Pymoo Problems

This repository contains problem implementations for the pymoo [1] framework which I use for my research work. Some of them are just shightly changed pymoo implementations, others are not found in pymoo by default and implemented here.

Multi-Objective Problems

Here is a short list of the multi-objective problems implemented.

MACO: Multi-Agent Coordinaation Problem

Reference implementation of the MACO problem as described in [2]. Besides the base-version the three variations (weights, p-norm, interaction classes) are also implemented.

from pymoo_problems.moo.maco import MACO

LZ Problems

The LZ problems 1 - 9 implemented after the reference in [3].

from pymoo_problems.moo.lz import LZ1, LZ2, LZ3, LZ4, LZ5, LZ6, LZ7, LZ8, LZ9

LZ Problems from jmetalpy

A port from the jmetalpy [4] implementation of the LZ problems. The implementation contains references to the PF which are a usefull check. However, the implementation does not stay true to the original LZ problems as described in [3], mainly as they shift the bounds of the problem to $[0.0,1.0]^1 x [0.5,1.0]^{n-1}$ for all problems. This still fits to the original Pareto front, however not the originally described Pareto set. For this reason we implemented our own reference which does fit in the original bounds and the original Pareto set as described in [3].

from pymoo_problems.moo.lz_jmetalpy import LZ09_F1, LZ09_F2, LZ09_F3, LZ09_F4, LZ09_F5, LZ09_F6, LZ09_F7, LZ09_F8, LZ09_F9

CEC 2009 Benchmark Problems

Currently six functions of the UF [5] Benchmarking set are implemented: UF1, UF2, UF3, UF8, UF9, and UF10. Four of these functions are a direct copy of the LZ [3] test suite described above:

• UF1 = LZ2
• UF2 = LZ5
• UF3 = LZ8
• UF8 = LZ6

from pymoo_problems.moo.uf import UF1, UF2, UF3, UF8, UF9, UF10

ZDT Problems

Added a pareto set calculation for ZDT [6] functions ZDT1, ZDT2, ZDT3, ZDT4, and ZDT6 (not ZDT5) to the pymoo [1] implementation.

from pymoo_problems.moo.zdt import ZDT1, ZDT2, ZDT3, ZDT4, ZDT6

DTLZ Problems

Added a pareto set calculation for DTLZ [7] functions DTLZ1, DTLZ2, DTLZ3, DTLZ5, and DTLZ6 (not DTLZ4 or DTLZ7) to the pymoo [1] implementation.

from pymoo_problems.moo.dtlz import DTLZ1, DTLZ2, DTLZ3, DTLZ5, DTLZ6

References

[1] J. Blank und K. Deb, „Pymoo: Multi-Objective Optimization in Python“, IEEE Access, Bd. 8, S. 89497–89509, 2020, doi: 10.1109/ACCESS.2020.2990567.

[2] S. Mai, T. Benecke, und S. Mostaghim, „MACO: A Real-World Inspired Benchmark for Multi-objective Evolutionary Algorithms“, in Evolutionary Multi-Criterion Optimization, in Lecture Notes in Computer Science. Cham: Springer Nature Switzerland, 2023, S. 305–318. doi: 10.1007/978-3-031-27250-9_22.

[3] H. Li und Q. Zhang, „Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II“, IEEE Transactions on Evolutionary Computation, Bd. 13, Nr. 2, S. 284–302, Apr. 2009, doi: 10.1109/TEVC.2008.925798.

[4] A. Benítez-Hidalgo, A. J. Nebro, J. García-Nieto, I. Oregi, und J. Del Ser, „jMetalPy: A Python framework for multi-objective optimization with metaheuristics“, Swarm and Evolutionary Computation, Bd. 51, S. 100598, Dez. 2019, doi: 10.1016/j.swevo.2019.100598.

[5] Q. Zhang, A. Zhou, S. Zhao, P. Suganthan, W. Liu, und S. Tiwari, „Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition“, Mechanical Engineering, Jan. 2008.

[6] E. Zitzler, K. Deb, und L. Thiele, „Comparison of Multiobjective Evolutionary Algorithms: Empirical Results“, Evol. Comput., Bd. 8, Nr. 2, S. 173–195, Juni 2000, doi: 10.1162/106365600568202.

[7] K. Deb, L. Thiele, M. Laumanns, und E. Zitzler, „Scalable multi-objective optimization test problems“, in Proceedings of the 2002 Congress on Evolutionary Computation. CEC’02 (Cat. No.02TH8600), Mai 2002, S. 825–830 Bd.1. doi: 10.1109/CEC.2002.1007032.