CS AI OR CS 3 Integration of Artificial Intelligence & **Operations** **Research** Techniques AI Representations Constraint Languages Logic Formalisms Object-Oriented Prog. Bayesian Nets Rule Based Systems Tools Constraint Propagation Systematic Search Stochastic Search Pros / Cons Rich Representations Computational Complexity OR Representations Mathematical Modeling Languages **Linear** & Non-**linear** (**In**)Equalities Tools **Linear** **Programming** Mixed-Integer Prog. Non-**linear** Models Pros / Cons More Tractable (LP) Primarily/

Bjørner Microsoft **Research** Tutorial Contents Bit-vector decision procedures by categories Bit-wise **operations** Vector Segments Bit-vector Arithmetic Fixed size Parametric, non-fixed size Some Bit-precise Microsoft Engines: -PREfix: The Static Analysis Engine for C/C++. -Pex: **Program** EXploration for./**program** variables. A matrix, b vector of coefficients [0.. 2 m -1] When at ℓ 2 : y is 0. c contains number of bits **in** x. ℓ 0 : y x; c 0; ℓ 1 : while y != 0 do [ y y&(y-1); c c+1 ] ℓ 2 : States are **linear**/

find the new bfs with the better objective function value. Go back to step 3. **Operations** **Research**, Wayne L. Winston **Linear** **Programming** – Simplex Method Review Simplex Handouts **Linear** **Programming** – Simplex Method Minimization Problems: Min Z = cx (-) Max Z = -cx /+ 2x2 < 5 2x1 - 3x3 > 10 x1, x2, x3 > 0 **Linear** **Programming** – Simplex Method: Computational Problems Breaking Ties **in** Selection of Non-Basic Variable – if tie for non-basic variable with largest relative profit ( ), arbitrarily select incoming/

simultaneous consideration of Process Integration and Control). The Centre is also an important contributor **in** the area of integration and **operation** of batch processes Current **research** **in** Process Integration Integrated batch processing Design and management of integrated Supply Chain processes Uncertainty and **operability** **in** process design Formulation of mathematical **programming** models to address problems **in** process synthesis and integration Consortium: Process Systems Engineering (PSE) with 17 members (2003/

**in** terms of vectors, vector spaces, and **linear** **operators** Example **Linear** ANA (LANA) : **Linear** Conjugate Gradients ANAs can be very mathematically sophisticated! ANAs can be extremely reusable! **Linear** Conjugate Gradient Algorithm Types of **operations** Types of objects **linear** **operator**/code to spit them out. More **research** end. Stratimikos Phalanx Field Manager Sacado/Package leads: Mike Heroux, Mark Hoemmen (many developers) A Simple Epetra/AztecOO **Program** // Header files omitted… int main(int argc, char *argv[]) { /

**Linear** **Programming** Stochastic **Programming** Forecasting Integer **Programming** Decision Analysis Nonlinear **Programming** Game Theory **Operations** **Research** Modeling Toolset 311 Queueing Theory 310 Markov Chains PERT/ CPM Network **Programming** Dynamic **Programming** Simulation Markov Decision Processes Inventory Theory **Linear** **Programming** 312 Stochastic **Programming** Forecasting Integer **Programming** Decision Analysis Nonlinear **Programming**/function Constraints Deriving solutions A common theme **in** O.R.: Search for an optimal /

Machines Reachability Algorithms Theory of Nested Words Fair Cycle Detection Algorithms **Linear** Temporal Logic CaRet Theory of Nested Trees Fixpoint Logic NT-mu Nested Trees / and modalities for concatenation? Proposal: NT-mu. <>f f **Operations** on Summaries local s u s Formulas sets of summaries /with Chaudhuri and Madhusudan; CAV’06) Available on my webpage **Research** **in** Software Model Checking Convergence of **program** analysis and model checking Efficient ways for property-guided abstraction/

TO LARGE-SCALE FACILITIES thereby ensuring Germanys international top position **in** basic **research** [Edelgard Bulmahn is the minister for **research**. There are four paragraphs **in** which she says how important basic **research** **in** science is for Germany. I dont have time to / the U.S. **program** be a high-energy, high-luminosity, electron-positron **linear** collider, wherever it is built **in** the world. This facility is the next major step **in** the field and should be designed, built and **operated** as a fully international/

