Markov Chain Analysis Example
|
|
- Benjamin Hensley
- 5 years ago
- Views:
Transcription
1 Markov Chain Analysis Example Example: single server with a queue holding up to requests 0 denotes the arrival rate denotes the service rate Steady-state analysis: mapping of Markov chain on a set of linear equations state : p = p state : p + p = p + p state : p0 + p = p + p steady state implies that arrivals = completions state 0: p = p0 normalization equation: p0 + p + p + p = resolution of system of equations to derive state probabilities p0 = / ( + / + ( / ) + ( / ) ) p = ( / ) / ( + / + ( / ) + ( / ) ); p =... derivation of mean values and distribution functions from state probabilities utilization: U = - p0; mean number of jobs in system: N = p + p + p ; blocking probability B; distribution functions for waiting time, response time, etc.
2 Queuing Network Analysis - Example Example: communication system (unbounded queues) prot. stack arrival rate: 5 packets/s = 5 /s = 00 MIps / MI = 50 /s MI prozessor 00 MIps = 0 /s medium Mb phy network 0 Mbps prot. stack = /s,8 MI prozessor 0 MIps Results (assuming exponential service times and arrivals): utilization = (e.g. physical network util. = 8 %) population per station n i = ( mean total population N = i n i =7,9 mean response time T = N/ = 96 msec (Little s law)
3 Discrete-event Simulation Idea: model the relevant events of the system process the events according to their temporal order (similar to the real execution with the exception that simple processing blocks are modeled only) Example: Execution on a -processor system (non-preemptive) / /5 Legend: green: blue: / / 5 / 6 /6 execution time process priority (=low) P P Discussion no assumptions danger of including too many details evaluation is time consuming problems with rare events large set of tools and models available 6
4 Comparision of Methods best case Analysis worst case average Analysis of multiprocessor systems Verification of Real Time requests Modelling of parallel processing (prec. constraints) Process graph no Task graph not really? Schedulability Utiliz.-based no no Resp.-based no no Markov chains no Queuing networks Operational analysis no no no no Simulation no Measurements no
5 Heuristic Search Most heuristics are based on an iterative search comprising the following elements: selection of an initial (intermediate) solution (e.g. a sequence) evaluation of the quality of the intermediate solution check of termination criteria select initial solution select next solution (based on previous solution) search strategy evaluate quality acceptance criteria satisfied y accept solution as best solution so far n termination criteria satisfied y 5
6 Hill-Climbing Discussion simple local optimizations only: algorithm is not able to pass a valley to finally reach a higher peak idea is only applicable to small parts of optimization algorithms but needs to be complemented with other strategies to overcome local optimas 6
7 Random Search also called Monte Carlo algorithm Idea: random selection of the candidates for a change of intermediate solutions or random selection of the solutions (no use of neighborhood) Discussion: simple (no neighborhood relation is needed) not time efficient, especially where the time to evaluate solutions is high sometimes used as a reference algorithm to evaluate and compare the quality of heuristic optimization algorithms idea of randomization is applied to other techniques, e.g. genetic algorithms and simulated annealing 7
8 Simulated Annealing Idea: simulate the annealing process of material: the slow cooling of material leads to a state with minimal energy, i.e. the global optimum Classification: Search strategy random local search Acceptance criteria unconditional acceptance of the selected solution if it represents an improvement over previous solutions otherwise probabilistic acceptance Termination criteria static bound on the number of iterations (cooling process) 8
9 Simulated Annealing Discussion and Variants Discussion: parameter settings for cooling process is essential (but complicated) slow decrease results in long run times fast decrease results in poor solutions discussion whether temperature decrease should be linear or logarithmic straightforward to implement Variants: deterministic acceptance nonlinear cooling (slow cooling in the middle of the process) adaptive cooling based on accepted solutions at a temperature reheating 9
10 Genetic Algorithms Basic Operations crossover mutation
11 Genetic Algorithms Basic Algorithm crossover Replacement and selection rely on some cost function defining the quality of each solution selection population replacement mutation Different replacement strategies, e.g. survival of the fittest General parameters: size of population mutation probability candidate selection strategy (mapping quality on probability) replacement strategy (replace own parents, replace weakest, influence of probability) Application-specific parameters: mapping of problem on appropriate coding handling of invalid solutions in codings Crossover selection is typically random
12 Genetische Algorithmen Minimum Spanning Tree small population results in inbreeding larger population works well with small mutation rate tradeoff between size of population and number of iterations
13 Genetic Algorithms Basic Operations Mutation => crating a new member of the population by changing one member
14 Genetic Algorithms Basic Operations Crossover => crating a new member of the population from two members
15 Genetische Algorithmen Traveling Salesman Problem minimal impact of mutation rate with small population negativ impact of high mutation rate with larger population (increased randomness) impact not quite clear 5
16 Genetic Algorithms Discussion finding an appropriate coding for the binary vectors for the specific application at hand is not intuitive problems are redundant codings, codings that do not represent a valid solution, e.g. coding for a sequencing problem tuning of genetic algorithms may be time consuming parameter settings highly depend on problem specifics suited for parallelization of optimization 6
