Removes the loops from a lineString (Test to outline a lineString without having weird overlaps) Please note that this algorithm is not optimized for performance. I recommend only using it in command line tools

beforeAndAfter.geojson

{
  "type": "FeatureCollection",
  "features": [
    {
      "type": "Feature",
      "properties": {
        "stroke": "#555555",
        "stroke-width": 7,
        "stroke-opacity": 1
      },
      "geometry": {
        "type": "LineString",
        "coordinates": [
          [
            23.37890625,
            57.61010702068388
          ],
          [
            16.5234375,
            53.225768435790194
          ],
          [
            23.37890625,
            50.064191736659104
          ],
          [
            23.203125,
            46.800059446787316
          ],
          [
            18.80859375,
            26.745610382199022
          ],
          [
            14.589843749999998,
            28.613459424004414
          ],
          [
            17.578125,
            35.31736632923788
          ],
          [
            28.30078125,
            33.137551192346145
          ],
          [
            30.585937499999996,
            11.523087506868514
          ],
          [
            30.234375,
            -20.797201434306984
          ],
          [
            21.09375,
            -21.125497636606266
          ],
          [
            10.1953125,
            -13.752724664396975
          ],
          [
            11.074218749999998,
            -5.0909441750333855
          ],
          [
            13.18359375,
            -0.7031073524364783
          ],
          [
            18.10546875,
            1.9332268264771233
          ],
          [
            22.67578125,
            2.986927393334876
          ],
          [
            46.05468749999999,
            -7.536764322084078
          ],
          [
            63.28125,
            -8.581021215641842
          ],
          [
            64.86328125,
            -3.513421045640032
          ],
          [
            65.21484375,
            2.986927393334876
          ],
          [
            60.64453125000001,
            4.565473550710278
          ],
          [
            54.140625,
            3.8642546157214084
          ],
          [
            51.67968749999999,
            0.17578097424708533
          ],
          [
            51.15234375,
            -11.350796722383672
          ],
          [
            51.328125,
            -20.632784250388013
          ],
          [
            49.39453125,
            -33.7243396617476
          ],
          [
            50.09765625,
            -46.07323062540835
          ],
          [
            44.29687499999999,
            -48.224672649565186
          ]
        ]
      }
    },
    {
      "type": "Feature",
      "properties": {
        "stroke": "#ffffff",
        "stroke-width": 2,
        "stroke-opacity": 1
      },
      "geometry": {
        "type": "LineString",
        "coordinates": [
          [
            23.37890625,
            57.61010702068388
          ],
          [
            16.5234375,
            53.225768435790194
          ],
          [
            23.37890625,
            50.064191736659104
          ],
          [
            23.203125,
            46.800059446787316
          ],
          [
            20.554340872593087,
            34.712329642573984
          ],
          [
            28.30078125,
            33.137551192346145
          ],
          [
            30.585937499999996,
            11.523087506868514
          ],
          [
            30.45499614735498,
            -0.5147787383520281
          ],
          [
            46.05468749999999,
            -7.536764322084078
          ],
          [
            51.31225567391882,
            -7.855472817116946
          ],
          [
            51.15234375,
            -11.350796722383672
          ],
          [
            51.328125,
            -20.632784250388013
          ],
          [
            49.39453125,
            -33.7243396617476
          ],
          [
            50.09765625,
            -46.07323062540835
          ],
          [
            44.29687499999999,
            -48.224672649565186
          ]
        ]
      }
    }
  ]
}

removeLoopsFromLineString.js

var ls = {
    "type": "Feature",
    "properties": {},
    "geometry": {
        "type": "LineString",
        "coordinates": [
            [23.37890625, 57.61010702068388],
            [16.5234375, 53.225768435790194],
            [23.37890625, 50.064191736659104],
            [23.203125, 46.800059446787316],
            [18.80859375, 26.745610382199022],
            [14.589843749999998, 28.613459424004414],
            [17.578125, 35.31736632923788],
            [28.30078125, 33.137551192346145],
            [30.585937499999996, 11.523087506868514],
            [30.234375, -20.797201434306984],
            [21.09375, -21.125497636606266],
            [10.1953125, -13.752724664396975],
            [11.074218749999998, -5.0909441750333855],
            [13.18359375, -0.7031073524364783],
            [18.10546875, 1.9332268264771233],
            [22.67578125, 2.986927393334876],
            [46.05468749999999, -7.536764322084078],
            [63.28125, -8.581021215641842],
            [64.86328125, -3.513421045640032],
            [65.21484375, 2.986927393334876],
            [60.64453125000001, 4.565473550710278],
            [54.140625, 3.8642546157214084],
            [51.67968749999999, 0.17578097424708533],
            [51.15234375, -11.350796722383672],
            [51.328125, -20.632784250388013],
            [49.39453125, -33.7243396617476],
            [50.09765625, -46.07323062540835],
            [44.29687499999999, -48.224672649565186]
        ]
    }
}
console.log(JSON.stringify(removeLoops(ls), null, 4));


function removeLoops(feature) {
    var segments = turf.lineSegment(feature);
    var hasIntersection = false;
    for (var i = 0; i < segments.features.length - 2; i++) {
        for (var j = i + 2; j < segments.features.length; j++) {
            var line1 = turf.lineString(segments.features[i].geometry.coordinates);
            var line2 = turf.lineString(segments.features[j].geometry.coordinates);
            var intersect = turf.lineIntersect(line1, line2);
            if (intersect.features.length > 0) {
                var intersectionCoordinates = intersect.features[0].geometry.coordinates;
                var throwAwayFromIndex = i + 1;
                var throwAwayToIndex = j + 1;
                var throwAwayNumber = throwAwayToIndex - throwAwayFromIndex;
                segments.features.splice(throwAwayFromIndex, throwAwayNumber);

                var newLineString = mergeLineStrings(segments);
                newLineString.geometry.coordinates.splice(throwAwayFromIndex, 0, intersectionCoordinates);
                return removeLoops(newLineString);
            }
        }
    }

    if (hasIntersection === false) {
        return feature;
    }
}

function mergeLineStrings(featureCollection) {
    var lineString = JSON.parse(JSON.stringify(featureCollection.features[0]));
    lineString.geometry.coordinates = [];
    delete lineString.bbox;
    delete lineString.id;

    for (var i = 0; i < featureCollection.features.length; i++) {
        var feature = featureCollection.features[i];
        lineString.geometry.coordinates.push(feature.geometry.coordinates[0]);
    }
    lineString.geometry.coordinates.push(featureCollection.features[featureCollection.features.length - 1].geometry.coordinates[1]);
    return lineString;
}