Add Optimal Job Scheduling (#3868)
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georgioct
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package com.thealgorithms.dynamicprogramming;
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/**
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* This class refers to the Optimal Job Scheduling problem with the following constrains:
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* - precedence relation between the processes
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* - machine pair dependent transportation delays
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*
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* https://en.wikipedia.org/wiki/Optimal_job_scheduling
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*
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* @author georgioct@csd.auth.gr
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*/
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public class OptimalJobScheduling {
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private final int numberProcesses;
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private final int numberMachines;
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private final int[][] Run;
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private final int[][] Transfer;
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private final int[][] Cost;
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/**
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* Constructor of the class.
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* @param numberProcesses ,refers to the number of precedent processes(N)
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* @param numberMachines ,refers to the number of different machines in our disposal(M)
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* @param Run , N*M matrix refers to the cost of running each process to each machine
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* @param Transfer ,M*M symmetric matrix refers to the transportation delay for each pair of machines
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*/
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public OptimalJobScheduling(int numberProcesses, int numberMachines, int[][] Run, int[][] Transfer) {
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this.numberProcesses = numberProcesses;
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this.numberMachines = numberMachines;
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this.Run = Run;
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this.Transfer = Transfer;
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this.Cost = new int[numberProcesses][numberMachines];
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}
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/**
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* Function which computes the cost of process scheduling to a number of VMs.
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*/
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public void execute(){
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this.calculateCost();
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this.showResults();
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}
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/**
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* Function which computes the cost of running each Process to each and every Machine
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*/
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private void calculateCost(){
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for (int i=0; i < numberProcesses; i++){ //for each Process
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for (int j=0; j < numberMachines; j++) { //for each Machine
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Cost[i][j] = runningCost(i, j);
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}
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}
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}
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/**
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* Function which returns the minimum cost of running a certain Process to a certain Machine.In order for the Machine to execute the Process ,he requires the output
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* of the previously executed Process, which may have been executed to the same Machine or some other.If the previous Process has been executed to another Machine,we
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* have to transfer her result, which means extra cost for transferring the data from one Machine to another(if the previous Process has been executed to the same
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* Machine, there is no transport cost).
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*
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* @param process ,refers to the Process
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* @param machine ,refers to the Machine
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* @return the minimum cost of executing the process to the certain machine.
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*/
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private int runningCost(int process, int machine) {
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if (process==0) //refers to the first process,which does not require for a previous one to have been executed
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return Run[process][machine];
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else {
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int[] runningCosts = new int[numberMachines]; //stores the costs of executing our Process depending on the Machine the previous one was executed
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for (int k=0; k < numberMachines; k++) //computes the cost of executing the previous process to each and every Machine
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runningCosts[k] = Cost[process-1][k] + Transfer[k][machine] + Run[process][machine]; //transferring the result to our Machine and executing the Process to our Machine
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return findMin(runningCosts); //returns the minimum running cost
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}
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}
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/**
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* Function used in order to return the minimum Cost.
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* @param cost ,an Array of size M which refers to the costs of executing a Process to each Machine
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* @return the minimum cost
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*/
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private int findMin(int[] cost) {
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int min=0;
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for (int i=1;i<cost.length;i++){
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if (cost[i]<cost[min])
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min=i;
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}
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return cost[min];
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}
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/**
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* Method used in order to present the overall costs.
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*/
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private void showResults(){
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for (int i=0; i < numberProcesses; i++){
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for (int j=0; j < numberMachines; j++) {
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System.out.print(Cost[i][j]);
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System.out.print(" ");
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}
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System.out.println();
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}
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System.out.println();
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}
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/**
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* Getter for the running Cost of i process on j machine.
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*/
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public int getCost(int process,int machine) {
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return Cost[process][machine];
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}
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}
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@ -0,0 +1,128 @@
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package com.thealgorithms.dynamicprogramming;
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import org.junit.jupiter.api.Test;
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import static org.junit.jupiter.api.Assertions.assertEquals;
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/**
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* @author georgioct@csd.auth.gr
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*/
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public class OptimalJobSchedulingTest {
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@Test
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public void testOptimalJobScheduling1(){
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int numberProcesses = 5;
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int numberMachines = 4;
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int[][] Run = {
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{5, 1, 3, 2},
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{4, 2, 1, 3},
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{1, 5, 2, 1},
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{2, 3, 4, 2},
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{1, 1, 3, 1}};
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int[][] Transfer = {
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{0, 1, 2, 4},
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{1, 0, 2, 3},
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{2, 2, 0, 1},
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{4, 3, 1, 0}};
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OptimalJobScheduling opt = new OptimalJobScheduling(numberProcesses,numberMachines,Run,Transfer);
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opt.execute();
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int[][] costs = {
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{5, 1, 3, 2},
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{6, 3, 4, 5},
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{5, 8, 6, 6},
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{7, 9, 10, 8},
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{8, 9, 12, 9}};
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for (int i=0; i < numberProcesses; i++){
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for (int j=0; j < numberMachines; j++){
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assertEquals(costs[i][j],opt.getCost(i,j));
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}
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}
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}
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@Test
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public void testOptimalJobScheduling2(){
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int numberProcesses = 3;
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int numberMachines = 3;
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int[][] Run = {
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{5, 1, 3},
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{4, 2, 1},
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{1, 5, 2}};
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int[][] Transfer = {
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{0, 1, 2},
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{1, 0, 2},
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{2, 2, 0}};
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OptimalJobScheduling opt = new OptimalJobScheduling(numberProcesses,numberMachines,Run,Transfer);
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opt.execute();
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int[][] costs = {
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{5, 1, 3},
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{6, 3, 4},
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{5, 8, 6}};
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for (int i=0; i < numberProcesses; i++){
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for (int j=0; j < numberMachines; j++){
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assertEquals(costs[i][j],opt.getCost(i,j));
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}
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}
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}
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@Test
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public void testOptimalJobScheduling3(){
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int numberProcesses = 6;
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int numberMachines = 4;
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int[][] Run = {
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{5, 1, 3, 2},
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{4, 2, 1, 1},
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{1, 5, 2, 6},
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{1, 1, 2, 3},
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{2, 1, 4, 6},
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{3, 2, 2, 3},
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};
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int[][] Transfer = {
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{0, 1, 2, 1},
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{1, 0, 2, 3},
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{2, 2, 0, 2},
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{1, 3, 2, 0},
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};
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OptimalJobScheduling opt = new OptimalJobScheduling(numberProcesses,numberMachines,Run,Transfer);
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opt.execute();
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int[][] costs = {
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{5, 1, 3, 2},
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{6, 3, 4, 3},
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{5, 8, 6, 9},
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{6, 7, 8, 9},
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{8, 8, 12, 13},
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{11, 10, 12, 12}};
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for (int i=0; i < numberProcesses; i++){
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for (int j=0; j < numberMachines; j++){
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assertEquals(costs[i][j],opt.getCost(i,j));
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}
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}
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}
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}
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