50 degrees C –The performance specifications of flight units shall be achieved over the **operational** temperature range of –10 to +25 degrees C Radiation Susceptibility –The /run GCFEv8 Submitted Aug 02 –Output buffer gain increase to get 2.5V **linear** output range –Add circuit for automatic preamp reset actuation. Modify Autoreset trigger gating /CALROWCALROW DAC **Programming** (Packaged **in** 80 pin QFP, 14 mm sq) GLAST LAT Project CAL Peer Design Review, Mar 17-18, 2003 J. Ampe Naval **Research** Lab Washington /

**Research** **Research** goals Related work Algorithms Conclusion Results Demo Bibliography Non **Linear** Filters topics Unified approach - definitions What is a window Example of Sliding window Types of non **linear** filters Neighborhood & Estimation Non **linear** filters examples Image enchantment Histogram equalization Other Unification approach definition Filters work **in** a moving window. For each window a filter generate output value by means of a certain estimation **operation**/“ High Level **Programming** for Real Time FPGA/

with their iterative processes (i.e., the repeated performance of a relatively simple set of **operations**) Optimization **in** Engineering Design Georgia Institute of Technology Systems Realization Laboratory 13 The Computer and **Linear** **Programming** Consider the case of **Linear** **Programming** (more **in** later lectures): The first large scale computer became a practical reality **in** 1946 at the University of Pennsylvania. This was just one year before the development of/

Roger Jones Jim Lewandowski Roger Miller Juwen Wang Nicoleta Baboi Gordon Bowden Technical Division/Accelerator **Research** Departments A & B SLAC Annual **Program** Review April 9-11, 2003 27 Mission We design, engineer and test accelerator structures for future **linear** colliders **operating** under extremely high gradient conditions with superior properties **in** higher modes suppression. The activities Accelerator Theoretical Studies. Simulation and Computer Aided Accelerator Design. Mechanical/

CDC Preparedness Modeling Unit Industrial/Systems Engineer –**Linear** **Programming** –Simulation/Queuing –Logistics –Other **research** Proposed issues “Don’t need to model” projects **Linear** **Programming** **Linear** Integer and binary Quadratic Conic Mixed **Linear** **Programming** Probably the number one **operations** **research** tool used Great for scheduling, determine product mix, and other things How is it being used **in** relationship to vaccinations? Scheduling Vaccine Age Birth 1 mo 2 mos 4 mos Hepatitis B/

Related Approaches Potential to Accelerate MP & NonMP **Research** Conclusion 33 1. Algorithms, **Programming** Languages, Compilers, **Operating** Systems, Architectures, Libraries, … not ready for 1000/-tuner search HW and algorithm space “Multiprocessor **Research** Watering Hole” ramp up **research** **in** multiprocessing via common **research** platform innovate across fields hasten sea change/ 8 Structured grid 3 using Adaptive Mesh Refinement 2 Sparse **linear** algebra 2 Particle methods 5 TBD: Ray tracer, Speech /

SMT Solvers; Lahiri, Qadeer; POPL ‘08 –Reachability A Numerical Abstract Domain Based on Expression Abstraction and Max **Operator** with Application **in** Timing Analysis; Gulavani, Gulwani; CAV ‘08 –Non-**linear** **operators** 41 Logic: References Identify a class of **programs** that make use of domain-specific constructs. –E.g., **Programs** manipulating bit-vectors, strings. Develop a language of facts with following properties: –Can describe useful properties of those/

the maximum or minimum of a function for a region defined by inequalities How is **Linear** **Programming** used **in** the Real World? **Linear** **programming** is used whenever one is interested **in** maximizing profit and minimizing costs. Fields that use **linear** **programming** include: – Business & Management – Telecommunications – Math & Industrial Engineering (**Operations** **Research**) – Manufacturing &Transportation – Scheduling **Linear** **Programming** Procedure 1. Define the Variables 2. Write a system of inequalities 3. Graph the/

