Abstract The hill climbing algorithm is an optimization technique that iteratively improves a solution by evaluating neighboring solutions in search of a local maximum or minimum. Starting with an initial guess, the algorithm examines nearby “neighbor” solutions, moving to a better neighbor if one is found. This process continues until no improvement can be made locally, at which point the algorithm may restart from a new random position.
This implementation focuses on discrete optimization problems, supporting integer and categorical parameters only.
Abstract The Multi-dimensional Knapsack Problem (MKP) is a fundamental combinatorial optimization problem that generalizes the classic knapsack problem to multiple dimensions. In this problem, each item has multiple attributes (e.g., weight, volume, size) and the goal is to maximize the total value of selected items while satisfying constraints on each attribute. Despite its conceptual simplicity, the MKP is NP-hard and appears frequently in real-world applications, such as resource allocation, capital budgeting, and project selection, as remarked in recent surveys e.