17 Tabu Search Idea: extension of hill-climbing to avoid being trapped in local optima allow intermediate solutions with lower quality maintain history to avoid running in cycles Classification: Search strategy deterministic local search Acceptance criteria acceptance of best solution in neighborhood which is not tabu Termination criteria static bound on number of iterations or dynamic, e.g. based on quality improvements of solutions 7
18 Tabu Search Algorithm select initial solution select neighborhood set (based on current solution) remove tabu solutions from set increase neigborhood set is empty y n evaluate quality and select best solution from set termination criteria satisfied n update tabu list y The brain of the algorithm is the tabu list that stores and maintains information about the history of the search. In the most simple case a number of previous solutions are stored in the tabu list. More advanced techniques maintain attributes of the solutions rather than the solutions itself 8
19 Tabu Search Organisation of the History The history is maintained by the tabu list Attributes of solutions are a very flexible mean to control the search Example of attributes of a HW/SW partitioning problem with 8 tasks assigned to of different HW entities: (A) change of the value of a task assignment variable (A) move to HW (A) move to SW (A) combined change of some attributes (A5) improvement of the quality of two subsequent solutions over or below a threshold value Aspiration criteria: Under certain conditions tabus may be ignored, e.g. if a tabu solution is the best solution found so far all solutions in a neighborhood are tabu a tabu solution is better than the solution that triggered the respective tabu conditions Intensification checks whether good solutions share some common properties Diversification searches for solution that do not share common properties Update of history information may be recency-based or frequency-based (i.e. depending on the frequency that the attribute has been activated) 9
20 Tabu Search Discussion easy to implement (at least the neighborhood search as such) non-trival tuning of parameters tuning is crucial to avoid cyclic search advantage of use of knowledge, i.e. feedback from the search (evaluation of solutions) to control the search (e.g. for the controlled removal of bottlenecks) 0
21 Heuristic Search Methods Classification Search strategy search area global search (potentially all solutions considered) local search (direct neighbors only stepwise optimization) selection strategy deterministic selection, i.e. according to some deterministic rules random selection from the set of possible solutions probabilistic selection, i.e. based on some probabilistic function history dependence, i.e. the degree to which the selection of the new candidate solution depends on the history of the search no dependence one-step dependence multi-step dependence Acceptance criteria deterministic acceptance, i.e. based on some deterministic function probabilistic acceptance, i.e. influenced by some random factor Termination criteria static, i.e. independent of the actual solutions visited during the search dynamic, i.e. dependent on the search history
22 Heuristic Search Methods Classification Heuristic Search strategy Acceptance criterion Termination criterion Search area Selection strategy History dependence det. prob. stat. dyn. local global det. prob. random none onestep multistep hillclimbing tabu search simulated annealing genetic algorithms random search x x x x x x x x x x x x x x x x x x x x x x x x x x x x
23 Single Pass Approaches The techniques covered so far search through a high number of solutions. Idea underlying single pass approaches: intelligent construction of a single solution (instead of updating and modification of a number of solutions) the solution is constructed by subsequently solving a number of subproblems Discussion: single-pass algorithms are very quick quality of solutions is often small not applicable where lots of constraints are present (which require some kind of backtracking) Important applications of the idea: list scheduling: subsequent selection of a task to be scheduled until the complete schedule has been computed clustering: subsequent merger of nodes/modules until a small number of cluster remains such that each cluster can be assigned a single HW unit
24 Single Pass Approaches Framework derive guidelines for solution construction select subproblem The guidelines are crucial and represent the intelligence of the algorithm decide subproblem based on guidelines possibly recompute or adapt guidelines n final solution constructed y
25 List Scheduling List scheduling: subsequent selection of a task to be scheduled on some processor (or HW entity) operation is similar to a dynamic task scheduler of an operating system assign priorities to the tasks according to some strategy priorisation strategy select executable task with highest priority assign task to a processor according to some strategy assignment strategy n schedule complete? y 5
26 List Scheduling Example () Problem: processors 6 tasks with precedence constraints find schedule with minimal execution time /8 HLFET (highest level first with estimated times) length of the longest (critical) path to the sink node (node 6) Assignment strategy /6 /5 / 5 /5 first fit 6 / Resulting schedule: P P 5 6 Legend: green: red: estimated times levels (priorities)
27 List Scheduling Example () Problem (unchanged): processors 6 tasks with precedence constraints find schedule with minimal execution time / SCFET (smallest co-level first with estimated times) length of the longest (critical) path to the source node (node ) Assignment strategy first fit / /7 /5 5 6 /8 /6 Resulting schedule: P P 5 6 Legend: green: blue: estimated times co-levels (priorities)
28 List Scheduling Example () Problem: processors 6 tasks with precedence constraints find schedule with minimal execution time /8 HLFET (highest level first with estimated times) length of the longest (critical) path to the sink node (node 6) Assignment strategy /6 /5 / 5 /5 first fit 6 / Resulting schedule: P P 5 6 Legend: green: red: estimated times levels (priorities)
