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Industrial Mathematics Final Year Topic: Gap between First-Fit-Decreasing Packing and Exact Solutions on Structured Instances

This Industrial Mathematics final year project examines a packing heuristic against verified optima in a finite instance family.

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Why choose this project topic?

A focused study of bin-packing bounds gives you a specific question in combinatorial optimisation. It examines a packing heuristic against verified optima in a finite instance family. The bounded comparison creates room to explain how your evidence supports an interpretation and where the method has limits.

How do selected item-size structures affect the gap between first-fit-decreasing and an exact bin-packing solution?

Agree the apparatus or dataset, comparison range and feasible measurement schedule for bin-packing bounds with your supervisor.

Proposed project objectives

  1. 01Define the materials, variables and comparison conditions for bin-packing bounds.
  2. 02Define the bin capacity and instance-generation rules, verify all feasible packings and compare the heuristic count with exact optima or certified bounds.
  3. 03Evaluate the measurements or model outputs in relation to this question: How do selected item-size structures affect the gap between first-fit-decreasing and an exact bin-packing solution?

A suggested research approach

Define the bin capacity and instance-generation rules, verify all feasible packings and compare the heuristic count with exact optima or certified bounds. Report the instance range rather than claiming universal performance. Agree the available resources and record uncertainty, deviations from the protocol and any observations that challenge the initial interpretation.

What you will need

  • A documented finite packing instance family
  • A specified first-fit-decreasing implementation
  • Exact-search or certified-bound tools

Keep your project scope clear

Results on a finite family do not establish a new worst-case approximation guarantee.

Industrial Mathematics project chapter outline

Use this outline as a starting point. You can edit the chapter titles to match your department’s format during setup.

  1. Chapter 1Introduction
  2. Chapter 2Literature Review
  3. Chapter 3Theory and Methodology
  4. Chapter 4Results and Applications
  5. Chapter 5Summary, Conclusion and Recommendations

Turn this topic into your own final year project.

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