told to: Mathematica : Matrix **operations** Mathematica: Menus exist but are /**in** other fields Math 317 is a first **linear** algebra course for math majors and emphasizes proof writing but is matrix oriented and uses technology Math 471 is numerical **linear** algebra Teaching **Linear** Algebra **Research** US-NSF **Research** Experiences for Undergraduates (REU) **program** ISU combinatorial matrix theory **research** group US-NSF **Research** Experiences for Undergraduates (REU) **program** ISU combinatorial matrix theory **research**/

decision problem under the limiting factor of limited resources Modern technological advance growth of scientific techniques **Operations** **Research** (O.R.) recent addition to scientific tools O.R. new outlook to many conventional / INTRODUCTION TO **LINEAR** **PROGRAMMING** Today many of the resources needed as inputs to **operations** are **in** limited supply. **Operations** managers must understand the impact of this situation on meeting their objectives. **Linear** **programming** (LP) is one way that **operations** managers can determine/

.” – Kimball and Morse OR – Industry Scope Defense **Operation** - **Linear** **Programming**, Game theory, and inventory models etc. Industry - decision trees, inventory model, **Linear** **Programming** model, Transportation model, Sequencing model, Assignment model and replacement models Planning for Economy - All major models Agriculture - All major models Traffic - queuing theory Hospitals queuing theory OR - Phases of solving Common models **in** OR **Linear** **Programming** Model - used for resource allocation when the resources/

Blue Cool) 01/21/2008CS267 - Lecture 1 29 Graph Algorithms Dynamic **Programming** Dense **Linear** Algebra Sparse **Linear** Algebra Unstructured Grids Structured Grids Model-view controller Iterator Map reduce Layered systems /**programming** models (software) and tools. Some important parallel applications and the algorithms Performance analysis and tuning Exposure to various open **research** questions 80 Extra slides 01/21/2008CS267 - Lecture 1 81 Transaction Processing Parallelism is natural **in** relational **operators**/

and coupled modes Model validation and refinement 50 2006 Wind **Program** Peer Review Acknowledgements Walt Musial & Sandy Butterfield of NREL for leading US offshore wind **research** **program** Erik Withee of US Navy for initiating study at MIT/ of motion True **Linear** Hydrodynamic Representation **in** the Time Domain: –satisfy the **linearized** governing BVPs exactly without restriction on platform size, shape, or manner of motion Response Amplitude **Operator** (RAO) 81 2006 Wind **Program** Peer Review Thesis Statement /

published/released –LINPACK Users Guide »Appendix: 17 machines PDP-10 to Cray-1.... 9 Basic **Linear** Algebra Subprograms BLAS 1973-1977 Consensus on: –Names –Calling sequences –Functional Descriptions –Low level **linear** algebra **operations** Success results from –Extensive Public Involvement –Careful consideration of implications A design tool software **in** numerical **linear** algebra Improve readability and aid documentation Aid modularity and maintenance, and improve robustness of software/

**in** britain came to known as Blacket circus.(radar OR Unit **in** gun site). The US military team named **operational** analysis,**operational** evaluation, **operational** **research**, system analysis,system evaluation, system **research** & management. But military team were dealing with **research** on (military) **operation**, the work of this team of scientists named as **Operation** **Research** **in**/ C.R.Krishna Prasad, BIT Bangalore-4 Guidelines for formulating **Linear** **Programming** model i) Identify and define the decision variable of the /

MV quantum computing. Here we include the absolute minimum amount of formalism sufficient to start independent software development by people who have sufficient background **in** EDA tools and algorithms such as search or evolutionary **programming** Quantum Circuits **In** terms of logic **operations**, anything that changes a vector of qudit states to another qudit vector satisfying measurement probability properties can be considered as a quantum/

potato chip samples for saltiness vs. potato complex intensity where 18 of 20 samples exhibit a strong **linear** trend between the two attributes 52 To summarize, after the first three steps of the example sample /**in**-plant **program** is considered a routine **program** requiring little improvements once it is **in** **operation**. 181 However, a sensory coordinator needs to expand his or her knowledge **in** panel training and leadership, data analysis, and other sensory areas related to the type of evaluation and **research**/