29 Clustering - Basics Partitioning of a set of nodes in a given number of subsets n assign each node to a different cluster compute the distance between any pair of clusters select the pair of clusters with the highest affinity merge the clusters termination criteria holds y Application: processor assignment (load balancing minimize interprocess communication) scheduling (minimize critical path) HW/SW partitioning Clustering may be employed as part of the optimization process, i.e. combined with other techniques 9
30 Clustering probabilistic Each node belongs with certain probabilities to different clusters deterministic A node belongs to exactly one cluster or not hierarchical Starts with a distance matrix of each pair of nodes Exact method: always the same result Termination after all nodes belong to one cluster partitioning Starts with given number of K clusters (independent from nodes) Results depend on the chosen initial set of clusters Termination after a given number of iterations 0
31 Hierarchical Clustering Stepwise reduction of the number of clusters Determine the distance between each pair of nodes Select the smallest distance Replace the selected pair in distance matrix by a cluster representative Recompute distance matrix Dendrogramm n All nodes in one cluster y Algorithm is kind of subsequent merger of nearest neighbors (nodes/clusters)
32 Hierarchical Clustering Dendrogramm Algorithm is kind of subsequent merger of nearest neighbors (nodes/clusters)
33 Partitioning Clustering (k-means) Choose positions of k initial cluster representative assign each node to the nearest cluster representative Recompute positions of the cluster representative Based on the positions of the nodes in each cluster n Number of iterations reached y
34 Clustering Application to Load Balancing assign each node to a different cluster compute the sum of the communication cost between any pair of clusters Optimization goal: minimize inter-process (intercluster) communication limit maximum load per processor (cluster) to 0 select the pair of clusters with the highest comm. cost that does not violate the capacity constraints merge the clusters y reduction of comm. cost without violation of constraints possible n
35 Clustering Application to Load Balancing
36 Clustering Variants Clustering methods Partitioning methods Hierarchical methods k-means Fuzzy-c-means SOM Clique One Pass Gustafson-Kessel algorithm Agglomeration (bottom up) Single linkage Complete linkage Average group Centroid MST ROCK Division (top down) Wards Tree Structural Vector Quantification Macnaughton-Smith algorithm Distance Metrics Euclidean Manhattan Minkowsky Mahalanobis Jaccard Camberra Chebychev Correlation Chi-square Kendalls s Rank Correlation 6
37 Clustering Hierarchical Algorithms Single linkage Complete Linkage Centroid-based Algorithms implement different methods to compute the distance between two clusters 7
38 Clustering Single Linkage P P P P P5 P7 P Distance between groups is estimated as the smallest distance between entities Example: d, d d. d(,)5 min Cluster # P P P P P5 P6 P7 P P P P P P P
39 Clustering Single Linkage P P P P P5 P7 P Cluster # P C P C57 P6 P C P C P Cluster # P C C57 P6 P Cluster # P P P P P5 C P6 -P P C P P P P P P P
40 Clustering Group Average P P P P P5 P7 P Distance between groups is defined as the average distance between all pairs of entities Example: d d d. 8 (,)5 5 5 Cluster # P P P P P5 P6 P7 P P P P P P P
41 Clustering Group Average P P P P P5 P7 P Cluster # P C P C57 P6 P C P C P Cluster # P P P P P5 P6 P7 C P C P P P P P P P Cluster # P C C57 P6 P
42 Clustering Centroid-based x P P P P x P5 P7 x P x Determine distances between centroids (k,l) Merge centroids with the least distance C C C C d ( k, l) xk xl yk y l Cluster # P P P P P5 P6 P7 P P P P P P P
43 Clustering Centroid-based x P P P P x P5 P7 x P x Cluster # C C C C57 C6 C C C C C Cluster # P P P P P5 P6 P7 P P P P P P P
44 Differences between Clustering Algorithms Y (m).5 x 0.5 x Y (m).5 x 0 Single Linkage x Complete Linkage - - Single Centroid K-means Complete WardLinkage X (m) 0 0 x x X (m) x 0 Y (m) X (m) x 0 - Centroid Linkage Y (m) Y (m).5 K-means X (m) x 0.5 x Ward X (m) x X (m) x 0
45 Clustering Discussion Results Exact results (single linkage) Not-exact results often several iterations are necessary (K-means) Metrics Strong impact to clustering results Not each metric is suitable for each clustering algorithm Decision for one- or multi-criteria metrics (separated or joint clustering) Selection of Algorithm Depends strongly on the structure of the data set and the expected results Some algorithms tend to separate outlayers in own clusters some large clusters and a lot of very small clusters (complete linkage) Only few algorithms are able to detect also branched, curved or cyclic clusters (single linkage) Some algorithms tend to return clusters with nearly equal size (K-means, Ward) Quality of clustering results The mean variance of the elements in each cluster (affinity parameter) is often used In general the homogeneity within clusters and the heterogeneity between clusters can be measured However, the quality prediction can be only as good as the quality of the used metric! 5
46 Branch and Bound with Underestimates Application of the A* algorithm to the scheduling problem Example: scheduling on a -processor system (processor A and B) Process graph communication processing f(x) = g(x) + h(x) g(x) exact value of partial schedule h(x) underestimate for remainder (min (altern.rem.proc, rem.comm. + rem.proc.) Legend: green: processing times blue: communication times Search is terminated when min {f(x)} is a terminal node (in the search tree) 6
47 Branch and Bound with Underestimates Example: computation of f() 5 5 -> A -> B f()=7 f()=7 8 6 case : path -- g(x) = = h(x) = f(x) = 6 case : path -- g(x) = 5 h(x) = f(x) = 9 A B A B -> A f()= -> > f(x) = g(x) + h(x) g(x) exact value of partial schedule h(x) underestimate for remainder
