最適化の基礎講義 / Basic lecture on optimization

Question

• question1
• question2
• question3
• question4

Evaluator (using query string) & Solver (written in python)

• evaluator1 (input=1)
• solver1 (solver1.py)
• evaluator2 (input=001)
• solver2 (solver2.py)
• evaluator3 (latitude=035.682500&longitude=139.752778)
• solver3 (solver3.py)
• evaluator4 (latitude=035.682500&longitude=139.752778&year=01&month=01)
• solver4 (solver4.py)

Answer

• answer1
• answer2
• answer3
• answer4

Image of multi-objective optimization test problems

Number of variables D = 5 (if possible).
Left image is Pareto front.
Center image is Pareto front and random points. Point size N = 200.
Right image is Pareto front and grid points. Point size N = 21^5.

Red points are Parto optimal solution.
Blue points are infeasible solution.
Grey points are feasible solution.

Examples (DTLZ1)

List of problems

• BT(Benchmark MOP with bias feature)
• CF(Constrained benchmark MOP)
• Combinatorial MOPs
• DASCMOP(Difficulty-adjustable and scalable constrained benchmark MOP)
• Distance minimization problems
• DOC(Benchmark MOP with constraints in both decision and objective spaces)
• DTLZ(Benchmark MOP proposed by Deb, Thiele, Laumanns, and Zitzler)
• IMOP(Benchmark MOP with irregular Pareto front)
• LIRCMOP(Constrained benchmark MOP with large infeasible regions)
• LSMOP(Large-scale benchmark MOP)
• MaF(Modified 15 test problems for many-objective optimization)
• Benchmark MOP for Inverse Modeling - MOEA
• Benchmark MOP for MOEA/D-DE
• Benchmark MOP for MOEA/D-M2M
• Benchmark MOP for Regularity Model-based - MEDA
• MW(Constrained benchmark MOP proposed by Ma and Wang)
• SMOP(Benchmark MOP with sparse Pareto optimal solutions)
• TREE(The time-varying ratio error estimation problems)
• UF(Unconstrained benchmark MOP)
• VNT(Benchmark MOP proposed by Viennet)
• WFG(Benchmark MOP proposed by Walking Fish Group)
• ZDT(Benchmark MOP proposed by Zitzler, Deb, and Thiele)

Reference

Y. Tian, R. Cheng, X. Zhang, and Y. Jin, PlatEMO: A MATLAB platform for evolutionary multi-objective optimization [educational forum], IEEE Computational Intelligence Magazine, 2017, 12(4): 73-87.

I use PlatEMO. Some Problems directory files and Public directory files are same as old version of PlatEMO.
I hope visitors can help their visual understanding of multi-objective optimization problem.