Madrid, U Manchester, U Umeå, U Wuppertal, U Zagreb **Research** Institutions INRIA, LBL Industrial Partners (predating ParLab) /**linear** algebra 4:00 – 4:25 Jason Riedy - Iterative Refinement **in** **linear** algebra 4:25 – 4:30 Break 4:30 – 5:00 Tony Keaveny - Medical Image Analysis **in** PAR Lab 5:00 - 5:30 Ras Bodik/ Armando Solar-Lezama - **Program** synthesis by Sketching 5:30 - 6:00 Vasily Volkov - **Linear**/tasks using decomposition (partitioning) and copying **operators** Goal: Remove chance for concurrency /

**in** the previous slide) and take some **operations** on the sets that preserve the representability. For example, affine image of a set is also SOCP representable. Not easy, but if you become familiar, very useful. 21 Journey to New Areas of Optimization SOCP: Robust LP Robust **Linear** **Programming** **In**/master SDP, there will be very interesting problems waiting for you! **Research** Topics As **in** the case of SOCP, most of the **research** focuses on the applicability of SDP. Besides engineering applications, /

for Approximating Piecewise **Linear** Concave Functions from Sample Gradients,” **Operations** **Research** Letters, Vol. 31, No. 1, pp. 66-76 (2003). »Powell, W.B., A. Ruszczynski and H. Topaloglu, “Learning Algorithms for Separable Approximations of Stochastic Optimization Problems,” Mathematics of **Operations** **Research**, Vol 29, No. 4, pp. 814-836 (2004). Convergence results for storage problems »J. Nascimento, W. B. Powell, “An Optimal Approximate Dynamic **Programming** Algorithm for/

PSE) with 17 members (2003) including **operating**, engineering & contracting companies, software vendors Current **research** **in** Process Integration Integrated batch processing Integrated batch processing Design and management of integrated Supply Chain processes Design and management of integrated Supply Chain processes Uncertainty and **operability** **in** process design Uncertainty and **operability** **in** process design Formulation of mathematical **programming** models to address problems **in** process synthesis and integration/

-0025-9 16.Linderoth, J.T., Ralphs, T.K.: Noncommercial software for mixed-integer **linear** pro-gramming. **In**: J. Karlof (ed.) Integer **Programming**: Theory and Practice, **Operations** **Research** Series, vol. 3 (2005) 17.Lougee-Heimer, R.: The Common Optimization INterface for **Operations** **Research**: Pro-moting open-source software **in** the **operations** **research** community. IBM Journal of **Research** and Development 47(1), 57–66 (2003) 18.Martins, A.X., Souza, M.C/

decisions regarding the best utilization of war materiel. After the war, the ideas advanced **in** military **operations** were adapted to improve efficiency and productivity **in** the civilian sector. This chapter will familiarize you with the basic terminology of **operations** **research**, including mathematical modeling, feasible solutions, optimization, and iterative computations M ODELS **Linear** **Programming** Typically, a single objective function, representing either a profit to be maximized or a/

GCCBA-42, CHANDIGARH EMAIL : MKBHAMBU@HOTMAIL.COMMKBHAMBU@HOTMAIL.COM MOBILE : +919888237733 SYLLABI PAPER 6 (ii) : **OPERATIONS** **RESEARCH** UNIT-I **Operations** **Research**—Meaning, Significance and Scope. Introduction to **Linear** **Programming**, Formulation of **Linear** **Programming**—Problem, Graphical Method,Simplex Method.Duality **in** **Linear** **Programming**, Definition of Dual Problem, General Rules **in** Converting any Primal into its Dual, Transportation problem, Assignment problem. UNIT-II Inventory – Types, Nature/

and **operational** tools for obtaining high-performance discharges **in** NSTX-U FY2015 **Research** Milestones No XPs **in** FY2015 emphasize analysis/modelling, **research** prep FY2015 **Research** Milestones shifted to FY2016 largely unchanged 9NSTX-U FY2015 Q4 **Program** Report NSTX/ Heating and Current Drive Topical Science Group **Research** Highlights 20NSTX-U FY2015 Q4 **Program** Report Reminder: Suppressed Li erosion and trapping at target observed **in** MAGNUM-PSI **linear** plasma device Mixed-material effect reduces erosion due/

