Add 2-opt-tsp solver

Author: RoundofThree

2-opt-tsp/2-opt-tsp.py

@@ -0,0 +1,113 @@
+import numpy as np
+
+# convert A of input to 0, when output
+
+class TSP:
+    def __init__(self, weights, tour, verticesMapping):
+        self.tour = tour  # preorder traversal of MST, ordered list of ints   
+        self.weights = weights # np 2D array of ints, cost matrix, keys are ints  
+        self.d = self.calculateWeight(tour)
+        self.verticesMapping = verticesMapping
+        print(f"Tour: {self.printTour(self.tour)}, total distance: {self.d}")
+    
+    # weight of the input tour 
+    def calculateWeight(self, tour):
+        ret = 0
+        for idx in range(len(tour)):
+            v_1 = tour[idx]
+            if idx == len(tour)-1:
+                v_2 = tour[0]
+            else:
+                v_2 = tour[idx+1]
+            ret += self.weights[v_1][v_2]
+        return ret
+
+    # optimize 
+    def optimize(self):
+        N = len(self.tour)
+        for i in range(N-3):
+            for j in range(i+2, N-1):
+                newTour = np.copy(self.tour)
+                newTour[i+1] = self.tour[j]
+                tmp = i+2
+                for k in range(j-1, i, -1):
+                    newTour[tmp] = self.tour[k]
+                    tmp += 1
+                newD = self.calculateWeight(newTour)
+                if newD < self.d:
+                    self.tour = np.copy(newTour)
+                    self.d = newD
+                    print(f"Tour: {self.printTour(self.tour)}, total distance: {self.d}")
+                    self.optimize()  # tail recursive 
+
+    # map a list of integers to the corresponding list of strings 
+    def printTour(self, tour):
+        return list(map(lambda x: self.verticesMapping[x], tour))
+from collections import defaultdict
+from typing import DefaultDict
+import heapq
+class MST:
+    def __init__(self, cost, root):
+        self.root = root 
+        self.cost_matrix = cost 
+        self.mst = self.prims()
+
+    def prims(self):
+        ret = defaultdict(set) 
+        visited = set([self.root])
+        edges = [(cost, self.root, v_2) for v_2, cost in enumerate(self.cost_matrix[self.root])]
+        heapq.heapify(edges)
+        while edges:
+            cost, start, to = heapq.heappop(edges)
+            if to not in visited:
+                visited.add(to)
+                ret[start].add(to) 
+                for to_next, cost in enumerate(self.cost_matrix[to]):
+                    if to_next not in visited:
+                        heapq.heappush(edges, (self.cost_matrix[to][to_next], to, to_next))
+        return ret
+
+    def preorder(self, root):
+        # convert mst a dictionary to list 
+        children = self.mst[root]
+        ret = [root]
+        for child in children:
+            ret = ret + self.preorder(child)
+        return ret 
+
+import argparse
+
+if __name__ == '__main__':
+    parser = argparse.ArgumentParser(description="Apply 2-opt algorithm to approximate TSP solution step by step. By Roundofthree.")
+    # ask for vertices, eg.: A,B,C,D,E
+    vertices = input("Enter the vertices separated by single comma: ").strip().split(",")  # ['A', 'B', 'C', 'D', 'E']
+    verticesMapping = []
+    N = len(vertices)
+    for i in range(0, N):
+        verticesMapping.append(vertices[i]) 
+    # ask for cost matrix nxn, eg.:
+    #  A | B | C | D | E
+    # A -> 0,13,23,4,2,4
+    # B -> 
+    print(' | '.join(vertices))
+    cost = [] 
+    for v in vertices:
+        input_array = list(map(int, input(v+"-> ").strip().split(",")))
+        if len(input_array) == N:
+            cost.append(input_array)
+        else: 
+            print("error") # and terminate 
+    np_cost = np.array(cost).reshape(N,N)
+    # calculate MST from np_cost and vertices --> Prim's starting from 0 
+    mst = MST(np_cost, 0) 
+    mst_preorder = mst.preorder(0) 
+    # mst_preorder = [0, 1, 2, 3, 4] 
+    # compute preorder traversal of tree as a list 
+    tsp_solver = TSP(np_cost, mst_preorder, verticesMapping)
+    tsp_solver.optimize()
+    
+
+        
+
+    
+        

2-opt-tsp/README.md

@@ -0,0 +1,28 @@
+## 2-opt TSP algorithm 
+
+Input: weighted complete graph 
+
+```
+Enter the vertices separated by single comma: A,B,C,D,E
+A | B | C | D | E
+A-> 0,1,1,1,1 # enter the cost matrix as an adjacency matrix, separated by single comma 
+B-> 1,0,1,1,1
+C-> 1,1,0,1,1
+D-> 1,1,1,0,1
+E-> 1,1,1,1,0
+```
+
+Output: Hamiltonian cycle, with step-by-step swaps 
+
+```
+Tour: ['A', 'B', 'C', 'D', 'E'], total distance: 5
+```
+
+Procedure:
+
+1. Construct Minimum Spanning Tree with Prim's algorithm.
+2. Preorder traversal, and set the `score` to the weight sum. 
+3. Heuristic: find the largest edge first, then other edges. 
+    1. Choose another edge. 
+    2. Cross: (a, b) with (c, d) --> (a,c)
+    3. If total weight of new tour is smaller, update tour and start from 3 again. 

README.md

@@ -3,3 +3,4 @@
 | Script | Description |
 | -- | -- |
 |[Signature parser](create_electronic_sign) | Parse handwritten signature in JPG/JPEG/PNG to a new JPG with black signature and transparent background. |
+|[2-opt TSP](2-opt-tsp) | Find local minimum weighted Hamiltonian cycle in a complete graph expressed with a cost adjacency matrix. |