タイブレークの目標を使用して同等のソリューションを解決する
複数のソリューションが類似したコストやパフォーマンスのメトリックを持つ場合、追加の基準に基づいて最適なソリューションを選択する方法が必要になります。tieBreakの目標は、許容可能なしきい値範囲を持つ主たる目標を定義し、その範囲内に収まるソリューション間の優劣を判別するために副次的な目標を使用できるようにすることで、この問題を解決します。
この階層的アプローチにより、主たる最適化目標を満たすだけでなく、複数の同等に妥当な選択肢が存在する場合に、他の重要な運用面の側面も改善するソリューションを見つけるのに役立ちます。具体的には、この機能は、旅程の重複の削減やルートのコンパクト化といった他の運用上のメリットと引き換えに、小さなコスト増加が許容されるシナリオにおいて有用です。
ビジネスシナリオの例：コスト最適化と運用効率のバランス
大都市の人口が密集した商業地区で運営されている配送サービスを考えてみましょう。このサービスは、通常1回の旅程で最大50件の注文を処理する2人のドライバーを雇用しています。
利益率を維持するために、このサービスは旅程のコストの最小化に重点を置いています。しかし問題は、ルートの組み合わせのコスト差がごくわずか (2～3ドル程度) であるにもかかわらず、運用効率には大きな差がある点です。このことは、コスト最適な旅程が重複してしまい、複数の車両が同じ地域をカバーすることにより、最適とは言えないルート、ドライバーの不満、配送ミスのリスクの増大につながる可能性があります。
tieBreakの目標を使用すると、最適化アルゴリズムは、運用効率の改善と引き換えにわずかなコスト増加を受け入れながら、コスト効率の高い旅程を提供します。ここでの運用効率の改善とは、よりコンパクトな旅程を意味します。
以下のセクションでは、このシナリオを取り上げ、HERE Tour Planning APIの問題設定において、tieBreakの目標をどのように設定するかを説明します。このセクションでは、tieBreakの目標を含まない基本的なシナリオと、この目標を含むシナリオを比較し、わずかながら許容範囲内のコスト増加によって、旅程の重複を減らす方法を示します。
tieBreakパラメーターを理解する
サンプルシナリオを見ていく前に、tieBreakの目標をどのように設定し、それを問題JSONにどのように適用するかを理解する必要があります。
注
これは開発中のテスト段階の機能です。この機能を有効にするには、問題仕様で
advancedObjectivesをexperimentalFeatures配列に追加します。詳細については、「テスト段階の機能」を参照してください。
以下のスニペットは、tieBreakの目標を含むadvancedObjectives設定の一例を示しており、ここでのminimizeCostは主たるtieBreakの目標、minimizeTourOverlapは副次的なtieBreakの目標です。
// Remaining problem components omitted for brevity
"advancedObjectives": [
[
{
"type": "minimizeUnassigned"
}
],
[
{
"type": "tieBreak",
"objectives": [
{
"objective": {
"type": "minimizeCost"
},
"tieThreshold": 0.04
},
{
"objective": {
"type": "minimizeTourOverlap"
},
"improvementThreshold": 0.05
}
]
}
]
]スニペットに示されているとおり、tieBreakの目標は複数の主要パラメーターを使用して、階層的な最適化プロセスを制御します。
tieThreshold：主たるtieBreakの目標の重要業績評価指標 (KPI) に対して許容される範囲を設定します。このしきい値内にあるソリューションは「同点」と見なされ、副次的な最適化の対象になります。言い換えれば、このパラメーターを設定する際には、副次的な目標の改善と引き換えに、主たる目標のKPIをどの程度許容できるかをパーセンテージで指定します。improvementThreshold：また、副次的なtieBreakの目標において、別のソリューションを選択することを正当化するために必要な最小限の改善量を設定します。
このスニペットでは、2段階の最適化構造を持つ階層的な目標設定の方法も示しています。
レベル1 - 主たる目標：minimizeUnassigned
- 優先度：最高
- 目的：可能な限りすべてのジョブを車両に割り当てる。
レベル2 - tieBreakの目標
これにより、この優先度レベル内で階層的なタイブレークシステムが作成されます。
主たるタイブレークの目標：minimizeCost
tieThreshold: 0.04：2つのソリューションのコスト差が4%以内であれば、それらは「同点」と見なされます。- 例：コストが
100と103のソリューションは、差が3%であるため (4%のしきい値未満)、同等と見なされます。
副次的なタイブレークの目標：minimizeTourOverlap
improvementThreshold: 0.05：minimizeCostの目標によってタイブレークするには、該当するソリューションのいずれかについて、旅程の重複の削減が少なくとも5%以上である必要があります。
例：旅程の重複をタイブレーカーとしてコストを最小化する
この例では、前述のユースケースを問題全体のJSONの文脈に当てはめています。この特定のユースケースでは、配送サービスが2台の車両を運用し、人口密度の高い地域で49件のジョブに対応しています。
主たる目標は総コストの最小化ですが、複数のソリューションのコストが類似している場合 (5%のしきい値内)、旅程の重複が最小のソリューションを優先することにより、運用効率を向上させ、ドライバーの混乱を減らすアルゴリズムとなる必要があります。
以下のセクションでは、tieBreakの目標を使用した場合と使用しない場合のアプローチを比較し、この目標タイプを用いることにより、コスト効率を保ちつつソリューションの質を向上できることを示します。
シナリオ1：tieBreakを使用しないデフォルトの最適化
最初のシナリオは、tieBreakを使用しない複数の目標の最適化を用いたベースラインのアプローチを示しています。この最適化では、未割り当てのジョブの最小化、コストの最小化、旅程重複の最小化という3つの個別目標レベルを使用しており、最も重要な目標が最上位に配置されていることが以下のスニペットに示されています。
"advancedObjectives": [
[
{
"type": "minimizeUnassigned"
}
],
[
{
"type": "minimizeCost"
}
],
[
{
"type": "minimizeTourOverlap"
}
]
]次のセクションでは問題JSONをすべて示します。
Click to expand/collapse the sample JSON
{
"configuration": {
"experimentalFeatures": [
"advancedObjectives"
]
},
"fleet": {
"types": [
{
"profile": "car",
"amount": 2,
"capacity": [
25
],
"costs": {
"time": 0.02,
"distance": 0.01,
"fixed": 10
},
"id": "vehicle_1",
"shifts": [
{
"start": {
"location": {
"lat": 52.61213641890272,
"lng": 13.368000177132913
},
"time": "2024-07-31T06:00:00+02:00"
},
"end": {
"location": {
"lat": 52.61213641890272,
"lng": 13.368000177132913
},
"time": "2024-07-31T19:00:00+02:00"
}
}
]
}
],
"profiles": [
{
"name": "car",
"type": "car"
}
]
},
"plan": {
"jobs": [
{
"id": "Job_1",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.63329,
"lng": 13.3138
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_2",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.62738533184079,
"lng": 13.3789
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_3",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.51635175288175,
"lng": 13.343661020679571
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_4",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.456,
"lng": 13.403260583257188
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_5",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.63256,
"lng": 13.37322
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_6",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.45810373923444,
"lng": 13.331808942475499
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_7",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.439442845393685,
