diff --git a/src/backend/optimizer/geqo/geqo_recombination.c b/src/backend/optimizer/geqo/geqo_recombination.c
index 652fadc745..ef433e54e5 100644
--- a/src/backend/optimizer/geqo/geqo_recombination.c
+++ b/src/backend/optimizer/geqo/geqo_recombination.c
@@ -29,39 +29,33 @@
  *
  *	 Randomly generates a legal "traveling salesman" tour
  *	 (i.e. where each point is visited only once.)
- *	 Essentially, this routine fills an array with all possible
- *	 points on the tour and randomly chooses the 'next' city from
- *	 this array.  When a city is chosen, the array is shortened
- *	 and the procedure repeated.
  */
 void
 init_tour(PlannerInfo *root, Gene *tour, int num_gene)
 {
-	Gene	   *tmp;
-	int			remainder;
-	int			next,
-				i;
+	int			i,
+				j;
 
-	/* Fill a temp array with the IDs of all not-yet-visited cities */
-	tmp = (Gene *) palloc(num_gene * sizeof(Gene));
+	/*
+	 * We must fill the tour[] array with a random permutation of the numbers
+	 * 1 .. num_gene.  We can do that in one pass using the "inside-out"
+	 * variant of the Fisher-Yates shuffle algorithm.  Notionally, we append
+	 * each new value to the array and then swap it with a randomly-chosen
+	 * array element (possibly including itself, else we fail to generate
+	 * permutations with the last city last).  The swap step can be optimized
+	 * by combining it with the insertion.
+	 */
+	if (num_gene > 0)
+		tour[0] = (Gene) 1;
 
-	for (i = 0; i < num_gene; i++)
-		tmp[i] = (Gene) (i + 1);
-
-	remainder = num_gene - 1;
-
-	for (i = 0; i < num_gene; i++)
+	for (i = 1; i < num_gene; i++)
 	{
-		/* choose value between 0 and remainder inclusive */
-		next = geqo_randint(root, remainder, 0);
-		/* output that element of the tmp array */
-		tour[i] = tmp[next];
-		/* and delete it */
-		tmp[next] = tmp[remainder];
-		remainder--;
+		j = geqo_randint(root, i, 0);
+		/* i != j check avoids fetching uninitialized array element */
+		if (i != j)
+			tour[i] = tour[j];
+		tour[j] = (Gene) (i + 1);
 	}
-
-	pfree(tmp);
 }
 
 /* alloc_city_table