Dynamic Programming Approach to Solve Real-World Application of Multi-Objective Unbounded Knapsack Problem

Knapsack problem is classified as a combinatorial optimization problem with the consideration of the optimal object being a part of the predefined set of finite objects allowed to be placed in the knapsack. The unbounded knapsack problem allows the repetition of objects, while demanding that the sum of the values of the objects in the optimal solution does not exceed the weight of the knapsack. In this paper, food order optimization problem is modeled as a multi-objective unbounded knapsack problem, as the problem has multiple objectives which need to be achieved simultaneously. Optimizing the number of given non-vegetarian dishes and maximizing the number of servings is considered as objective functions. These objectives are to be satisfied restricting to the budget constraint. Dynamic programming approach is applied to generate an optimal solution while satisfying the set constraints. The proposed approach successfully returns an optimal solution for all test cases.