I Heuristic Knapsack Solver Algorithm
The I Heuristic Knapsack Solver Algorithm is a type of optimization algorithm specifically designed to solve the 0/1 knapsack problem, which is a classic combinatorial optimization problem. The problem consists of a set of items, each with its own weight and value, and a knapsack with a limited capacity. The goal is to determine the combination of items to include in the knapsack to maximize the total value, while ensuring that the combined weight of the selected items does not exceed the knapsack's capacity. This problem is known to be NP-hard, meaning that there is no known algorithm that can solve it efficiently for all instances. The I Heuristic Knapsack Solver, therefore, aims to provide an approximate solution to the problem, rather than finding the exact optimal solution.
The algorithm is based on an iterative improvement technique that starts with an initial solution and progressively refines it, ultimately converging on a solution that is either optimal or close to it. The I Heuristic Knapsack Solver utilizes a combination of greedy and local search heuristics to achieve this. The greedy heuristic is used to generate an initial solution by iteratively selecting the item with the highest value-to-weight ratio and adding it to the knapsack until no more items can be added. The local search heuristic is then applied to improve the solution by exploring the solution space in the neighborhood of the current solution. This can be achieved by swapping items in and out of the knapsack or by performing other operations, such as changing the order of the items. The algorithm iterates between these two heuristics until a stopping criterion is met, such as reaching a time limit or not finding any further improvement for a certain number of iterations.
using System;
namespace Algorithms.Knapsack
{
/// <summary>
/// Solves knapsack problem using some heuristics
/// Sum of values of taken items -> max
/// Sum of weights of taken items. <= capacity.
/// </summary>
/// <typeparam name="T">Type of items in knapsack.</typeparam>
public interface IHeuristicKnapsackSolver<T>
{
/// <summary>
/// Solves knapsack problem using some heuristics
/// Sum of values of taken items -> max
/// Sum of weights of taken items. <= capacity.
/// </summary>
/// <param name="items">All items to choose from.</param>
/// <param name="capacity">How much weight we can take.</param>
/// <param name="weightSelector">Maps item to its weight.</param>
/// <param name="valueSelector">Maps item to its value.</param>
/// <returns>Items that were chosen.</returns>
T[] Solve(T[] items, double capacity, Func<T, double> weightSelector, Func<T, double> valueSelector);
}
}
