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Artificial Neural Network Metamodel for Semi-Expensive Simulation Optimization

A Comparative Study of ANN vs. Kriging Metamodels

This repository contains the code and supplementary materials for an article developed as part of a Master's thesis (completed in 2018). The manuscript was accepted and published in 2025 following an extended editorial and publication process.

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Overview

MATLAB implementation of the ANN-Semi-Metamodel-Based (ANN-SMB) algorithm for semi-expensive simulation optimization. Compares ANN and Kriging metamodels in a two-phase framework for simulations taking 2–5 minutes per replication.

New to simulation optimization? See Introduction to Inventory Simulation Optimization for context.

Key Innovation

Two-phase approach solving the model-based vs. metamodel-based dilemma:

• Phase 1: Direct simulation (faster exploration)
• Phase 2: Validated metamodel (efficient exploitation)

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Algorithm Flowchart

Figure 2: Two-phase ANN-SMB framework with spatial-hole PSO

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Main Results

(s,S) Inventory Control Model

Metric	ANN-SMB	Kriging-SMB
Avg. Objective Value	595.28	603.71
Std. Deviation	10.61	14.99
Function Evaluations	262.5	264

Analytical Test Functions (5 Benchmarks)

Function	ANN-SMB Superior	Kriging-SMB Superior
Sphere	✓
Griewank	✓
Schaffer's F6	✓
Rosenbrock	✓
Rastrigin		✓

Key Finding: ANN-SMB superior on 4/5 test functions with 5–10% fewer function evaluations.

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Features

✅ Two-phase semi-metamodel-based optimization
✅ Artificial Neural Network metamodel with Levenberg-Marquardt training
✅ Spatial-Hole Particle Swarm Optimization (SH-PSO) for enhanced exploration
✅ Leave-one-out cross-validation for metamodel validation
✅ Comparison with Kriging-based approach
✅ Applied to both test functions and realistic (s,S) inventory model
✅ MATLAB 8.4+ implementation

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Usage

Prerequisites

• MATLAB 8.4 or later
• Statistics and Machine Learning Toolbox (for neural network functions)

Running the Algorithm

cd Main
main_core_ANN

Customize parameters in main_core_ANN.m: idp, r, m, h, epsilon

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Mathematical Framework

ANN Architecture

Input Layer → Hidden Layer (tan-sigmoid) → Output Layer (linear)

Transfer Functions:

• Hidden layer: $f_{tan}(x) = \frac{2}{1 + e^{-2x}} - 1$
• Output layer: $f_{lin}(x) = x$

Metamodel Validation

Leave-one-out cross-validation with studentized prediction error

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Practical Applications

Applications: Inventory optimization, production scheduling, logistics design

Benefits:

• 5–10% fewer function evaluations
• Same-shift vs. overnight optimization
• Compatible with Arena, AnyLogic, Simio

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Citation

@article{Behbahani2025,
  author = {Mohammad Behbahani and Seyed Taghi Akhavan Niaki and Mehran Moazeni},
  title = {An artificial neural network metamodel to solve semi-expensive simulation optimization problems: A comparative study},
  journal = {Journal of Industrial Engineering},
  doi = {10.71720/joie.2025.1183309},
  year = {2025}
}

DOI: https://doi.org/10.71720/joie.2025.1183309

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Download Article

You can download the full article here.

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Key Findings

• Statistically equivalent solution quality (p = 0.913)
• ANN-SMB superior on 4/5 test functions
• 5–10% reduction in function evaluations
• Real-world speedup: overnight to same-shift optimization

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Limitations & Future Work

Limitations: Tested up to 3D, ~6% neuron sensitivity, continuous/low-noise only

Future: RBF/regression comparison, noisy/discrete problems, real-world benchmarks

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Last Updated: February 2026
License: Academic Use (See paper for full terms)
Status: Published