Beispiel #1
0
        /////////////////////////////////////////////////////////////////////////////////////////////////
        /////////////////////////////////////// BB Algorithm ////////////////////////////////////////////
        /////////////////////////////////////////////////////////////////////////////////////////////////
        #region MainBBAlgorithm
        /// <summary>
        /// performs a Branch and Bound search of the state space of partial tours
        /// stops when time limit expires and uses BSSF as solution
        /// Time Complexity: O((n^2)*(2^n) as that is the most dominant factor in the code, and it is a result
        /// of the loop, for more details scroll to the comment above the loop in the function.
        /// Space Complexity: O((n^2)*(2^n) as that is the most dominant factor in the code, and it is a result
        /// of the loop, for more details scroll to the comment above the loop in the function.
        /// </summary>
        /// <returns>results array for GUI that contains three ints: cost of solution, time spent to find solution, number of solutions found during search (not counting initial BSSF estimate)</returns>

        public string[] bBSolveProblem()
        {
            string[] results = new string[3];
            
            // Helper variables
            /* This part of the code takes O(1) space and time as we are just initializing some data */
            int numOfCitiesLeft = Cities.Length;
            int numOfSolutions = 0;
            int numOfStatesCreated = 0;
            int numOfStatesNotExpanded = 0;

            // Initialize the time variable to stop after the time limit, which is defaulted to 60 seconds
            /* This part of the code takes O(1) space and time as we are just initializing some data */
            DateTime start = DateTime.Now;
            DateTime end = start.AddSeconds(time_limit/1000);

            // Create the initial root State and set its priority to its lower bound as we don't have any extra info at this point
            /* This part of the code takes O(n^2) space and time as explained above */
            State initialState = createInitialState();
            numOfStatesCreated++;
            initialState.setPriority(calculateKey(numOfCitiesLeft - 1, initialState.getLowerBound()));

            // Create the initial BSSF Greedily
            /* This part of the code takes O(n^2) time and O(n) space as explained above */
            double BSSFBOUND = createGreedyInitialBSSF();

            // Create the queue and add the initial state to it, then subtract the number of cities left
            /* This part of the code takes O(1) time since we are just creating a data structure and 
            O(1,000,000) space which is just a constant so O(1) space as well*/
            PriorityQueueHeap queue = new PriorityQueueHeap();
            queue.makeQueue(Cities.Length);
            queue.insert(initialState);

            // Branch and Bound until the queue is empty, we have exceeded the time limit, or we found the optimal solution
            /* This loop will have a iterate 2^n times approximately with expanding and pruning for each state, then for each state it
            does O(n^2) work by reducing the matrix, so over all O((n^2)*(2^n)) time and space as well as it creates a nxn 
            matrix for each state*/
            while (!queue.isEmpty() && DateTime.Now < end && queue.getMinLB() != BSSFBOUND)
            {
                // Grab the next state in the queue
                State currState = queue.deleteMin();

                // check if lower bound is less than the BSSF, else prune it
                if (currState.getLowerBound() < BSSFBOUND)
                {
                    // Branch and create the child states
                    for (int i = 0; i < Cities.Length; i++)
                    {
                        // First check that we haven't exceeded the time limit
                        if (DateTime.Now >= end)
                            break;

                        // Make sure we are only checking cities that we haven't checked already
                        if (currState.getPath().Contains(Cities[i]))
                            continue;

                        // Create the State
                        double[,] oldCostMatrix = currState.getCostMatrix();
                        double[,] newCostMatrix = new double[Cities.Length, Cities.Length];
                        // Copy the old array in the new one to modify the new without affecting the old
                        for (int k = 0; k < Cities.Length; k++)
                        {
                            for (int l = 0; l < Cities.Length; l++)
                            {
                                newCostMatrix[k, l] = oldCostMatrix[k, l];
                            }
                        } 
                        City lastCityinCurrState = (City)currState.getPath()[currState.getPath().Count-1];
                        double oldLB = currState.getLowerBound();
                        setUpMatrix(ref newCostMatrix, Array.IndexOf(Cities, lastCityinCurrState), i, ref oldLB);
                        double newLB = oldLB + reduceMatrix(ref newCostMatrix);
                        ArrayList oldPath = currState.getPath();
                        ArrayList newPath = new ArrayList();
                        foreach (City c in oldPath)
                        {
                            newPath.Add(c);
                        }
                        newPath.Add(Cities[i]);
                        State childState = new State(ref newPath, ref newLB, ref newCostMatrix, Cities.Length);
                        numOfStatesCreated++;

                        // Prune States larger than the BSSF
                        if (childState.getLowerBound() < BSSFBOUND)
                        {
                            City firstCity = (City)childState.getPath()[0];
                            City lastCity = (City)childState.getPath()[childState.getPath().Count-1];
                            double costToLoopBack = lastCity.costToGetTo(firstCity);

                            // If we found a solution and it goes back from last city to first city
                            if (childState.getPath().Count == Cities.Length && costToLoopBack != double.MaxValue)
                            {
                                childState.setLowerBound(childState.getLowerBound() + costToLoopBack);
                                bssf = new TSPSolution(childState.getPath());
                                BSSFBOUND = bssf.costOfRoute();
                                numOfSolutions++;
                                numOfStatesNotExpanded++; // this state is not expanded because it is not put on the queue
                            }
                            else
                            {
                                // Set the priority for the state and add the new state to the queue
                                numOfCitiesLeft = Cities.Length - childState.getPath().Count;
                                childState.setPriority(calculateKey(numOfCitiesLeft, childState.getLowerBound()));
                                queue.insert(childState);
                            }
                        }
                        else
                        {
                            numOfStatesNotExpanded++; // States that are pruned are not expanded
                        }             
                    }           
                }
                currState = null;
            }
            numOfStatesNotExpanded += queue.getSize(); // if the code terminated before queue is empty, then those states never got expanded
            Console.WriteLine("Number of states generated: " + numOfStatesCreated);
            Console.WriteLine("Number of states not Expanded: " + numOfStatesNotExpanded);
            Console.WriteLine("Max Number of states put in queue: " + queue.getMaxNumOfItems());
            end = DateTime.Now;
            TimeSpan diff = end - start;
            double seconds = diff.TotalSeconds;
            results[COST] = System.Convert.ToString(bssf.costOfRoute());    // load results into array here, replacing these dummy values
            results[TIME] = System.Convert.ToString(seconds);
            results[COUNT] = System.Convert.ToString(numOfSolutions);

            return results;
        }