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The Successive Approximation Genetic Algorithm (SAGA) for Optimization Problems with Single Constraint

Author

Listed:
  • Zhihua Chen

    (State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China
    Department of Civil Engineering, Tianjin University, Tianjin 300072, China)

  • Xuchen Xu

    (Department of Civil Engineering, Tianjin University, Tianjin 300072, China)

  • Hongbo Liu

    (State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China
    Department of Civil Engineering, Hebei University of Engineering, Handan 056038, China)

Abstract
A limited feasible region restricts individuals from evolving optionally and makes it more difficult to solve constrained optimization problems. In order to overcome difficulties such as introducing initial feasible solutions, a novel algorithm called the successive approximation genetic algorithm (SAGA) is proposed; (a) the simple genetic algorithm (SGA) is the main frame; (b) a self-adaptive penalty function is considered and the penalty factor is adjusted automatically by the proportion of feasible and infeasible solutions; (c) a generation-by-generation approach and a three-stages evolution are introduced; and (d) dynamically enlarging and reducing the tolerance error of the constraint violation makes it much easier to generate initial feasible solutions. Then, ten benchmarks and an engineering problem were adopted to evaluate the SAGA in detail. It was compared with the improved dual-population genetic algorithm (IDPGA) and eight other algorithms, and the results show that SAGA finds the optimum in 5 s for an equality constraint and 1 s for an inequality constraint. The largest constraint violation can be accurate to at least three decimal fractions for most problems. SAGA obtains a better value, of 1.3398, than the eight other algorithms for the engineering problem. In conclusion, SAGA is very suitable for solving nonlinear optimization problems with a single constraint, accompanied by more accurate solutions, but it takes a longer time. In reality, SAGA searched for a better solution along the bound after several iterations and converged to an acceptable solution in early evolution. It is critical to improve the running speed of SAGA in the future.

Suggested Citation

  • Zhihua Chen & Xuchen Xu & Hongbo Liu, 2023. "The Successive Approximation Genetic Algorithm (SAGA) for Optimization Problems with Single Constraint," Mathematics, MDPI, vol. 11(8), pages 1-26, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1928-:d:1127720
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    References listed on IDEAS

    as
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    4. Qiu, Qingan & Cui, Lirong & Gao, Hongda & Yi, He, 2018. "Optimal allocation of units in sequential probability series systems," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 351-363.
    Full references (including those not matched with items on IDEAS)

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