DST Project
Extention Request Report


Approved duration of the project   : From November 26, 1998 to November 26, 2001

Requested extension                      : From November 26, 2001 to November 26, 2003 ( 2 years )

Original Objectives ( quoted from the project proposal)

Results achieved so far (in relation to attainment of objectives)

Summary of Progress
For the result accomplished during November, 1998 to May, 2000, please refer our progress report mailed to you earlier. We reproduce here the summary.
Research Accomplishments. Under this project the following five classes of problems have been integrated with the sole aim of linking them to industrial applications. The summary of these classes of problems is given as under.

  1. Genetic Algorithms (GA's) and Economic Dispatch Problem

    2. A survey on Genetic Algorithms has been completed. This includes some hybrid algorithms alongwith Simulated Annealing. The CAI Lab of the Industrial Mathematics Group now has a good glossary of algorithms related to GAs.
    These algorithms have been subsequently used for economic dispatch problems posed as Travelling Salesman Problem and Bus Scheduling Problem. A comparative study (on Bus Scheduling) between GAs and Classical Techniques has also been undertaken.
    Recently, the IMG group is working at the use of neural network algorithms for solving Stiff Differential Equations and Differential Algebratic Equations.
  2. Dynamic Simulation by Differential Algebraic Equations (DAE's)

    3. The following developmental works have been undertaken :
    1. Role of index in numerical solution to the system of DAE's:

      2. When a class of numerical methods say-- backward difference formula -- is applied to the differential algebraic equations, it has been noted that the index of the problem is instrumental in amplifying the truncation error (the amount by which the exact solution does not satisfy the difference scheme) and the algebraic error due to early termination of the iterative methods for solving the resulting system of nonlinear algebraic equations. Further, it is observed that for higher index problems, the algebraic variables can be categorized as index one, index two, index three and higher index. Depending on the types of algebraic variables, special scaling is needed in order to preserve the overall order of convergence.
    2. Automatic index determination:

      3. Most of the existing software packages like DASSAL, RADAU etc. for solving DAEs numerically, requires the supply of index by the user. By adopting a Graph theoretic algorithm of Pantelides, which has been developed for consistent initialization of DAE's, the index has been detected for a wide range of problems.

    Research Outcome
    The mathematical model developed in the project for an industrial slurry high density polyethylene reactor gives rise to a class of discontinuous dynamical systems consisting of DAE's. This problem which is worked out in collaboration with NOCIL results in
    Recently, following problems have been investigated by the members of the IMG:
  3. On-line Optimization: Algorithms and Implementations

    4. On-Line Optimization involves networking of various modules. Each module requires a thorough study of techniques used therein - Data Reconciliation, Parameter Estimation and Error Detection.
    A theoretical study of these modules has been completed. Subsequently, two robust algorithms - Generalized Reduced Gradient and Sequential Quadratic Programming - have been tested on standard examples. They now form part of Resources generated under the Project.
  4. Market Assessment and Forecasting Models

    5. The developmental work undertaken by the group for three different industries Pfizer Ltd., Associated Cement Company Pvt. Ltd. (Thane), A.F. Fergusson & Co., Mumbai resulted in
  5. Computer Aided Geometric Design (CAGD) (Convexity Issues in Surface Designing).

    6.             Under this category, the main objective is to provide user friendly software package on convex surfaces to the designer. The software module developed by our group provides the Graphical User Interface(GUI) to determine whether surface is convex. Graphical User Interface displays the surface along with its Gaussian Curvature plot. If the Gaussian Curvature plot goes below the X-Y plane along Z-axis, then the designer can safely conclude that the surface is non-convex. The GUI uses freely available public domain software package called `Geomview' to display the surfaces. Then if the user wants, the module will search for the convex surface around the given surface.The search algorithm used in the module is heuristic in nature.
                The group has also developed a software which can compute the surface interpolating a given set of points, which makes designers job to provide the input for the prospective surface extremely easy.

                The Software has been written in JAVA programming language. It provides applets to the designer to give the control points of the surface and has control over Geomview camera.The designer is also provided with the facility to indicate the control points by just clicking on the Geomview camera.
    Recently, the group has carried out following :

IIT(IMG) - INDUSTRY MEET
  1. IIT-Industry Meet between NRB and IMG at IIT Bombay on November 20, 1999.

