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Efficiently handling constraints in mixed-integer nonlinear programming problems using gradient-based repair

Daniel Molina-Pérez1, Edgar Alfredo Portilla-Flores2, Efrén Mezura-Montes3

  • 1Centro de Innovación y Desarrollo Tecnológico en Cómputo, Instituto Politécnico Nacional, Ciudad de Mexico, México.

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|June 10, 2024
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Summary
This summary is machine-generated.

A new gradient-based repair method (G-DEmi) effectively solves mixed integer nonlinear programming (MINLP) problems by fixing infeasible solutions. This approach enhances evolutionary algorithms for complex optimization tasks.

Keywords:
Differential evolutionGradient-based repair methodInteger constraint handlingMINLP problemsReal-world optimization

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Area of Science:

  • Optimization
  • Computational Mathematics
  • Algorithm Development

Background:

  • Mixed integer nonlinear programming (MINLP) problems involve both continuous and discrete variables with nonlinear functions.
  • Integer variables introduce discontinuities, creating multiple feasible subproblems that challenge standard evolutionary algorithms (EAs).
  • EAs struggle with constraints, often generating many infeasible solutions for MINLP.

Purpose of the Study:

  • To propose a novel variant of the differential evolution algorithm (DE) with a gradient-based repair method for MINLP problems, termed G-DEmi.
  • To enhance the performance of EAs in solving MINLP by addressing the issue of infeasible solutions within discontinuous feasible parts.
  • To evaluate the effectiveness of the proposed G-DEmi on benchmark MINLP problems and a real-world case.

Main Methods:

  • Development of a gradient-based repair method to fix promising infeasible solutions in MINLP subproblems.
  • Integration of the repair method into a differential evolution algorithm (DE) variant, creating G-DEmi.
  • Extensive experimental evaluation of G-DEmi on diverse MINLP benchmark instances and a practical application.

Main Results:

  • G-DEmi demonstrated superior performance compared to several state-of-the-art algorithms on MINLP benchmark problems.
  • The algorithm achieved effective exploration within subproblems without needing specialized diversity-promoting operators.
  • The gradient-based repair method proved generalizable and was successfully extended to other DE variants.

Conclusions:

  • The proposed G-DEmi algorithm offers an effective solution for MINLP problems by leveraging gradient information for repairing infeasible solutions.
  • The gradient-based repair mechanism enhances EA performance in MINLP without compromising exploration capabilities.
  • The repair method's adaptability suggests broader applicability in evolutionary computation for constrained optimization.