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Fast Computing in Global Optimization: Sequential


Fast Computing in Global Optimization:

Sequential and Parallel Environment


Participants and Contacts

Delft University of Technology

Nizhny Novgorod State University

Full list of participants


Project Summary

The project is aimed at researching a wide class of time-consuming scientific and engineering optimization problems in order to formulate a uniform approach to their effective solution in the environment of high-performance multiprocessor computers including cluster systems built from standard computer elements. The theoretical work within the framework of the project includes:

  • Forming a class of mathematical decision making problems which model many important scientific and engineering applications and which can be analyzed with the use of uniform algorithmic approach.
  • Development and theoretical study of a uniform scheme of parallel computations, within the framework of which effective numerical methods for the formulated class of problems will be offered.
  • Establishing the conditions of convergence, efficiency, reliability, non-redundancy and scalability for the methods developed.

The practical part of the project contains:

  • Specifying structure of the multiprocessor system and environment necessary for development of the application software for parallel computations.
  • Developing the software for implementation of the methods proposed and conducting a number of computing experiments to estimate the efficiency and reliability of the proposed schemes of computations in multiprocessor systems.
  • Solving practical optimization problems from different areas of applications (CAD/CAM, mechanics, pattern recognition, etc.)

The project implementation includes the following principal tasks and corresponding stages:

  1. Forming a class of mathematical problems to be studied within the framework of the project;
  2. Elaborating efficient sequential and parallel algorithms for solving the problems based on the fundamental method of dimensionality reduction and multistage simulation approach;
  3. Theoretical substantiation of the computational methods and schemes proposed.
  4. Development of a new approach to parallel computations (without a single control center), characterized by high scalability and reliability;
  5. Software development and realization of computing experiments to estimate the efficiency of the proposed schemes of computations on multiprocessor systems.
  6. Solving applied optimal decision making problems.


Computational methods, decision making, global optimization, multiprocessor systems, parallelism, efficiency, reliability


Content of project

- Problem definition and central hypothesis of project

The essence of the project is to develop new computational schemes that can be used effectively in high-performance (including multi-processor) computer systems for solving problems of global optimization. Application of the developed method of global optimization to real-life problems.

- Method of approach:

The approach to the development of new computation schemes consists of applying and further developing the new fundamental method for reduction of complexity of the problem (based on the Peano curve type mapping, nested optimisation scheme, index method, etc.), developed by the Russian participants of the project in the problems of numerical analysis, in combination with multistage simulation approximation based approach developed by the Netherlands research group. As a result of application of the essentially new reduction schemes, the multidimensional problem with constraints is reduced to a family of one-dimensional subproblems with no constraints. It is important to note that each problem of this family serves to obtain the required solution of the initial multidimensional problem; at the same time, the process of getting the estimates can be accelerated significantly by means of solving simultaneously (in parallel) all or some part of the problems of the family, provided that the search information obtained during computations is shared. As a result of such an approach, the multiprocessor system used for organizing the computations can be inhomogeneous; its processors can have different performance and their quantity can change during the computations.

- Objectives of the project:

The main objectives of the project consist in the development of an integrated system of mathematical models, effective and reliable sequential and parallel methods and software tools for solving time-consuming decision making problems in different application areas and the definition of practical methods for constructing high-performance parallel computing systems with architecture adapted to the class of optimisation problems investigated.

Adapting of the developed system to be applicable to real-life optimization problems using the approximation concepts.

Application of the developed system to some real-life optimization problems in mechanics and medical diagnostics.


Significance and innovative aspects of the project

Significance and innovative aspects of the project consist of:

  • designing a new dynamic model of optimal choice generalizing known statements of decision making problems;
  • developing new unified computational scheme based on the methods for efficient parallel analysis of complex models with multi-extremes functionals that require searching global optimal solutions in complex regions and allow to investigate new classes of models with discontinuous criteria and partially defined constraints;
  • theoretical validation of the proposed methods;
  • developing inhomogeneous architecture of multiprocessor systems adjusted to efficient solving problems under consideration;
  • elaborating new software for high-performance multiprocessor systems;
  • solving applied optimisation problems in mechanics and medical diagnostics.