    2. After a few rounds of discussion with NRB ( NRB Bearing ), the IMG organized a meeting on 20th November 1999 at IIT Bombay to discuss the mathematical aspects of the industrial problems pertaining to NRB. A total number of 31 participants out of which seven senior executives from NRB attended the meeting.
    The participants from NRB presented some typical problems faced by their industry. After a due deliberation, eight possible projects (see the report for details) were identified. However, on priority basis the following three projects are taken up by IMG.
  2. IIT - Central Railway Meet

    3. Mr. S. C. Sengupta, Chief Mechanical Engineer, Central Railway briefly described the specific problems with wheel breakage (fracture, bending etc) faced by Central Railway after adopting air breakage system. he concluded his talke with broad outline of areas such as in which Central Railway is looking for some co-operation.
    After detail discussion, the following possible broad based projects are identified with group members.
    1. Mechanism and Optimization
    2. Excess stress including thermal stress
    3. New material characteristic of composite breaks
    4. Statistical Data Analysis
    The group alongwith other faculty members from Metallurgical Engineering Department are working on some time bound viable project with Central Railway.
Study Group Meetings

Study Group Meeting held on 19th February, 2000, in the MS University Baroda, Vadodara.
The main theme of the meeting was Eco-Modeling. A total number of 30 (out of which there were 9 senior scientists and executives from industry) participants drawn from IIT Bombay, MS University, Industry and R & D Organizations in and around Baroda attended the meeting.
After a day long presentation and deliberation, the following two projects were proposed:

Our resource persons in MS Univ. Baroda are working on these two issues and we hope to provide some preliminary results in future. Study Group Meeting held on 11th March, 2000 at IIT Bombay.
The general theme was to understand the types of problems faced by TRDDC, ABB Ltd., Crompton and Greaves Ltd., ADE, TIL etc. A total number of 15 participants from IIT Bombay, MS University Baroda and Industries attended the meeting. Out of 15, there were 7 senior scientists from industries represented the meeting.
The problems presented by the participating industry and R & D organizations were technical in nature. We expect that some of these problems will lead to research and developmental projects at least of the level of M.Sc as well M. Tech.

Industrial Interactions through Individual Contacts.
Apart from these group meetings mentioned above, from time to time, the members of the IMG are interacting with senior executives of various industries, namely; Hindustan Lever Ltd., Cytel Software (India) pvt. Ltd. (Pune), Associated Cement Companies Ltd. (Thane), Pfizer Ltd., A. F. Fergusson & Co. (Mumbai), Hindustan Motors, Godrej Soap.
Some of the major developmental works already completed or in progress are as follows:

After the submission of the report, the group is involved in following two projects :
  1. Organization: Mahindra and Mahindra Ltd., Tractor Division, Mumbai.

    2. Basic Theme: Failure Data Analysis
    Present Status: Ongoing
  2. Organization: Indira Gandhi National Centre for the Arts, New Delhi.

    3. Basic Theme: Identification and Enhancement of Cultural Heritage in Indian Villages- A Statistical Analysis
    Present Status: Ongoing
The group had some discussions with Hindustan Lever Ltd. to explore the possibility of doing a project on crystallization for them. Hindustan Lever is using crystallization as a way of purifying speciality chemicals. The main focus of this proposed project is to obtain good purity in shorter time. Substantial ground work has been done in this direction.
The IMG had Some preliminary discussions with Foxboro in Chennai to explore the possibilities of working on problems of quality control in sugar industry. The objective in this case is to produce the desired crystal size distribution without material loss and in a short time.

WORKSHOPS AND CONTINUING EDUCATION PROGRAMME

Workshop on Mathematical / Statistical Software Packages for Data Analysis, Modeling And Simulation, April 22-24,1999 in the IMG Lab at IIT Bombay.
A total number of 25 from various industries and R \& D Organizations - (NRB, TRDDC, ABB Ltd, Crompton Greaves, ADE, CDAC, TIL, CICFRI, GES, Kirloskar Consultancy, GUIDE, WWFI, ORG-MARG, MSU Baroda) registered for the workshop. The registration was on payment basis.
Objectives : To train the participants in the following aspects:

            The workshop was conducted under Computer Aided Instructional (CAI ) environment using Industrial Case Studies and Algorithms. Professional Development Workshop in Engineering Optimization, February 29th - March 3rd, 2000

            This workshop has been exclusively designed to cater the need of Optimization Techniques in Industry. A novel feature of this workshop was real life problem solving session. The main features were: Constrained and Unconstrained optimization, Linear and Nonlinear Programming, Evolutionary Algorithms (Genetic Algorithms, Simulated Annealing). Most of the techniques were motivated through case studies. The tutorial sessions were supplemented with hands-on experience on the in-house developed educational software ``OPTIMIZE''.
 
            A total number of 13 participants from Industry were trained and this was done on payment basis.

In-House Workshop on Industrial Statistics held in the premises of Sterlite Copper company Ltd, July 22--23, 2000
A two days inhouse workshop was organized in the premises of Sterlite Copper company Ltd. during July 22--23, 2000. About 23 employees participated in the programme. The main focus was on the Sampling and Statistical Quality Control. Starting with basics, a large number of case studies were presented in the workshop.

