Search Techniques for Multi-Objective Optimization of Mixed-Variable Systems Having Stochastic Responses

Abstract

A research approach is presented for solving stochastic, multi-objective optimization problems. First, the class of mesh adaptive direct search (MADS) algorithms for nonlinearly constrained optimization is extended to mixed variable problems. The resulting algorithm, MV-MADS, is then extended to stochastic problems (MVMADS-RS), via a ranking and selection procedure. Finally, a two-stage method is developed that combines the generalized pattern search/ranking and selection (MGPS-RS) algorithms for single-objective, mixed variable, stochastic problems with a multi-objective approach that makes use of interactive techniques for the specification of aspiration and reservation levels, scalarization functions, and multi-objective ranking and selection. A convergence analysis for the general class of algorithms establishes almost sure convergence of an iteration subsequence to stationary points appropriately defined in the mixed-variable domain. Seven specific instances of the new algorithm are implemented and tested on 11 multi-objective test problems from the literature and an engineering design problem.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 2007
Accession Number
ADA472308

Entities

People

  • Jennifer G. Walston

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies
  • Human Systems
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Aircraft Design
  • Algorithms
  • Central Processing Units
  • Computer Programming
  • Engineering
  • Evolutionary Algorithms
  • Experimental Design
  • Fuzzy Logic
  • Genetic Algorithms
  • Graphical User Interface
  • Heuristic Methods
  • Mach Number
  • Multiobjective Optimization
  • Optimization
  • Random Variables
  • Systems Engineering

Readers

  • Operations Research