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KNAPSACK ALGORITHM CODE

Suppose that we want to create a maximum of 30 generations and 50 individuals for the optimization process. Now here’s the interesting part: the optimization process using the genetic algorithm. #create the function that we want to optimize fitness=function(x) The fitness the function will we use in the ga function from the GA library.

KNAPSACK ALGORITHM CODE

Then, we create the objective function that we want to optimize with the constraint function by writing these lines of code below. > data item weight survival 2 pocket knife 1 3 3 mineral water 6 15 9 snacks 3 8 #1 means that we bring the item, while 0 means that we left the item chromosomes=c(0,1,1,0,0,0,0,0,1) data We can write it as the “chromosome”, and since the problem that we want to solve is a 0–1 knapsack problem, then from these lines of codes below, 1 means that we bring the item, while 0 means that we left the item. To give you a better understanding of the genetic algorithm in this problem, suppose that we only bring a pocket knife, mineral water, and snacks in your knapsack, initially. First, we need to input the data and the parameters that we used by writing these lines of code. From the problem statement, we can define the weight of the items as the constraint function, while the survival points cumulated from the items in the knapsack as the objective function.įor the implementation in this article, here we using the GA library in R created by Luca Scrucca. The goal is: you want to maximize your knapsack capacity while maximizing your survival points as well. Suppose too that you have a knapsack that can contain items with a maximum capacity of 25 kilograms, where you can only bring one copy for each item. The image available, with the weight and survival point for each item, respectively (Image by the author) Suppose that you want to go hiking with your friends, and you have the items that you can use for hiking, with the weight (in kilograms) and survival point of each item, respectively, as follows. To give you a better understanding of the genetic algorithm, let’s jump to the case study where we will use the genetic algorithm to solve the knapsack problem in R.Ĭase Study: Solving Knapsack Problem using Genetic Algorithm These all individuals will be used for training the next generation until the number of generations is reaching the limit.

Repeat steps 3 and 4 until all individuals in one generation are trained.

Then, perform mutation between two individuals with probability p (usually the probability of mutation are really low).

From the population, select two individuals, then perform crossover between two individuals with probability p.

Initialize the population size, maximum iteration number (the number of generations), crossover probability, mutation probability, and the number of elitism (the best or fittest individual that won’t undergo mutation).

Initialize the data and/or the function that we will optimize.

So, maximum possible value that can be put into the knapsack = 7.Genetic Algorithm flowchart (Image by the author).

The last entry represents the maximum possible value that can be put into the knapsack.

T (i, j) = max Īfter all the entries are computed and filled in the table, we get the following table. Start filling the table row wise top to bottom from left to right.

Fill all the boxes of 0 th row and 0 th column with zeroes as shown.

Draw a table say ‘T’ with (n+1) number of rows and (w+1) number of columns.