An Algorithmic Approach to Knapsack Problems

Survey of 0-1, fractional, and multi-dimensional knapsack; implementations of dynamic programming, a scaling FPTAS, and a 1/2-approximate greedy (fractional greedy proved optimal). Python benchmarks for MDKP and baselines; GA and local- search heuristics explored.

Overview

  • Surveyed $0–1$, fractional, and multi-dimensional knapsack (MDKP).
  • Implemented dynamic programming, a scaling FPTAS, and a $1/2$-approximate greedy; proved fractional greedy is optimal.
  • Built Python benchmarks for MDKP and baselines; explored GA and local-search heuristics.

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