48 Branch and Bound with Underestimates Application of the A* algorithm to the scheduling problem Example: scheduling on a -processor system (processor A and B) Process graph Search Tree Legend: green: processing times blue: comm. times 9 -> A -> B 5 -> A 6 -> B f()= f()=8 f(5)=8 f(6)= f(x) = g(x) + h(x) g(x) exact value of partial schedule h(x) underestimate for remainder -> A -> B f()=7 f()=7 7 -> A 8 -> B f(7)=5 f(8)=8 9 -> A 0 -> B f(9)= f(0)=8 Search is terminated when min {f(x)} is a terminal node (in the search tree) 8
49 References A. Mitschele-Thiel: Systems Engineering with SDL Developing Performance- Critical Communication Systems. Wiley, 00. (section.5) C.R. Reeves (ed.): Modern Heuristic Techniques for Combinatorial Problems. Blackwell Scientific Publications, 99. H.U. Heiss: Prozessorzuteilung in Parallelrechnern. BI-Wissenschaftsverlag, Reihe Informatik, Band 98, 99. M. Garey, D. Johnson: Computer and Intractability. W.H. Freeman, New York,
Evaluation of Temporal and Performance Aspects
TECHNISCHE UNIVERSITÄT ILMENAU Evaluation of Temporal and Performance Aspects Integrated Hard- and Software Systems http://www.tu-ilmenau.de/ihs Problem Statement Performance Modeling Performance Evaluation
More informationOptimization Techniques for Design Space Exploration
0-0-7 Optimization Techniques for Design Space Exploration Zebo Peng Embedded Systems Laboratory (ESLAB) Linköping University Outline Optimization problems in ERT system design Heuristic techniques Simulated
More informationNon-deterministic Search techniques. Emma Hart
Non-deterministic Search techniques Emma Hart Why do local search? Many real problems are too hard to solve with exact (deterministic) techniques Modern, non-deterministic techniques offer ways of getting
More informationUnsupervised Learning and Clustering
Unsupervised Learning and Clustering Selim Aksoy Department of Computer Engineering Bilkent University saksoy@cs.bilkent.edu.tr CS 551, Spring 2009 CS 551, Spring 2009 c 2009, Selim Aksoy (Bilkent University)
More informationUnsupervised Learning and Clustering
Unsupervised Learning and Clustering Selim Aksoy Department of Computer Engineering Bilkent University saksoy@cs.bilkent.edu.tr CS 551, Spring 2008 CS 551, Spring 2008 c 2008, Selim Aksoy (Bilkent University)
More informationUninformed Search Methods. Informed Search Methods. Midterm Exam 3/13/18. Thursday, March 15, 7:30 9:30 p.m. room 125 Ag Hall
Midterm Exam Thursday, March 15, 7:30 9:30 p.m. room 125 Ag Hall Covers topics through Decision Trees and Random Forests (does not include constraint satisfaction) Closed book 8.5 x 11 sheet with notes
More informationClustering CS 550: Machine Learning
Clustering CS 550: Machine Learning This slide set mainly uses the slides given in the following links: http://www-users.cs.umn.edu/~kumar/dmbook/ch8.pdf http://www-users.cs.umn.edu/~kumar/dmbook/dmslides/chap8_basic_cluster_analysis.pdf
More informationHardware-Software Codesign
Hardware-Software Codesign 4. System Partitioning Lothar Thiele 4-1 System Design specification system synthesis estimation SW-compilation intellectual prop. code instruction set HW-synthesis intellectual
More informationINF4820. Clustering. Erik Velldal. Nov. 17, University of Oslo. Erik Velldal INF / 22
INF4820 Clustering Erik Velldal University of Oslo Nov. 17, 2009 Erik Velldal INF4820 1 / 22 Topics for Today More on unsupervised machine learning for data-driven categorization: clustering. The task
More informationClassification. Vladimir Curic. Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University
Classification Vladimir Curic Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University Outline An overview on classification Basics of classification How to choose appropriate
More informationECS 234: Data Analysis: Clustering ECS 234
: Data Analysis: Clustering What is Clustering? Given n objects, assign them to groups (clusters) based on their similarity Unsupervised Machine Learning Class Discovery Difficult, and maybe ill-posed
More informationAlgorithms & Complexity
Algorithms & Complexity Nicolas Stroppa - nstroppa@computing.dcu.ie CA313@Dublin City University. 2006-2007. November 21, 2006 Classification of Algorithms O(1): Run time is independent of the size of
More informationParallel Computing in Combinatorial Optimization
Parallel Computing in Combinatorial Optimization Bernard Gendron Université de Montréal gendron@iro.umontreal.ca Course Outline Objective: provide an overview of the current research on the design of parallel
More informationUsing Penalties instead of Rewards: Solving OCST Problems with Problem-Specific Guided Local Search
Using Penalties instead of Rewards: Solving OCST Problems with Problem-Specific Guided Local Search Wolfgang Steitz, Franz Rothlauf Working Paper 01/2011 March 2011 Working Papers in Information Systems
More informationJob Shop Scheduling Problem (JSSP) Genetic Algorithms Critical Block and DG distance Neighbourhood Search
A JOB-SHOP SCHEDULING PROBLEM (JSSP) USING GENETIC ALGORITHM (GA) Mahanim Omar, Adam Baharum, Yahya Abu Hasan School of Mathematical Sciences, Universiti Sains Malaysia 11800 Penang, Malaysia Tel: (+)
More informationCluster Analysis. Ying Shen, SSE, Tongji University
Cluster Analysis Ying Shen, SSE, Tongji University Cluster analysis Cluster analysis groups data objects based only on the attributes in the data. The main objective is that The objects within a group
More informationHeuristic Optimisation
Heuristic Optimisation Revision Lecture Sándor Zoltán Németh http://web.mat.bham.ac.uk/s.z.nemeth s.nemeth@bham.ac.uk University of Birmingham S Z Németh (s.nemeth@bham.ac.uk) Heuristic Optimisation University
More informationMidterm Examination CS540-2: Introduction to Artificial Intelligence
Midterm Examination CS540-2: Introduction to Artificial Intelligence March 15, 2018 LAST NAME: FIRST NAME: Problem Score Max Score 1 12 2 13 3 9 4 11 5 8 6 13 7 9 8 16 9 9 Total 100 Question 1. [12] Search
More informationClustering. Informal goal. General types of clustering. Applications: Clustering in information search and analysis. Example applications in search
Informal goal Clustering Given set of objects and measure of similarity between them, group similar objects together What mean by similar? What is good grouping? Computation time / quality tradeoff 1 2
