rymdresa.js

let pos = [
  [0, 0],
	[-35, -12],
	[-50, -50],
	[-80, -40],
	[-50, 50],
	[0, -66],
	[35, -35],
	[68, -50],
	[70, -4],
	[35, 12],
	[0, 12],
];

function dist(ii, jj) {
	return Math.max(Math.abs(pos[ii][0] - pos[jj][0]), Math.abs(pos[ii][1] - pos[jj][1]));
}

let best = Infinity;
let best_arr;

function search(cur_pos, cur_dist, mask) {
	/* jshint bitwise:false*/
	let m = 1;
	let b = false;
	let r = false;
	for (let ii = 0; ii < pos.length - 1; ++ii) {
		if (!(m & mask)) {
			b = true;
			if (search(ii, cur_dist + dist(cur_pos, ii), mask | m)) {
				best_arr.push(cur_pos);
				r = true;
			}
		}
		m = m << 1;
	}
	if (!b) {
		cur_dist += dist(cur_pos, pos.length - 1);
		if (cur_dist < best) {
			best = cur_dist;
			best_arr = [pos.length - 1, cur_pos];
			return true;
		}
	}
	return r;
}

search(0, 0, 1);
best_arr = best_arr.reverse();
// best_arr = [0,1,2,3,4,5,6,7,8,9,10];
let sum = 0;
for (let ii = 1; ii < best_arr.length; ++ii) {
	sum += dist(best_arr[ii-1], best_arr[ii]);
}
console.log(sum, best_arr.map(function (idx, ii) { return pos[idx].toString(', ') + (ii > 0 ? ' (' + dist(best_arr[ii-1], idx) + ')' : ''); }));