Intelligent Optimization Design of Engineering Structures · 工程结构智能优化设计

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A computer-lab course project applying Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) — powered by scikit-opt — to the section optimization of three typical structural members. All designs strictly follow Chinese national codes (GB 50010 / GB 50017), minimizing cost or steel weight under capacity, detailing, and stiffness constraints, handled with the penalty-function method.

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📌 Overview

Task	Algorithm	Member	Variables	Objective	Optimum
Task 1	GA	RC simply-supported beam	b, h, A_s	Total cost	¥492.55
Task 2	PSO	H-section steel column	h, b, t_w, t_f	Steel weight	395.64 kg
Task 3	GA	Circular CFST short column	D, t	Unit cost	¥383.28 /m

Common methodology:

• Penalty-function constraint handling — each violated constraint contributes M·g² (M = 10⁶) to the objective, guiding the search into the feasible region
• Engineering modularization — dimensions rounded to practical construction modules (beam 50 mm, H-section 5 mm, tube 10 mm / 1 mm)
• Automatic code verification — every optimum is re-checked against the full code requirements (capacity, slenderness, local stability, reinforcement ratio) and reported

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🧱 Task 1 — RC Simply-Supported Beam (GA)

A single-reinforced rectangular RC beam, span L = 6.0 m, uniform design load q = 30 kN/m. Find the section (b, h) and tensile steel area (A_s) minimizing total cost (concrete ¥400/m³ + rebar ¥6000/t).

Item	Value
Concrete / Steel	C30 (f_c = 14.3 N/mm²) / HRB400 (f_y = 360 N/mm²)
Cover a_s	40 mm
Design moment M_max	qL²/8 = 135.00 kN·m
Variables	b ∈ [200, 400] mm, h ∈ [400, 800] mm, A_s ∈ [100, 8000] mm²
GA settings	pop = 1000, max_iter = 500, prob_mut = 0.05

Constraints: bending capacity M_u ≥ M_max · min/max reinforcement ratio (0.2% ≤ ρ ≤ 2.5%) · depth-span ratio h ≥ L/15 · ductile failure x ≤ ξ_b·h₀

✅ Optimal Result

Optimum	Cost	Capacity check	Ductility	ρ	ρ_h0	h ≥ L/15
b = 200 mm, h = 600 mm, A_s = 730 mm²	¥492.55	M_u = 135.09 ≥ 135.00 kN·m ✅	x = 91.9 ≤ 290.1 mm ✅	0.608% ✅	0.652% ✅	600 ≥ 400 ✅

GA convergence curve (left) & optimal beam section diagram (right)

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🏗️ Task 2 — H-Section Steel Column (PSO)

An axially loaded H-section column, effective height H = 4.0 m (pinned-pinned), design axial force N = 2000 kN. Find the section (h, b, t_w, t_f) minimizing total steel weight.

Item	Value
Steel	Q355 (f = 310 N/mm², f_y = 355 N/mm²), E = 2.06×10⁵ N/mm²
Variables	h ∈ [200, 500], b ∈ [150, 200], t_w ∈ [6, 16], t_f ∈ [8, 20] mm
PSO settings	pop = 500, max_iter = 300, w = 0.8, c1 = c2 = 1.5

Constraints: overall stability φAf ≥ N (class-b buckling curve per GB 50017-2017) · weak-axis slenderness λ_y ≤ 150 · web h₀/t_w ≤ 65√(235/f_y) · flange b/t_f ≤ 13√(235/f_y)

✅ Optimal Result

Optimum	Weight	Stability N_u	λ_y	Web h₀/t_w	Flange b/t_f
H 500×200×10×20	395.64 kg	2000.6 ≥ 2000 kN ✅	86.9 ≤ 150 ✅	46.0 ≤ 52.9 ✅	10.0 ≤ 10.6 ✅

The optimum is constraint-active: the stability capacity N_u = 2000.6 kN just satisfies the 2000 kN demand — the PSO drove the section to the theoretical lightest weight.

PSO convergence curve (left) & optimal H-section diagram (right)

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🔩 Task 3 — Circular CFST Short Column (GA)

A circular concrete-filled steel tube (CFST) short column, length L = 1.0 m, design axial force N = 4000 kN. Find the outer diameter D and wall thickness t minimizing unit-length cost (steel ¥6500/t + concrete ¥450/m³).

Item	Value
Steel / Concrete	Q355 (f_s = 310 N/mm²) / C30 (f_c = 26.8 N/mm²)
Variables	D ∈ [300, 800] mm, t ∈ [6, 20] mm
GA settings	pop = 1000, max_iter = 500, prob_mut = 0.1

Constraints: axial capacity N_u = 0.9(f_c·A_c + f_s·A_s) ≥ N · diameter-thickness ratio D/t ≤ 100

✅ Optimal Result

Optimum	Unit cost	Capacity N_u	D/t
D = 360 mm, t = 6 mm	¥383.28 /m	4155.9 ≥ 4000 kN ✅	60 ≤ 100 ✅

GA convergence curve (left) & optimal CFST section diagram (right)

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🧠 Key Techniques

Technique	Detail
Penalty function	Quadratic penalty M·g² with M = 10⁶ for each violated normalized constraint; infeasible geometries return 10⁹ directly
Normalized constraints	Every constraint scaled by its design value so all violations are comparable
Engineering modularity	b/h → multiples of 50 mm; H-section → multiples of 5 mm, integer thicknesses; tube D → multiples of 10 mm
Full verification output	Each script re-runs every code check (capacity / slenderness / local stability / ratio) on the optimum and prints pass/fail with margin

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📁 Repository Structure

structure-design-optimization/
├── src/
│   ├── task1.py        # Task 1: GA — RC beam section optimization
│   ├── task2.py        # Task 2: PSO — H-section column optimization
│   └── task3.py        # Task 3: GA — CFST column optimization
├── results/
│   ├── Task1.png       # GA convergence curve + optimal beam section
│   ├── Task2.png       # PSO convergence curve + optimal H-section
│   └── Task3.png       # GA convergence curve + optimal CFST section
├── requirements.txt
├── LICENSE
└── README.md / README_zh.md

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🚀 Quick Start

# 1. Install dependencies (conda or venv recommended)
pip install -r requirements.txt

# 2. Run each task (saves figures to results/ and prints the full verification report)
python src/task1.py    # RC beam  — GA, ~1 min
python src/task2.py    # H column — PSO, ~30 s
python src/task3.py    # CFST    — GA, ~1 min

Scripts resolve the results/ path relative to their own location, so they run from any working directory. A laptop CPU is sufficient.

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📦 Dependencies

Package	Purpose
numpy	Numerical computation
matplotlib	Convergence curves & section diagrams
scikit-opt	GA / PSO implementations

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License

MIT © 2026 Ke Yang (杨珂)