moocore: Core Algorithms for Multi-Objective Optimization#
Version: 0.1.7.dev0 (What’s new)
Date Jun 02, 2025
Useful links: Install | Source Repository | Issue Tracker
This webpage documents the moocore Python package. There is also a moocore R package.
The goal of the moocore project (multi-objective/moocore) is to collect fast implementations of core mathematical functions and algorithms for multi-objective optimization and make them available to different programming languages via similar interfaces. These functions include:
Identifying and filtering dominated vectors.
Quality metrics such as (weighted) hypervolume, epsilon, IGD, etc.
Computation of the Empirical Attainment Function. The empirical attainment function (EAF) describes the probabilistic distribution of the outcomes obtained by a stochastic algorithm in the objective space.
Most critical functionality is implemented in C, with the R and Python packages providing convenient interfaces to the C code.
Keywords: empirical attainment function, summary attainment surfaces, EAF differences, multi-objective optimization, bi-objective optimization, performance measures, performance assessment
The reference guide contains a detailed description of the functions, modules, and objects.
Detailed examples and tutorials.
Benchmarks#
The following plots compare the performance of moocore, pymoo, BoTorch, jMetalPy, and DEAP-er. Other optimization packages are not included in the comparison because they are based on these packages so they are at least as slow as them. For example Xopt uses BoTorch, pysamoo is an extension of pymoo, and DESDEO uses pymoo internally.
Not all packages provide the same functionality. For example, pymoo does not provide the epsilon indicator whereas jMetalPy does not provide the IGD+ indicator. BoTorch provides neither of them.
The following plots compare the speed of computing the hypervolume indicator in 3D and 4D. As the plots show, moocore is nearly 100 times faster than the other packages and 1000 times faster than BoTorch and, by extension, Xopt, which is an order of magnitude slower than the second slowest.
The following plots compare the speed of finding nondominated solutions, equivalent to moocore.is_nondominated(), in 2D and 3D. As the plots show, moocore is nearly 100 times faster in 2D and 1000 times faster in 3D than the other packages. Here, pymoo quickly becomes even slower than BoTorch.
The following plot compares the speed of computing the epsilon indicator metric and IGD+ indicator. Despite the algorithms for computing these metrics are relatively simple and easy to vectorize in Python, the moocore implementation is still 10 to 100 times faster.
The source code for the benchmarks above can be found at multi-objective/moocore .