More informationMachine Learning. Unsupervised Learning. Manfred Huber
Machine Learning Unsupervised Learning Manfred Huber 2015 1 Unsupervised Learning In supervised learning the training data provides desired target output for learning In unsupervised learning the training
More informationBBS654 Data Mining. Pinar Duygulu. Slides are adapted from Nazli Ikizler
BBS654 Data Mining Pinar Duygulu Slides are adapted from Nazli Ikizler 1 Classification Classification systems: Supervised learning Make a rational prediction given evidence There are several methods for
More informationUnsupervised Learning Hierarchical Methods
Unsupervised Learning Hierarchical Methods Road Map. Basic Concepts 2. BIRCH 3. ROCK The Principle Group data objects into a tree of clusters Hierarchical methods can be Agglomerative: bottom-up approach
More informationNew algorithm for analyzing performance of neighborhood strategies in solving job shop scheduling problems
Journal of Scientific & Industrial Research ESWARAMURTHY: NEW ALGORITHM FOR ANALYZING PERFORMANCE OF NEIGHBORHOOD STRATEGIES 579 Vol. 67, August 2008, pp. 579-588 New algorithm for analyzing performance
More informationLesson 3. Prof. Enza Messina
Lesson 3 Prof. Enza Messina Clustering techniques are generally classified into these classes: PARTITIONING ALGORITHMS Directly divides data points into some prespecified number of clusters without a hierarchical
More informationLocal Search and Optimization Chapter 4. Mausam (Based on slides of Padhraic Smyth, Stuart Russell, Rao Kambhampati, Raj Rao, Dan Weld )
Local Search and Optimization Chapter 4 Mausam (Based on slides of Padhraic Smyth, Stuart Russell, Rao Kambhampati, Raj Rao, Dan Weld ) 1 2 Outline Local search techniques and optimization Hill-climbing
More informationACO and other (meta)heuristics for CO
ACO and other (meta)heuristics for CO 32 33 Outline Notes on combinatorial optimization and algorithmic complexity Construction and modification metaheuristics: two complementary ways of searching a solution
More informationLocal Search and Optimization Chapter 4. Mausam (Based on slides of Padhraic Smyth, Stuart Russell, Rao Kambhampati, Raj Rao, Dan Weld )
Local Search and Optimization Chapter 4 Mausam (Based on slides of Padhraic Smyth, Stuart Russell, Rao Kambhampati, Raj Rao, Dan Weld ) 1 2 Outline Local search techniques and optimization Hill-climbing
More informationInformation Retrieval and Web Search Engines
Information Retrieval and Web Search Engines Lecture 7: Document Clustering December 4th, 2014 Wolf-Tilo Balke and José Pinto Institut für Informationssysteme Technische Universität Braunschweig The Cluster
More informationWorkload Characterization Techniques
Workload Characterization Techniques Raj Jain Washington University in Saint Louis Saint Louis, MO 63130 Jain@cse.wustl.edu These slides are available on-line at: http://www.cse.wustl.edu/~jain/cse567-08/
More informationLocal Search and Optimization Chapter 4. Mausam (Based on slides of Padhraic Smyth, Stuart Russell, Rao Kambhampati, Raj Rao, Dan Weld )
Local Search and Optimization Chapter 4 Mausam (Based on slides of Padhraic Smyth, Stuart Russell, Rao Kambhampati, Raj Rao, Dan Weld ) 1 Outline Local search techniques and optimization Hill-climbing
More informationClustering. Lecture 6, 1/24/03 ECS289A
Clustering Lecture 6, 1/24/03 What is Clustering? Given n objects, assign them to groups (clusters) based on their similarity Unsupervised Machine Learning Class Discovery Difficult, and maybe ill-posed
More informationA Steady-State Genetic Algorithm for Traveling Salesman Problem with Pickup and Delivery
A Steady-State Genetic Algorithm for Traveling Salesman Problem with Pickup and Delivery Monika Sharma 1, Deepak Sharma 2 1 Research Scholar Department of Computer Science and Engineering, NNSS SGI Samalkha,
More informationCluster Analysis. Angela Montanari and Laura Anderlucci
Cluster Analysis Angela Montanari and Laura Anderlucci 1 Introduction Clustering a set of n objects into k groups is usually moved by the aim of identifying internally homogenous groups according to a
More informationGene Clustering & Classification
BINF, Introduction to Computational Biology Gene Clustering & Classification Young-Rae Cho Associate Professor Department of Computer Science Baylor University Overview Introduction to Gene Clustering
More informationHEURISTIC OPTIMIZATION USING COMPUTER SIMULATION: A STUDY OF STAFFING LEVELS IN A PHARMACEUTICAL MANUFACTURING LABORATORY
Proceedings of the 1998 Winter Simulation Conference D.J. Medeiros, E.F. Watson, J.S. Carson and M.S. Manivannan, eds. HEURISTIC OPTIMIZATION USING COMPUTER SIMULATION: A STUDY OF STAFFING LEVELS IN A
More informationTheorem 2.9: nearest addition algorithm
There are severe limits on our ability to compute near-optimal tours It is NP-complete to decide whether a given undirected =(,)has a Hamiltonian cycle An approximation algorithm for the TSP can be used
More informationDesign and Analysis of Algorithms
CSE 101, Winter 2018 Design and Analysis of Algorithms Lecture 17: Coping With Intractability Class URL: http://vlsicad.ucsd.edu/courses/cse101-w18/ Branch-and-Bound (B&B) Variant of backtrack with costs
More informationMETAHEURISTICS. Introduction. Introduction. Nature of metaheuristics. Local improvement procedure. Example: objective function
Introduction METAHEURISTICS Some problems are so complicated that are not possible to solve for an optimal solution. In these problems, it is still important to find a good feasible solution close to the
More informationUsing Machine Learning to Optimize Storage Systems
Using Machine Learning to Optimize Storage Systems Dr. Kiran Gunnam 1 Outline 1. Overview 2. Building Flash Models using Logistic Regression. 3. Storage Object classification 4. Storage Allocation recommendation
More informationx n+1 = x n f(x n) f (x n ), (1)
1 Optimization The field of optimization is large and vastly important, with a deep history in computer science (among other places). Generally, an optimization problem is defined by having a score function
More informationOlmo S. Zavala Romero. Clustering Hierarchical Distance Group Dist. K-means. Center of Atmospheric Sciences, UNAM.
