Add more visualization features for multi-objective optimization (e.g., constraint handling, animation)

Motivation

When I used multi-objective optimization, I wanted new features of plot_pareto_front. I’m not fully sure if they are useful for the other people, but let me share the ideas.

[DONE] 1. Constraint-aware pareto-front plot

Recently, Optuna enables us to add constraints to multi-objective optimization. The plot_paret_front function, however, does not consider whether the solution is feasible or not. So, I needed to modify it to visualize the constraint optimization.

For example, the following plot is an example of multi-objective knapsack problem. The objectives are to be maximized, but infeasible solutions are likely to be seen in the up-right region. In this case, I couldn’t find the shape of Pareto front without removing the infeasible solutions.

[REJECTED] 2. Animation of evolution

Since the NSGA-II is an evolution-based algorithm, we can traverse parents/ancestors of solutions. When I used the NSGA-II Sampler, I visualized the evolution of solutions using the animation and checked if the genetic operators produced good solutions. I think it is useful if we provide a new visualization feature that shows pareto-front trial by trial including the parents of the newly added point.

The following plots are snapshots of the animation. …

Description

We may not necessarily implement both features. I think the first one is relatively well-defined.

[DONE] 1. Constraint-aware pareto-front plot

We can add a new argument to plot_pareto_front. I think the design discussion is needed about the way to pass the thresholds and constraint values. Currently, both BoTorchSampler and NSGAIISampler employ the following settings, but we don’t decide it should be kept by upcoming samplers for constraint optimization.

• Threshold is always zero.
• The constraint values are stored in Trial’s system_attr.

[REJECTED] 2. Animation of evolution

I drew the example plots for each trial, but it may be verbose to call the visualization function by the number of trials. So, I think we can use the plotly’s animation functionality to visualize the evolution interactively. We may need to start with some prototypical implementation.

[not522]

Following 2 features may be useful.

• Optimization history of hypervolume
• Parallel coordinate for objective values

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