find_optimal_alt: Find Optimal ALT Design Using Hybrid Algorithm

In minimaxALT: Generate Optimal Designs of Accelerated Life Test using PSO-Based Algorithm

Find Optimal ALT Design Using Hybrid Algorithm

Description

Runs hybrid algorithm combining PSO and Nelder-Mead to find the optimal design of accelerated life test (ALT).

Usage

find_optimal_alt(
  design_type,
  distribution,
  design_info,
  pso_info,
  coef = NULL,
  coef_lower = NULL,
  coef_upper = NULL,
  init_values = NULL,
  highest_level = TRUE,
  n_threads = 1,
  verbose = TRUE,
  seed = 42
)

Arguments

design_type	Integer. 1: Locally optimal design, 2: Minimax design.
distribution	Integer. The assumed failure time distribution, 1: Weibull, 2: Log-normal, 3: Model robust (both distribution Weibull and Log-normal).
design_info	A list from 'set_design_info()' containing design specifications.
pso_info	A list from 'pso_setting()' defining PSO hyperparameters.
coef	Optional. Fixed model coefficients. Required if design_type = 1.
coef_lower	Optional. Lower bounds for model parameters. Required if design_type = 2.
coef_upper	Optional. Upper bounds for model parameters. Required if design_type = 2.
init_values	Optional. A list of initial values from 'initialize_values()'.
highest_level	Logical. Whether the highest stress level of the generated design is the upper bound of stress range x_h. Default value is TRUE.
n_threads	Integer. Number of threads for parallel processing.
verbose	Logical. If TRUE, print optimization progress.
seed	Integer. Seed for reproducibility

Value

g_best

The global best design found by the hybrid algorithm.

coef_best

The parameters corresponding to the global best design.

distribution_best

The distribution corresponding to the global best design.

max_directional_derivative

Maximum directional derivative within design space, evaluated using equivalence theorem.

fg_best

The objective function value corresponding to the global best design.

fg_best_hist

A vector tracking the best objective function value of each iteration.

p_best

A matrix containing each particle's personal best design found during the optimization.

fp_best

A vector containing the objective function values corresponding to each particle's personal best.

g_hist

All particle positions of each iteration.

coef_best_hist

The parameters corresponding to the global best designs of each iteration.

distribution_best_hist

The distribution corresponding to the global best designs of each iteration.

model_set

A matrix containing distribution and model parameters of global best particles of each iteration, duplicated models are removed.

model_weight

The weight assigned to each model in the model set.

equivalence_data

Generated designs and their corresponding directional derivative given the optimal design g_best. Each design is a combination of factors with value in [0, 1]. These designs are data for plotting equivalence theorem plot.

References

1. Chen P (2024). _globpso: Particle Swarm Optimization Algorithms and Differential Evolution for Minimization Problems_. R package version 1.2.1, <https://github.com/PingYangChen/globpso>.

2. Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks (ICNN) (Vol. 4, pp. 1942–1948).

3. Lee, I. C., Chen, R. B., Wong, W. K., (in press). Optimal Robust Strategies for Accelerated Life Tests and Fatigue Testing of Polymer Composite Materials. Annals of Applied Statistics. <https://imstat.org/journals-and-publications/annals-of-applied-statistics/annals-of-applied-statistics-next-issues/>

4. Meeker, W. Q., & Escobar, L. A. (1998). Statistical methods for reliability data. New York: Wiley-Interscience.

5. Nelder, J. A. and Mead, R. (1965). A simplex algorithm for function minimization. Computer Journal, 7, 308–313. 10.1093/comjnl/7.4.308.

Examples

design_info <- set_design_info(k_levels=2, j_factor=1, n_unit=300, 
                               censor_time=183, p=0.1, use_cond=0, sigma=0.6)

pso_info <- pso_setting(n_swarm=32, max_iter=128, early_stopping=10, tol=0.01)

set.seed(42)
res <- find_optimal_alt(design_type=1, distribution=1, design_info=design_info, 
                        pso_info=pso_info, coef=c(0.001, 0.9), verbose = FALSE)

summary(res)
plot(res, x_l=0, x_h=1)

minimaxALT documentation built on Nov. 5, 2025, 5:35 p.m.