Center of Atmospheric Sciences, UNAM November 16, 2016 Cluster Analisis Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster)
More informationAdministrative. Local Search!
Administrative Local Search! CS311 David Kauchak Spring 2013 Assignment 2 due Tuesday before class Written problems 2 posted Class participation http://www.youtube.com/watch? v=irhfvdphfzq&list=uucdoqrpqlqkvctckzqa
More informationAn evolutionary annealing-simplex algorithm for global optimisation of water resource systems
FIFTH INTERNATIONAL CONFERENCE ON HYDROINFORMATICS 1-5 July 2002, Cardiff, UK C05 - Evolutionary algorithms in hydroinformatics An evolutionary annealing-simplex algorithm for global optimisation of water
More informationMultivariate Analysis
Multivariate Analysis Cluster Analysis Prof. Dr. Anselmo E de Oliveira anselmo.quimica.ufg.br anselmo.disciplinas@gmail.com Unsupervised Learning Cluster Analysis Natural grouping Patterns in the data
More informationUnsupervised Learning. Presenter: Anil Sharma, PhD Scholar, IIIT-Delhi
Unsupervised Learning Presenter: Anil Sharma, PhD Scholar, IIIT-Delhi Content Motivation Introduction Applications Types of clustering Clustering criterion functions Distance functions Normalization Which
More informationSYDE Winter 2011 Introduction to Pattern Recognition. Clustering
SYDE 372 - Winter 2011 Introduction to Pattern Recognition Clustering Alexander Wong Department of Systems Design Engineering University of Waterloo Outline 1 2 3 4 5 All the approaches we have learned
More informationUnsupervised Learning : Clustering
Unsupervised Learning : Clustering Things to be Addressed Traditional Learning Models. Cluster Analysis K-means Clustering Algorithm Drawbacks of traditional clustering algorithms. Clustering as a complex
More informationA Genetic Algorithm for Multiprocessor Task Scheduling
A Genetic Algorithm for Multiprocessor Task Scheduling Tashniba Kaiser, Olawale Jegede, Ken Ferens, Douglas Buchanan Dept. of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB,
More informationINF4820 Algorithms for AI and NLP. Evaluating Classifiers Clustering
INF4820 Algorithms for AI and NLP Evaluating Classifiers Clustering Murhaf Fares & Stephan Oepen Language Technology Group (LTG) September 27, 2017 Today 2 Recap Evaluation of classifiers Unsupervised
More informationConstraint Satisfaction Problems
Constraint Satisfaction Problems Frank C. Langbein F.C.Langbein@cs.cf.ac.uk Department of Computer Science Cardiff University 13th February 2001 Constraint Satisfaction Problems (CSPs) A CSP is a high
More informationCHAPTER 4: CLUSTER ANALYSIS
CHAPTER 4: CLUSTER ANALYSIS WHAT IS CLUSTER ANALYSIS? A cluster is a collection of data-objects similar to one another within the same group & dissimilar to the objects in other groups. Cluster analysis
More informationB553 Lecture 12: Global Optimization
B553 Lecture 12: Global Optimization Kris Hauser February 20, 2012 Most of the techniques we have examined in prior lectures only deal with local optimization, so that we can only guarantee convergence
More information3. Cluster analysis Overview
Université Laval Multivariate analysis - February 2006 1 3.1. Overview 3. Cluster analysis Clustering requires the recognition of discontinuous subsets in an environment that is sometimes discrete (as
More informationContents. List of Figures. List of Tables. List of Algorithms. I Clustering, Data, and Similarity Measures 1
Contents List of Figures List of Tables List of Algorithms Preface xiii xv xvii xix I Clustering, Data, and Similarity Measures 1 1 Data Clustering 3 1.1 Definition of Data Clustering... 3 1.2 The Vocabulary
More informationOperations Research and Optimization: A Primer
Operations Research and Optimization: A Primer Ron Rardin, PhD NSF Program Director, Operations Research and Service Enterprise Engineering also Professor of Industrial Engineering, Purdue University Introduction
More informationINF4820, Algorithms for AI and NLP: Evaluating Classifiers Clustering
INF4820, Algorithms for AI and NLP: Evaluating Classifiers Clustering Erik Velldal University of Oslo Sept. 18, 2012 Topics for today 2 Classification Recap Evaluating classifiers Accuracy, precision,
More informationCHAPTER 3 A FAST K-MODES CLUSTERING ALGORITHM TO WAREHOUSE VERY LARGE HETEROGENEOUS MEDICAL DATABASES
70 CHAPTER 3 A FAST K-MODES CLUSTERING ALGORITHM TO WAREHOUSE VERY LARGE HETEROGENEOUS MEDICAL DATABASES 3.1 INTRODUCTION In medical science, effective tools are essential to categorize and systematically
More informationDERIVATIVE-FREE OPTIMIZATION
DERIVATIVE-FREE OPTIMIZATION Main bibliography J.-S. Jang, C.-T. Sun and E. Mizutani. Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence. Prentice Hall, New Jersey,
More informationIntroduction to Design Optimization: Search Methods
Introduction to Design Optimization: Search Methods 1-D Optimization The Search We don t know the curve. Given α, we can calculate f(α). By inspecting some points, we try to find the approximated shape
More informationHardware/Software Codesign
Hardware/Software Codesign 3. Partitioning Marco Platzner Lothar Thiele by the authors 1 Overview A Model for System Synthesis The Partitioning Problem General Partitioning Methods HW/SW-Partitioning Methods
More informationGeometric data structures:
Geometric data structures: Machine Learning for Big Data CSE547/STAT548, University of Washington Sham Kakade Sham Kakade 2017 1 Announcements: HW3 posted Today: Review: LSH for Euclidean distance Other
More informationGenetic Algorithm for Circuit Partitioning
