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Multi-Objective Knapsack Problem

Multi-Objective Knapsack Problem

This is a Multi-Objective Optimization problem: a variation of uni-objective Knapsack Problem: In this case instead of maximizing profits we look at multiple objectives.

Project Selection Problem

We want to select projects for investing some money

  • the budget is 900k euros (this this the constraint)

Objectives:

  • Maximize expected profits
  • Maximize the number of employees

| Projects $\to$ | $P_1$ | $P_2$ | $P_3$ | $P_4$ | Investment, k-euro | 200 | 300 | 400 | 500 || # of employees | 2 | 3 | 5 | 6 || Exp. return, % | 2.5 | 4.5 | 4 | 2.5 | For example

  • $P_3 + P_4 \leqslant 900$, can employ 11 people

Image

We see that there are only two interesting solutions

  • all other solutions are dominated by these two

Sources