Introduction to EvoMO#

Multiobjective optimization: inputs and outputs#

A multiobjective problem optimizes several objectives that may conflict. For example, faster robot motion may require more energy. An evolutionary algorithm maintains a population of candidate solutions and updates it through evaluation, selection, crossover, or mutation.

Under minimization, solution A dominates B if A is no worse in every objective and strictly better in at least one. Points that are not dominated by other points in the current set form the first non-dominated front. This does not establish that they lie on the problem’s true Pareto front; reference fronts, metrics, and repeated runs help assess solution quality.

EvoMO uses the following batched tensor conventions:

Data

Shape

Meaning

population / pop

(N, D)

N candidate solutions with D decision variables each

fitness / fit

(N, M)

M objective values per candidate

lb, ub

(D,)

Lower and upper bounds for each decision variable

cv

(N, C)

Nonnegative violations for C constraints; some operators also accept total violations of shape (N,)

rank

(N,)

Non-domination ranks starting at 0

Keep input tensors, algorithm state, problems, and reference fronts on consistent devices with compatible dtypes.

Relationship with EvoX#

EvoMO uses EvoX’s Algorithm, Problem, Workflow, and state management abstractions. EvoX supplies general operators, monitors, and neural network parameter adapters. EvoMO provides its own multiobjective algorithms, benchmarks, selection operators, metrics, and UnifiedWorkflow, which preserves constraint violations.

from evomo.algorithms import NSGA2
from evomo.problems.numerical import DTLZ2
from evomo.workflows import UnifiedWorkflow

from evox.workflows import EvalMonitor

evomo.algorithms.NSGA2 and evox.algorithms.NSGA2 are different implementations. Record the actual import path when reproducing an experiment.

Parts of a run#

  1. Problem: implements batched evaluate, returning objectives and, for constrained problems, violations.

  2. Algorithm: stores the population and objectives, then generates and selects the next population.

  3. Workflow: connects the algorithm and problem, handling objective directions, transforms, and monitor callbacks.

  4. Analysis: extracts the final population or monitor history, filters feasible non-dominated solutions, and computes metrics.

Call workflow.init_step() to initialize a run, then call workflow.step() repeatedly. The examples assume that algorithm evaluation is connected through a workflow.

Version scope#

This documentation describes the current PyTorch implementation. The documentation build reads the version from pyproject.toml. The historical JAX implementation is on the v0.0.1-dev branch and pairs with EvoX 0.9.0; its state and invocation conventions do not apply to these examples.