MARES **operational** roles and responsibilities between ESA and NASA. PLOT Sept. 2, 2009 Human **Research** **Program** (HRP) Stuart Johnston **Operational** Hardware Configuration VIF MARES Main Box Pantograph Chair PLOT Sept. 2, 2009 Human **Research** **Program** (HRP) Stuart Johnston -301 -302 -303 **Linear** Adapter/motor box (chair and short arm removed for clarity) 12.Restow -301 on-orbit bag and **Linear** Adapter **in** front of items shown **in** step 10 13.Rotate Short Arm and Chair into Place (as shown) 14.Arrange Shoulder Structures /

**operating** procedure and to rectify any flaws **in** the solutions that are then uncovered. **Linear** **programming** uses a mathematical model to describe the problem. ” **linear**” means that all the mathematical functions **in** this model are required to be **linear** functions. “**programming**“ does not refer here to computer **programming** ; it refers to planning. Thus, **linear** **programming**/ do not exceed the maxima indicated by the market **research**. (a) Formulate a **linear** **programming** model for this problem. (b) Use the graphical/

survey on non-**linear** services –Interviews –Desk **research** –Extensive internal discussion within the consortium. 6.2 **Operational** Procedures Two distinct legal scenarios within which **operational** procedures can exist: –1) Self-declarations from service providers –2) Independent evaluation For **linear** channels: Self-declarations are supplied by broadcasters, and are then verified by internal evaluation (as seen **in** the work on **linear** **programming** **in** this study) For non-**linear** services: Independent evaluation/

**Linear** **Programming** to accompany **Operations** **Research**: Applications and Algorithms 4th edition by Wayne L. Winston Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc. 2 3.1 What Is a **Linear** **Programming** Problem? **Linear** **Programming** (LP) is a tool for solving optimization problems. **Linear** **programming** problems involve important terms that are used to describe **linear** **programming**/ and negative values, the decision variable x i is unrestricted **in** sign (often abbreviated urs). 9 Ex. 1 - Solution /

3.13 that is achieved. Thus, for any given fraction achieved, the total annual cost would be roughly that fraction of the corresponding quantity **in** Table 3.14. 重庆大学制造工程研究所副所长 博士 重庆大学制造工程研究所副所长 杨育 博士 2002 Introduction to **Operation** **Research** Formulation as a **Linear** **Programming** Problem. This problem has six decision variables x j, j=1, 2,..., 6, each representing the use of one of the three abatement methods for one of/

**in** mobile banking Innovation **in** retail payments The impact of social media Data protection and privacy Managing risk and compliance 2013 Signature **Research** Delivering innovation **in** payments: **operational**/ **linear** **operations** rather than acting as an integrated **linear** and multi-platform business management system hub. **In** 2013, Ovum will be assessing developments **in**/while maintaining regulatory compliance, and how this can exploited for **programming** decisioning and ad spot innovation. Analysts Adrian Drury Richard /

of model is used to address the general problem of allocating limited resources among competing activities **in** a best possible (optimal) way. All mathematical functions **in** **linear** **programming** models are **linear**. We now look at some simple examples of **linear** **programming** models that can be solved graphically. 456/556 Introduction to **Operations** **Research** 3.1: Prototype Examples 4 Example 1 (File Cabinets) An office manager needs to purchase new/

4 Basic **operation** on vectors **in** Rn A Gentle Intro to SVMs **in** Biomedicine Basic **operation** on vectors **in** Rn November 2009 5. Dot product (continued) Property: **In** the classical/ the underlying quadratic **program** may not be solvable. Popular kernels A kernel is a dot product **in** some feature space: Examples: **Linear** kernel Gaussian kernel Exponential/ Lack of parametric statistical significance tests Power size analysis and **research** design considerations are less developed than for classical statistics Bibliography /

(Borning) Logic **Programming** unification --> constraint solving **Operations** **Research** NP-hard combinatorial problems Let’s look at this 11 KNOWLEDGE REPRESENTATION & REASONING Integer **Programming** (IP) Consider the manufacture of television sets. A **linear** **programming** model might give/ REPRESENTATION & REASONING Solving CSPs There are two general approaches to solving CSPs that are used **in** practice Systematic Search Explore systematically the space of all assignments systematic = every valuation/

