{"data":{"kind":"file","path":"README.md","version_id":"ouv7zj0nddopmrfwehm4hahh","entry":{"name":"README.md","path":"README.md","is_directory":false,"size":2557,"modified_at":"2026-09-11T13:49:02.218000","content_hash":"00e8eed2bf203f8230972fa4b97bb1105696c6b86222d00072273ca103051cc6"},"entries":[],"content":"# Multi-objective Optimization (Pareto front) Challenge\n\nVersion: 1.1.1\n\n## Overview\n\nThis environment evaluates an LLM's ability to solve multi-objective optimization problems involving Pareto fronts. The model must reason about trade-offs between conflicting objectives, identify dominated and non-dominated solutions, compute Pareto-optimal sets, and provide rigorous mathematical analysis.\n\n## Problem Types\n\n### 1. Pareto Dominance Identification\nGiven a set of solution vectors, determine which solutions are Pareto-optimal (non-dominated) and which are dominated by others.\n\n### 2. Pareto Front Computation\nGiven objective function values for multiple solutions, compute the exact Pareto front and classify solutions.\n\n### 3. Multi-objective Problem Solving\nGiven explicit multi-objective optimization problems (2-4 objectives), find Pareto-optimal solutions with mathematical justification.\n\n### 4. Trade-off Analysis\nAnalyze trade-offs between conflicting objectives and recommend solutions based on different preference structures.\n\n### 5. Scalarization Methods\nApply weighted-sum, epsilon-constraint, and Chebyshev scalarization to convert multi-objective problems to single-objective.\n\n### 6. Real-world Scenario Optimization\nSolve practical multi-objective problems: cost vs quality, speed vs accuracy, risk vs return.\n\n## Evaluation Metrics\n\n- **Dominance Correctness** (weight: 0.30): Accurately identifies dominated vs non-dominated solutions\n- **Pareto Front Quality** (weight: 0.25): Correctly computes the Pareto-optimal set\n- **Mathematical Rigor** (weight: 0.20): Proper use of definitions, proofs, and formal reasoning\n- **Trade-off Reasoning** (weight: 0.15): Quality of trade-off analysis and recommendations\n- **Solution Coverage** (weight: 0.10): Breadth of Pareto front exploration\n\n## Difficulty Levels\n\n- **Level 1**: 2 objectives, 2D, 5-10 solutions\n- **Level 2**: 2-3 objectives, discrete sets, 10-20 solutions\n- **Level 3**: 3 objectives, continuous problems, analytical Pareto fronts\n- **Level 4**: 4+ objectives, real-world scenarios with constraints\n- **Level 5**: Algorithmic design — propose and analyze multi-objective optimization algorithms\n\n## Example Problem\n\n```\nGiven three solutions for a production optimization problem:\n- Solution A: cost=10, quality=85, time=12h\n- Solution B: cost=8, quality=90, time=15h\n- Solution C: cost=12, quality=80, time=10h\n- Solution D: cost=9, quality=88, time=14h\n\nIdentify the Pareto-optimal solutions and explain why each dominated solution is dominated.\n```\n\n## License\n\nMIT\n","encoding":"utf-8","truncated":false,"total_bytes":2557},"status":null}