> ## Documentation Index
> Fetch the complete documentation index at: https://doc.blueapi.ir/llms.txt
> Use this file to discover all available pages before exploring further.

# Multi-Objective Optimization with NSGA-II

> Specification for multi-objective optimization in EMEP using NSGA-II, covering non-dominated sorting, crowding distance, and Pareto front management.

EMEP supports multi-objective optimization through NSGA-II (Deb et al. 2002). When multiple competing objectives matter (for example accuracy vs. efficiency), the EvolutionEngine searches for the Pareto front rather than a single best candidate. This page specifies the multi-objective sub-loop, ranking mechanics, and front management.

## Multi-Objective Flow

```mermaid theme={null}
flowchart TD
    START([START]) --> INPUT[Population + Fitness Vectors]
    INPUT --> SORT[Non-Dominated Sorting]
    SORT --> RANK[Assign Rank / Front]
    RANK --> CROWD[Crowding Distance]
    CROWD --> SELECT[Selection by Rank + Distance]
    SELECT --> BREED[Mutation + Crossover]
    BREED --> OFFSPRING[Offspring Population]
    OFFSPRING --> MERGE[Merge Parent + Offspring]
    MERGE --> SORT2[Non-Dominated Sorting]
    SORT2 --> TRUNC[Truncate to Population Size]
    TRUNC --> TERM{Termination?}
    TERM -->|No| INPUT
    TERM -->|Yes| OUTPUT[Return Pareto Front]
    OUTPUT --> END([END])
```

## Non-Dominated Sorting

A candidate A dominates candidate B if A is better than or equal to B on all objectives, and strictly better on at least one. The non-dominated sorting algorithm partitions the population into fronts:

* **Front 1**: candidates dominated by no one
* **Front 2**: candidates dominated only by Front 1
* **Front 3**: candidates dominated by Front 1 or 2
* And so on

Sorting runs in O(MN^2) time where M is the number of objectives and N is the population size. For typical EMEP configurations (M less than or equal to 5, N less than or equal to 64), this is computationally negligible compared to model evaluation.

## Crowding Distance

Within each front, candidates are ranked by crowding distance. This measures the density of solutions around a candidate in objective space. Candidates with larger crowding distance are preferred.

```text theme={null}
crowding_distance[i] = sum_j((objective[j][i+1] - objective[j][i-1]) / (objective[j][max] - objective[j][min]))
```

Boundary candidates (best and worst per objective within the front) receive infinite crowding distance to ensure they are preserved.

## Selection in Multi-Objective Mode

Parents are selected by iterating through fronts in order. Within a front, selection uses crowding distance as a tiebreaker. The binary tournament compares:

1. Front rank (lower is better)
2. Crowding distance (higher is better)

This ensures convergence toward the Pareto front while maintaining diversity along it.

## Population Truncation

After offspring generation, parent and offspring populations are merged. The combined set is re-sorted by non-dominated rank. The new population is filled front by front. If the last front that fits exceeds the remaining slots, candidates from that front are selected by highest crowding distance.

## Pareto Front Output

Upon termination, the EvolutionEngine returns:

* All Front 1 candidates from the final generation
* Their full fitness vectors
* Their genomes
* Their evaluation metrics from all splits (Optimization, Validation, Hidden Test)

The front is stored in the ExperimentTracker as a single artifact with references to individual candidate records.

## Supported Objectives

Common objective combinations in EMEP:

| Objective 1 | Objective 2 | Objective 3 | Use Case             |
| ----------- | ----------- | ----------- | -------------------- |
| Accuracy    | Latency     | Memory      | Edge deployment      |
| Accuracy    | Safety      | Robustness  | Production models    |
| Perplexity  | Exact Match | Safety      | Research exploration |
| English     | Persian     | Code        | Multilingual balance |

## NSGA-III Extension

NSGA-III (Deb & Jain 2014) is planned as a future alternative for problems with more than three objectives. NSGA-III replaces crowding distance with reference point-based selection. The EvolutionEngine architecture supports pluggable selectors, so NSGA-III can be added without structural changes.

<Info>
  Multi-objective mode is selected at experiment initialization. Switching between single and multi-objective mid-experiment is not supported. The choice affects fitness computation, selection, and output format.
</Info>