Proposal for In-House Course on ``Engineering Optimization'' to be conducted in Hindustan Motors Ltd.
On a specific request from the General Manager-QA & TQM, Hindustan Motors Ltd. a proposal on the above In-House Course has been submitted.
The prime objective of the proposal is to share with participants the power of state-of-art Optimization Techniques that are available in the form of Software packages. It is also intended to describe to the participants the systematic approach of optimization which includes the problem definition, its mathematical formulation, selection of a suitable method (algorithm) and a detail analysis of the solution obtained.

CONFERENCE / WORKSHOP PARTICIPATION PERTAINING TO THE PROJECT

Sanjeev Sabnis:
Participated the Workshop on "Modeling Real Systems : a Hands-On First Encounter with Industrial Mathematics", during 27th September-22nd October, 1999 held in ICTP, Trieste, Italy. During his stay there, Dr. Sabnis also participated in the following two projects:

A group of three faculty members ( Amiya Kumar Pani, Sanjiv Sabnis, Alladi Subramanyam and one JRF (Mr. Vishwas Jadav ) from Industrial Mathematics Group attended a series of Lectures on `Stochastic Process and Option Pricing', given by Professor Rajiv Karandikar (ISI, Delhi) in the IGIDR, Goregaon during Nov. 23- Nov. 26,1999.

Ashish Misra (SRA, DST Project)}:
Attended three days short term course on "Optimizing Engineering Design Using Evolutionary Algorithms", held in I.I.T. Kanpur ( Organized by Prof. K. Deb) during 24th Nov. to 26th Nov. 1999.

Kannan M. Moudgalya:

  1. One hour Invited talk on `` Dynamical model of an industrial slurry high density polyethylene reactor'' in the Workshop on Simulation and Computing for Industrial Applications under Technology Appreciation Programme in IIT Madras in February'2000.
  2. Attended, as a representative from IMG, an Industrial Mathematics Workshop organized by Institut Teknologi Bandung in collaboration with University of Twente, Netherlands in Bandung, Indonesia, July 10-14, 2000.} Dr. Kannan worked on the problem of "The effects of increasing the frequency and velocity on the operation and structure of trains" for the company PT Kereta Api. The objective of this work was to increase the throughput of trains between Jakarta and Bandung. A smaller version of this case study was posed in the form of a linear programming problem.
Amiya K Pani:
  1. One hour Invited Bama Charan Das Memorial Lecture on ``Industrial Mathematics: Key to Key Technologies and Its Impact on Mathematical Research and Education in Mathematics'', National Conference on ``Recent Trends in Mathematics \& Computing'' at ``27th Annual Conference of Orissa Mathematical Society'', held in Bhubaneshwar, during 11th-12th March 2000.
  2. One hour Invited talk on `` Particle Size Distribution in Emulsion Polymerization: Some Computational Issues'', in the session `Applied Analysis and Industrial Problems' of the third World Congress of Nonlinear Analysts held in Catania (Italy) during 19th - 26th July, 2000.
Mohan C Joshi:
One hour invited talk on `` Doing Industrial Mathematics via Optimization, DAE, CAGD and Market Forecasting'', in the Third World Congress of Nonlinear Analysts held in Catania (Italy) during 19th - 26th July, 2000.

Sachin B. Patkar:
Presented a talk on ``Applications of Submodular Functions to Algorithms in VLSI CAD'', in the 17th International Symposium on Mathematical Programming-ISMP2000, held in Georgia Institute of Technology, Atlanta, GA (USA) during August 7-11, 2000.

Kirankumar R. Hiremath (SRF), A. K. Pani, \& Kannan Moudgalya :
Presented a talk on ``Semi Implicit Finite Difference Method for Particle Size Distribution in Emulsion Polymerization'' at International Conference on Nonlinaer Systems : Modelling, Simulation and Applications held at Nanded, Maharashtra during December 26-29, 2000.

M. K. Ramaprasad (SRF) \& M. C. Joshi :
Presented a talk on ``Online Optimizaion Algorithums and Implimentations '' at International Conference on Nonlinaer Systems : Modelling, Simulation and Applications held at Nanded, Maharashtra during December 26-29, 2000.}

Ravi Shankar Gautam (SRF) \& S. B. Patkar :
Presented a talk on ``Geometric Modeller for Convex Surfaces'' at International Conference on Nonlinaer Systems : Modelling, Simulation and Applications held at Nanded, Maharashtra during December 26-29, 2000.}

Techniques / Software Developed In-House.

Educational Technology. Resource Persons

             We have a network of resource persons for popularizing industrial mathematics and arranging locally Study Group Meetings at MS University, Baroda, IISc, Bangalore, IIT Madras and IIT Kharagpur etc. One of our resource persons Professor P. R. Parthsarathy from IIT Madras conducted a workshop on Simulation and Computing for Industrial Applications under Technology Appreciation Programme ,held in IIT Chennai Feb'2000. Our representative Professor Kannan Moudgalya attended the meeting and presented a talk.