Genetic Algorithm for Circuit Partitioning ZOLTAN BARUCH, OCTAVIAN CREŢ, KALMAN PUSZTAI Computer Science Department, Technical University of Cluj-Napoca, 26, Bariţiu St., 3400 Cluj-Napoca, Romania {Zoltan.Baruch,
More informationMachine Learning for Software Engineering
Machine Learning for Software Engineering Introduction and Motivation Prof. Dr.-Ing. Norbert Siegmund Intelligent Software Systems 1 2 Organizational Stuff Lectures: Tuesday 11:00 12:30 in room SR015 Cover
More informationCluster analysis. Agnieszka Nowak - Brzezinska
Cluster analysis Agnieszka Nowak - Brzezinska Outline of lecture What is cluster analysis? Clustering algorithms Measures of Cluster Validity What is Cluster Analysis? Finding groups of objects such that
More informationCS 2750 Machine Learning. Lecture 19. Clustering. CS 2750 Machine Learning. Clustering. Groups together similar instances in the data sample
Lecture 9 Clustering Milos Hauskrecht milos@cs.pitt.edu 539 Sennott Square Clustering Groups together similar instances in the data sample Basic clustering problem: distribute data into k different groups
More informationHierarchical Clustering
Hierarchical Clustering Produces a set of nested clusters organized as a hierarchical tree Can be visualized as a dendrogram A tree like diagram that records the sequences of merges or splits 0 0 0 00
More informationN-Queens problem. Administrative. Local Search
Local Search CS151 David Kauchak Fall 2010 http://www.youtube.com/watch?v=4pcl6-mjrnk Some material borrowed from: Sara Owsley Sood and others Administrative N-Queens problem Assign 1 grading Assign 2
More informationMonte Carlo Methods; Combinatorial Search
Monte Carlo Methods; Combinatorial Search Parallel and Distributed Computing Department of Computer Science and Engineering (DEI) Instituto Superior Técnico November 22, 2012 CPD (DEI / IST) Parallel and
More informationComputational Complexity CSC Professor: Tom Altman. Capacitated Problem
Computational Complexity CSC 5802 Professor: Tom Altman Capacitated Problem Agenda: Definition Example Solution Techniques Implementation Capacitated VRP (CPRV) CVRP is a Vehicle Routing Problem (VRP)
More informationINF 4300 Classification III Anne Solberg The agenda today:
INF 4300 Classification III Anne Solberg 28.10.15 The agenda today: More on estimating classifier accuracy Curse of dimensionality and simple feature selection knn-classification K-means clustering 28.10.15
More informationMarch 19, Heuristics for Optimization. Outline. Problem formulation. Genetic algorithms
Olga Galinina olga.galinina@tut.fi ELT-53656 Network Analysis and Dimensioning II Department of Electronics and Communications Engineering Tampere University of Technology, Tampere, Finland March 19, 2014
More informationOverview of Tabu Search
Overview of Tabu Search The word tabu (or taboo) comes from Tongan, a language of Polynesia, where it was used by the aborigines of Tonga island to indicate things that cannot be touched because they are
More informationInteractive segmentation, Combinatorial optimization. Filip Malmberg
Interactive segmentation, Combinatorial optimization Filip Malmberg But first... Implementing graph-based algorithms Even if we have formulated an algorithm on a general graphs, we do not neccesarily have
More informationApplication of fuzzy set theory in image analysis. Nataša Sladoje Centre for Image Analysis
Application of fuzzy set theory in image analysis Nataša Sladoje Centre for Image Analysis Our topics for today Crisp vs fuzzy Fuzzy sets and fuzzy membership functions Fuzzy set operators Approximate
More information3. Cluster analysis Overview
Université Laval Analyse multivariable - mars-avril 2008 1 3.1. Overview 3. Cluster analysis Clustering requires the recognition of discontinuous subsets in an environment that is sometimes discrete (as
More informationINTRODUCTION TO HEURISTIC SEARCH
INTRODUCTION TO HEURISTIC SEARCH What is heuristic search? Given a problem in which we must make a series of decisions, determine the sequence of decisions which provably optimizes some criterion. What
More informationComplete Local Search with Memory
Complete Local Search with Memory Diptesh Ghosh Gerard Sierksma SOM-theme A Primary Processes within Firms Abstract Neighborhood search heuristics like local search and its variants are some of the most
More informationMidterm Examination CS 540-2: Introduction to Artificial Intelligence
Midterm Examination CS 54-2: Introduction to Artificial Intelligence March 9, 217 LAST NAME: FIRST NAME: Problem Score Max Score 1 15 2 17 3 12 4 6 5 12 6 14 7 15 8 9 Total 1 1 of 1 Question 1. [15] State
More informationPROBLEM SOLVING AND SEARCH IN ARTIFICIAL INTELLIGENCE
Artificial Intelligence, Computational Logic PROBLEM SOLVING AND SEARCH IN ARTIFICIAL INTELLIGENCE Lecture 10 Tree Decompositions Sarah Gaggl Dresden, 30th June 2015 Agenda 1 Introduction 2 Uninformed
More information10701 Machine Learning. Clustering
171 Machine Learning Clustering What is Clustering? Organizing data into clusters such that there is high intra-cluster similarity low inter-cluster similarity Informally, finding natural groupings among
More informationChapter 1. Introduction
Chapter 1 Introduction A Monte Carlo method is a compuational method that uses random numbers to compute (estimate) some quantity of interest. Very often the quantity we want to compute is the mean of
More informationINF4820 Algorithms for AI and NLP. Evaluating Classifiers Clustering
INF4820 Algorithms for AI and NLP Evaluating Classifiers Clustering Erik Velldal & Stephan Oepen Language Technology Group (LTG) September 23, 2015 Agenda Last week Supervised vs unsupervised learning.
