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| Classification | Name | Characteristic |
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| Numerical optimization method | Exterior point (EP) penalty function | (1) Finding the real target value in the case of a minimum
(2) Penalty function: improving reliability |
| Generalized reduced gradient (LSGRG2) | (1) A large number of design variables (>20) and constraints (>2000)
(2) Optimization equation based on the Kutta condition |
| Generalized Hooke’s law direct search (DHS) |
Local optimization, not requiring the objective function to be continuous
(2) Providing convergence coefficient, ensuring convergence |
| Feasible direction (CONMIN) | (1) Reducing the objective function value to maintain the feasible solution
(2) Achieving the target value quickly |
| Mixed integer optimization (MOST) | (1) Designing a continuous variable
(2) The handle mixed or unmixed real, integer, and discrete variable |
| Sequential Linear Programming | Being easy to achieve, being commonly used in engineering |
| Sequential Quadratic Programming |
Gradient cannot handle user-supplied data |
Sequential Quadratic Programming
(NLPQ) | (1) Assuming that the target function is continuously differentiable
(2) Adding the linear search which improves the stability of the algorithm |
| Successive approximation | The nonlinear problem as a linear problem to deal with |
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| Exploration optimization | Multi-island genetic algorithm (MIGA) | (1) Handling equality or inequality constraints
(2) Starting until you can get a good target
(3) From the point of looking for a series of designs rather than from a single point |
| Adaptive simulated annealing (ASA) algorithm | (1) Solving highly nonlinear optimization problem, identifying the different local optima
(2) Being able to obtain the optimal solution with the minimum cost |
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| Expert system optimization | Directed heuristic search (DHS) algorithm | (1) High speed nonlinear problem
(2) Focusing on the parameters that can directly affect the optimization solution |
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