New Initiatives

Initiatives with Industry

As a byproduct of this project, the group is also actively engaged in the following Research and Development programmes with Indian Industries.

  1. High Density Polyethylene Reactor (Source of Problem; NOCIL)

    2. Apart from modeling and simulation, the group is presently working at a new research and development problem on tracking discontinuities efficiently in DAE modeled by the HDPE.
  2. Emulsion Polymerization (with Hindustan Lever Limited)

    3. Emulsion polymerization is a process of great industrial importance which is used for manufacture of latex paints, adhesives, coating, binders in papers, textile products and synthetic rubber. The mathematical model gives rise to a system of nonlinear ODE, integro-differential equations and single first order nonlinear hyperbolic integro-differential equation. The group has been working on a numerical simulator for the last one and half years. Apart from computational issues, this class of problems gives rise to some interesting theoretical questions related to convergence of numerical schemes, existence and uniqueness results for large time. More importantly, the question of asymptotic behaviour remains a challenge in the field of analysis.
  3. Modeling and Control of a Crystal Size Distribution in an Industrial Crystallizer. (interested Industry: HCL, Foxboro in Chennai)

    4. The first part of the project involves modeling the system. This yields a mathematical model consisting of a first order hyperbolic PDE (population balance of the crystal size distribution) coupled through its boundary condition with an ODE (mass balance of concentration) to which a control can be applied. Solving the PDE yields a nonlinear hereditary system for which standard control theory can be applied. The output quality (shape of the crystal size distribution) and yield (volume of crystals produced) depends strongly on the concentration evolution. The general case (which is nonlinear and where the control is to yield a concentration which is optimal over a range of time, instead of at some fixed time which is the usual case) is not yet documented in literature from a control point of view.
  4. Online Optimization : Algorithms and Implementation

    5. It has been observed that in Error Detection Module, one can use Neural Network Algorithms in conjunction with Genetic Algorithm to obtain faster and more accurate convergence. It is perceived that this approach will lead to some interesting problems involving differential equations, optimization and numerical analysis--culminating to new modular development techniques pertaining to On-Line Optimization.
  5. Financial Engineering

    6. The main focus is on the Numerical Simulation of Option Pricing Models and validating it using data from Indian Financial Markets. By adopting the existing models to compute the volatility (roughly the market trend), some experiments were conducted on the data obtained from some Indian companies and the option pricing using Black -Scholes Model has been computed with the help of finite difference schemes.
  6. Bus Scheduling

    7. It concerns with the problem of scheduling a fleet of buses to a given set of trips encountered by BEST in Mumbai. As a preliminary step, a single depot vehicle scheduling problem has been formulated as Zero One integer linear programming problem and is solved using primal-dual algorithm. The model is tested on real world data obtained from BEST.
Collaborative Research with Academic Institutes.
  1. Interaction with Foreign Universities

    2.             Professor Mohan C Joshi visited University of Kaiserslautern, Germany and University of Twente, Netherlands during May-June, 1999 to explore the possibility of collaborative research programmes between IMG, Bombay and these universities. Both institutions are receptive to the idea of collaborative programmes and efforts are on progress to come up with a joint programme. It may be mentioned that University of Kaiserslautern has a very strong group on Industrial Mathematics and is one of the core universities among European Consortium on Mathematics for Industry ( ECMI). A linkage with ECMI will not only help IMG in generating solutions for industry based problems but might also lead to new academic programmes involving both institutions-IIT Bombay and ECMI Universities. As a result of the IMG effort towards cooperation, the following students worked with members of IMG for their dissertation.
    1. Jitendra V. Kadam, a M. Tech. student in Chemical Engineering Department of IIT Bombay spent a year in the Process Technology, RWTH, Univ. Aachen (Germany) for his dissertation on `Index Analysis and Adaptive Refinement in the Multiscale Dynamic Optimization', see for details, M. Tech. Project Report 2000-01.
    2. Frederik H.W. Litjens, a five year integrated Master of Science student in Applied Mathematics, Department of Systems, Signals and Control from the University of Twente, Netherlands, worked with the members of IMG for his final year project work on  Modeling and control of a crystallization system.
  2. Generation of Possible Research Projects

    3. EU-Asia Research Projects. A joint project entitled `Strengthening the Application of Mathematics in Industry and Society'  was generated in collaboration with University Twenty (Netherlands), University of Kaiserslautern (Germany), and Institut Teknologi Bandung (Indonesia). The main objectives of this proposal are:
APPLICATION POTENTIAL

LONG TERM

IMMEDIATE Project Progress Indictors: Clear statement of the objectives that have not been achieved so far but will be achieved during the extension period :
       

      Back to top