More informationEXECUTION PLAN OPTIMIZATION TECHNIQUES
EXECUTION PLAN OPTIMIZATION TECHNIQUES Július Štroffek Database Sustaining Engineer Sun Microsystems, Inc. Tomáš Kovařík Faculty of Mathematics and Physics, Charles University, Prague PostgreSQL Conference,
More informationECLT 5810 Clustering
ECLT 5810 Clustering What is Cluster Analysis? Cluster: a collection of data objects Similar to one another within the same cluster Dissimilar to the objects in other clusters Cluster analysis Grouping
More informationModule 1 Lecture Notes 2. Optimization Problem and Model Formulation
Optimization Methods: Introduction and Basic concepts 1 Module 1 Lecture Notes 2 Optimization Problem and Model Formulation Introduction In the previous lecture we studied the evolution of optimization
More informationBased on Raymond J. Mooney s slides
Instance Based Learning Based on Raymond J. Mooney s slides University of Texas at Austin 1 Example 2 Instance-Based Learning Unlike other learning algorithms, does not involve construction of an explicit
More informationUnsupervised Learning
Outline Unsupervised Learning Basic concepts K-means algorithm Representation of clusters Hierarchical clustering Distance functions Which clustering algorithm to use? NN Supervised learning vs. unsupervised
More informationSUITABLE CONFIGURATION OF EVOLUTIONARY ALGORITHM AS BASIS FOR EFFICIENT PROCESS PLANNING TOOL
DAAAM INTERNATIONAL SCIENTIFIC BOOK 2015 pp. 135-142 Chapter 12 SUITABLE CONFIGURATION OF EVOLUTIONARY ALGORITHM AS BASIS FOR EFFICIENT PROCESS PLANNING TOOL JANKOWSKI, T. Abstract: The paper presents
More informationSimulated Annealing. Slides based on lecture by Van Larhoven
Simulated Annealing Slides based on lecture by Van Larhoven Iterative Improvement 1 General method to solve combinatorial optimization problems Principle: Start with initial configuration Repeatedly search
More informationLecture 9: Load Balancing & Resource Allocation
Lecture 9: Load Balancing & Resource Allocation Introduction Moler s law, Sullivan s theorem give upper bounds on the speed-up that can be achieved using multiple processors. But to get these need to efficiently
More informationCombinatorial Search; Monte Carlo Methods
Combinatorial Search; Monte Carlo Methods Parallel and Distributed Computing Department of Computer Science and Engineering (DEI) Instituto Superior Técnico May 02, 2016 CPD (DEI / IST) Parallel and Distributed
More informationTask Description: Finding Similar Documents. Document Retrieval. Case Study 2: Document Retrieval
Case Study 2: Document Retrieval Task Description: Finding Similar Documents Machine Learning for Big Data CSE547/STAT548, University of Washington Sham Kakade April 11, 2017 Sham Kakade 2017 1 Document
More informationUnsupervised Learning. Supervised learning vs. unsupervised learning. What is Cluster Analysis? Applications of Cluster Analysis
7 Supervised learning vs unsupervised learning Unsupervised Learning Supervised learning: discover patterns in the data that relate data attributes with a target (class) attribute These patterns are then
More informationECLT 5810 Clustering
ECLT 5810 Clustering What is Cluster Analysis? Cluster: a collection of data objects Similar to one another within the same cluster Dissimilar to the objects in other clusters Cluster analysis Grouping
More informationA Two-Dimensional Mapping for the Traveling Salesman Problem
Computers Math. Apphc. Vol. 26, No. 12, pp. 65-73, 1993 0898-1221/93 $6.00 + 0.00 Printed in Great Britain. All rights reserved Copyright 1993 Pergarnon Press Ltd A Two-Dimensional Mapping for the Traveling
More informationUniversity of Florida CISE department Gator Engineering. Clustering Part 4
Clustering Part 4 Dr. Sanjay Ranka Professor Computer and Information Science and Engineering University of Florida, Gainesville DBSCAN DBSCAN is a density based clustering algorithm Density = number of
More informationChapter 14 Global Search Algorithms
Chapter 14 Global Search Algorithms An Introduction to Optimization Spring, 2015 Wei-Ta Chu 1 Introduction We discuss various search methods that attempts to search throughout the entire feasible set.
More informationUniversity of Florida CISE department Gator Engineering. Clustering Part 2
Clustering Part 2 Dr. Sanjay Ranka Professor Computer and Information Science and Engineering University of Florida, Gainesville Partitional Clustering Original Points A Partitional Clustering Hierarchical
More informationA GENETIC ALGORITHM APPROACH TO OPTIMAL TOPOLOGICAL DESIGN OF ALL TERMINAL NETWORKS
A GENETIC ALGORITHM APPROACH TO OPTIMAL TOPOLOGICAL DESIGN OF ALL TERMINAL NETWORKS BERNA DENGIZ AND FULYA ALTIPARMAK Department of Industrial Engineering Gazi University, Ankara, TURKEY 06570 ALICE E.
More informationThe Algorithm Design Manual
Steven S. Skiena The Algorithm Design Manual With 72 Figures Includes CD-ROM THE ELECTRONIC LIBRARY OF SCIENCE Contents Preface vii I TECHNIQUES 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 2 2.1 2.2 2.3
More information