"lng": 13.336118100685782
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_8",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.53213114000045,
"lng": 13.373517153879769
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_9",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.4823,
"lng": 13.4703
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_10",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.5313,
"lng": 13.35356
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_11",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.457844833248835,
"lng": 13.322525701671735
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_12",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.4329271708958,
"lng": 13.376558539227483
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_13",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.48128598928299,
"lng": 13.4944
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_14",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.580380893737356,
"lng": 13.304479222218161
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_15",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.444597854004236,
"lng": 13.42729037972278
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_16",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.5102,
"lng": 13.3444
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_17",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.48903177127663,
"lng": 13.495944342993262
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_18",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.62863,
"lng": 13.3621182
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_19",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.65831976801964,
"lng": 13.359646771531477
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_20",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.61955,
"lng": 13.29845
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_21",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.49949154428338,
"lng": 13.40857671284082
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_22",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.465255531970406,
"lng": 13.511537556934355
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_23",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.4312,
"lng": 13.45023
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_24",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.5293,
"lng": 13.38507204916371
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_25",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.6378,
"lng": 13.48675
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_26",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.53754,
"lng": 13.34152
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_27",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.48811100200862,
"lng": 13.376
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_28",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.4745,
"lng": 13.42
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_29",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.58884270031872,
"lng": 13.352068415230912
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_30",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.60079217247425,
"lng": 13.339813254226156
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_31",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.4779,
"lng": 13.5012
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_32",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.60066027234286,
"lng": 13.502741838681837
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_33",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.55437436208552,
"lng": 13.503142187091647
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_34",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.48446152479127,
"lng": 13.392004256315916
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_35",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.482203294624796,
"lng": 13.391214601891551
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_36",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.60842932011795,
"lng": 13.46922174529483
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_37",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.47651505101506,
"lng": 13.459944175857151
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_38",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.50488105730338,
"lng": 13.355333507786808