Management Science **Operations** **Research** Decision Science **Operations** Management Industrial Engineering Industrial Management Systems Management Systems Science It has its early roots **in** World War II and is flourishing **in** business and industry with the aid of computers. What is OR? Cont’ Origins **in** the 1940s with the management of the Cold War armed forces. Currently used **in** a very broad range of organizations and systems. The **linear** **programming** model/

**in** Spacesuits Yiteng (Arden) Huang WeVoice, Inc., Bridgewater, New Jersey, USA arden_huang@ieee.org 9/2/2010 Phase I feasibility **research**: Jan. 2008 – July 2008 About the Project Financially sponsored by the NASA SBIR (Small Business Innovation **Research**) **program** Phase I feasibility **research**/ EVA **operations**, which/**Linear** Wiener Filter New filter for SCNR: Error signal: Widely **linear** MSE: Then the widely **linear** Wiener filter or MVDR type of filters can be developed. Section 4 Problem Identification and **Research**/

University Press, 1998. G. Infanger, Planning under uncertainty -- Solving large-scale stochastic **linear** **programs**, Boyd & Fraser, 1994. W.T. Ziemba, R.G. Vickson (eds.), Stochastic Optimization Models **in** Finance, World Scientific (1975, reprinted 2006). Series of Handbooks **in** **Operations** **Research** and Management Science, Elsevier, includes several relevant volumes (e.g., Vol. 10, 2003, “Stochastic **Programming**”, A. Ruszczynski, A. Shapiro (eds.), Vol. 9, 1995, “Finance”, Jarrow, Maksimovic, Ziemba/

2, F=ma, … OR-1 2014 9 Nature of OR “**research** on **operations**” Applied mathematics + computer science + management Models : Deterministic models ( 확정적 모형, OR-I) Stochastic models ( 확률적 모형, OR-II) Needed background: Algebra, calculus, discrete mathematics, probability, statistics, data structure, algorithm, data base, **programming** skills, …) Important thrusts **in** early stages 1. Technical progress (Simplex method for **linear** **programming**, Dantzig, 1947) 2. Invention of computer and PC OR-1 2014/

Real world problem Model Real world solution Analysis Abstraction Interpretation Assessment 11.05.2015 10 **Operations** **Research** Techniques **Linear** ProgrammingLinear **Programming** Dynamic ProgrammingDynamic **Programming** Integer ProgrammingInteger **Programming** Nonlinear programmingNonlinear **programming** Goal ProgrammingGoal **Programming** Network ProgrammingNetwork **Programming** The principal phases for implementing OR **in** practice Definition of the problem 1.Decision alternative definition 2.Objective determination 3/

(SCK.CEN) (2009-2010) A fuzzy multi attribute decision making approach for nuclear safeguards information management Ph.D. **in** ITU Industrial Engineering programme (2008) Modeling supply chain network using possibilistic **linear** **programming** and an application **Research** interests **Operations** **Research** (Mathematical **programming**) Supply chain management Fuzzy decision making 16 Prof. Dr. Y. İlker Topcu Office address Management Faculty C301, Maçka, Istanbul Phone (212) 293 1300 /2069 office/

**Research** Innovative-Teaching by Using Current **Research** **in** Teaching !! Specialized Courses & **Programs** C. Courses “ Environmental Engineering & Technology” Based on Case- Studies Invited Guest- Seminars & Lectures Project Based Learning -PBL D. M.Eng / M.Sc. & **Research** Collaboration Inter/ Multi-DICPLINARY /Inter-Faculty/Inter-Departmental **Research** (M.Eng /M.Sc) **Program** **in**/the optimal maximum power **operating** point. MPPT controller is/the main features **in** discrimination between **linear** and non-**linear** arc faults. /

-Point Solver for Stochastic **Programming** (PIPS) Convex QP SAA SP problems Input: users specify the scenario tree Object-oriented design based on OOQP **Linear** algebra: tree vectors, tree matrices, tree **linear** systems Scenario based parallelism –tree nodes (scenarios) are distributed across processors –inter-process communication based on MPI –dynamic load balancing Mehrotra predictor-corrector IPM 18 Tree **Linear** Algebra – Data, **Operations** & **Linear** Systems Data –Tree vector/

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