Outlook of Applications in Multi-Objective Optimization Design

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1.

Steel and Concrete Frame Design

• Objectives:

  
  

  • Minimize material cost (steel weight, concrete volume).

  • Minimize deflection / drift.

  • Maximize safety margin or ductility.

  
  

• Application: Optimal cross-sections of beams/columns while satisfying strength + serviceability constraints.

2.

Truss Optimization

• Objectives:

  
  

  • Minimize structural weight.

  • Minimize displacement at nodes.

  • Minimize fabrication cost (discrete bar sizes).

  
  

• Classic benchmark problem — many studies use trusses to test new MOPSO variants.

3.

Tall Building / Seismic Design

• Objectives:

  
  

  • Minimize material (cost/weight).

  • Minimize inter-story drift under earthquakes.

  • Minimize base shear.

  
  

• Used in optimizing lateral load–resisting systems (shear walls, braced frames, or core + outrigger).

4.

Bridge Design

• Objectives:

  
  

  • Minimize deck weight or cable tension.

  • Minimize deflections under live loads.

  • Minimize construction cost.

  
  

• Example: Suspension bridge cable layout optimization.

5.

Post-Tensioned Slabs & RC Sections

• Objectives:

  
  

  • Minimize tendon/cable cost.

  • Minimize slab thickness (self-weight).

  • Maximize serviceability (crack control, deflection).

  
  

6.

Structural Vibration Control with TMD, TLD

• Objectives:

  
  

  • Minimize construction cost.

  • Minimize obstruction to the occupancy space.

  • Maximize serviceability (displacement, acceleration).

  
  

🔹 Applications of MOPSO in Geotechnical Engineering

1.

Foundation (Shallow & Deep)

• Objectives:

  
  

  • Minimize foundation cost (geometry, reinforcement, pile length).

  • Maximize safety factor against bearing/settlement.

  • Minimize settlement.

  
  
  
  

2.

Slope Stability

• Objectives:

  
  

  • Maximize factor of safety.

  • Minimize excavation/retaining wall cost.

  • Minimize displacement.

  
  

• Commonly solved with limit equilibrium or FEM, then optimized with MOPSO.

3.

Tunneling & Underground Structures

• Objectives:

  
  

  • Minimize lining cost (thickness, reinforcement).

  • Minimize surface settlement.

  • Minimize construction time.

  
  

4.

Soil Improvement / Ground Reinforcement

• Objectives:

  
  

  • Minimize reinforcement cost (stone columns, grouting, geosynthetics).

  • Minimize long-term settlement.

  • Maximize improvement in bearing capacity.

  
  

5.

Pile Groups & Pile Raft Foundations

• Objectives:

  
  

  • Minimize number/length of piles (cost).

  • Minimize differential settlement.

  • Maximize load-carrying efficiency.

  
  

🔹 Why MOPSO Fits These Problems

• Structural/geotechnical problems are inherently multi-objective: cost vs safety, stiffness vs ductility, material vs performance.

• Pareto fronts give engineers choices: instead of one “optimal” solution, you get a design trade-off curve to negotiate with owners, code requirements, or safety factors.

• Constraints are complex: codes, soil nonlinearities, seismic drift — MOPSO handles these via penalty functions.

✅ Summary

• Structural: truss/frame sizing, tall building seismic optimization, bridges, post-tensioned slabs.

• Geotechnical: slope stability, shallow/deep foundations, soil improvement, pile rafts.

• Common objectives: cost, weight, safety factor, settlement, drift, ductility.

• Benefit: instead of a single “best” design, MOPSO provides a Pareto set so engineers can balance economy vs safety vs performance.