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_39",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.6029,
"lng": 13.3113
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_40",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.6543,
"lng": 13.39278
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_41",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.51508491755749,
"lng": 13.38
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_42",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.63313572894435,
"lng": 13.506488581249922
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_43",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.459450803409204,
"lng": 13.396015195980405
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_44",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.54433793446157,
"lng": 13.49579242116612
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_45",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.486517527979494,
"lng": 13.382057792236846
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_46",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.55606147412602,
"lng": 13.41517487839967
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_47",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.591995183321515,
"lng": 13.36000789424169
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_48",
"tasks": {
"deliveries": [
{
"places": [
{
"location": {
"lat": 52.56223251898173,
"lng": 13.471999398223556
},
"duration": 30
}
],
"demand": [
1
]
}
]
}
},
{
"id": "Job_49",
"tasks": {
"deliveries": [
{
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{
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},
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}
],
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1
]
}
]
}
}
]
},
"advancedObjectives": [
[
{
"type": "minimizeUnassigned"
}
],
[
{
"type": "minimizeCost"
}
],
[
{
"type": "minimizeTourOverlap"
}
]
]
}ソリューション
次の図は最適化アルゴリズムが最適と判断した、前述の問題のソリューションを視覚化したものです。
ソリューションの概要が示すとおり、すべての車両が、未割り当てのジョブなしで旅程を完了し、コスト効率良く実行されています。このソリューションは主たる目標を達成していますが、旅程の重複の最小化という点においては、最適なトレードオフを必ずしも示しているとは限りません。具体的には、2つの旅程が相互に大きく重複しています。
以下のセクションでは、ソリューションの完全なJSONを示します。
Click to expand/collapse the sample JSON
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]
}シナリオ2：tieBreakを使用した階層的な目標
このシナリオでは、tieBreakの目標を使用し、コストと旅程の重複間のインテリジェントなトレードオフを作る高度なアプローチを示しています。複数のソリューションが5%以内のコスト差で存在する場合、アルゴリズムは旅程の重複パフォーマンスがより優れたものを選択します。
このシナリオは、前のシナリオとまったく同じ問題設定を使用していますが、以下の点が異なります。
"advancedObjectives": [
[
{
"type": "minimizeUnassigned"
}
],
[
{
"type": "tieBreak",
"objectives": [
{
"objective": {
"type": "minimizeCost"
},
"tieThreshold": 0.04
},
{
"objective": {
"type": "minimizeTourOverlap"
},
"improvementThreshold": 0.05
}
]
}
]
]この構成での主な違いは、tieBreakの目標の構造です。
- 主たる目標：
tieThresholdが0.04(4%) のminimizeCost - 副次的な目標：
improvementThresholdが0.05(5%) のminimizeTourOverlap
この変更により、アルゴリズムはまずコストを最小化するソリューションを見つけます。次に、複数のソリューションのコストが最良値の4%以内であれば、改善が5%以上であるという条件を満たす限り、旅程の重複パフォーマンスが最も優れたものが選択されます。
ソリューション
次の図は、tieBreakの目標を用いた問題のソリューションを可視化したものです。
タイブレークを用いたアプローチでは、コスト効率と運用上の利点のバランスが取れたソリューションが生成されます。
- コストへの影響：強化されたソリューションでは総コストがわずかに高くなる可能性がありますが、それでも4%のしきい値内に収まっています。具体的には、
tieBreakの目標を含むソリューションのコストは2629であり、よりコスト効率の高い代替案の2575と比べて、増加率はわずか**2.01%**で、許容されるコストの同点しきい値内に十分収まっています。 - 旅程の重複の改善：このソリューションでは車両の旅程間の重複が発生しておらず、明確な担当エリアの分離が実現され、より効率的な運用につながる可能性があります。次の図は、2つのソリューションにおける旅程の重複の比較を示しています。
- 運用上のメリット：旅程の重複の削減により、ドライバーの混乱が軽減され、カスタマーサービスの競合リスクが低下し、運行管理全体の連携が向上します。
以下のセクションでは、ソリューションの完全なJSONを示します。
Click to expand/collapse the sample JSON
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"break": 0
}
},
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{
"vehicleId": "vehicle_1_1",
"typeId": "vehicle_1",
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"end": "2024-07-31T07:19:47Z"
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{
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},
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"activities": [
{
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"type": "arrival",
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"lng": 13.368000177132911
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"time": {
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}
],
"statistic": {
"cost": 1203.59,
"distance": 94403,
"duration": 12478,
"times": {
"driving": 11728,
"serving": 750,
"waiting": 0,
"stopping": 0,
"break": 0
}
},
"shiftIndex": 0
}
]
}結論
このチュートリアルでは、tieBreakの目標を使用することによって、主たる最適化の目標と副次的な運用要件の両方を考慮したインテリジェントなトレードオフが可能となり、実運用により適したソリューションが得られることを示しました。
次のステップ
詳細については、以下を参照してください。
26 日前の更新