of the research output of the University. Copyright and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable, the material made available in SRO has been checked for eligibility before being made available. Copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. http://sro.sussex.ac.uk Dynamic temporary blood facility location-allocation during and post-disaster periods Bhuvnesh Sharma Department of Industrial & Systems Engineering Indian Institute of Technology Kharagpur Kharagpur – 721302, West Bengal, India e-mail: [email protected] M. -
A Comparative Analysis of a Tabu Search and a Genetic Algorithm for Solving a University Course Timetabling Problem
DEGREE PROJECT, IN COMPUTER SCIENCE , FIRST LEVEL STOCKHOLM, SWEDEN 2015 A comparative analysis of a Tabu Search and a Genetic Algorithm for solving a University Course Timetabling Problem CASPER RENMAN AND HAMPUS FRISTEDT KTH ROYAL INSTITUTE OF TECHNOLOGY CSC SCHOOL www.kth.se iii Abstract This work implements a Tabu search (TS) algorithm for solving an instance of the University Course Timetabling Problem (UCTP). The algorithm is com- pared to a Genetic algorithm (GA) implemented by Yamazaki and Pertoft (2014) that solves the same instance. The purpose of the work is to explore how the approaches differ for this particular instance, and specifically inves- tigate whether a TS algorithm alone is sufficient, considering the small size of the UCTP instance. The TS was based on the OpenTS library (Harder, 2001) and reuses parts from Yamazaki and Pertoft’s (2014) GA. The results show that the TS alone is too slow. Even in a small instance of the UCTP, the search space is too big for the TS to be fast. This confirms the state of the art, that a combination of TS and GA would perform better than either of them individually. Further improvements on the TS would involve reducing the number of moves generated each iteration. iv Sammanfattning Detta arbete implementerar en Tabu search-algoritm (TS) för att lösa en in- stans av University Course Timetabling Problem (UCTP). Algoritmen jämförs med en Genetic algoritm (GA) implementerad av Yamazaki och Pertoft (2014) som löser samma instans. Syftet med arbetet är att utforska hur angreppssätten skiljer sig för denna instans, och specifikt undersöka om det räcker att endast använda en TS-algoritm, eftersom instansen är liten. -
An Evolutionary Algorithm for Minimizing Multimodal Functions
An Evolutionary Algorithm for Minimizing Multimodal Functions D.G. Sotiropoulos, V.P. Plagianakos, and M.N. Vrahatis Department of Mathematics, University of Patras, GR–261.10 Patras, Greece. University of Patras Artificial Intelligence Research Center–UPAIRC. e–mail: {dgs,vpp,vrahatis}@math.upatras.gr Abstract—A new evolutionary algorithm for are precluded. In such cases direct search approaches the global optimization of multimodal functions are the methods of choice. is presented. The algorithm is essentially a par- allel direct search method which maintains a If the objective function is unimodal in the search populations of individuals and utilizes an evo- domain, one can choose among many good alterna- lution operator to evolve them. This operator tives. Some of the available minimization methods in- has two functions. Firstly, to exploit the search volve only function values, such as those of Hook and space as much as possible, and secondly to form Jeeves [2] and Nelder and Mead [5]. However, if the an improved population for the next generation. objective function is multimodal, the number of avail- This operator makes the algorithm to rapidly able algorithms is reduced to very few. In this case, converge to the global optimum of various diffi- the algorithms quoted above tend to stop at the first cult multimodal test functions. minimum encountered, and cannot be used easily for finding the global one. Index Terms—Global optimization, derivative free methods, evolutionary algorithms, direct Search algorithms which enhance the exploration of the search methods. feasible region through the use of a population, such as Genetic Algorithms (see, [4]), and probabilistic search techniques such as Simulated Annealing (see, [1, 7]), I.