A Novel Heuristic For The Traveling Salesman Problem: maxS

Abstract

In this study, a new initial solution heuristic was proposed for the traveling salesman problem. The proposed maxS method is based on a new distance matrix obtained by normalizing the distance matrix of the problem being addressed according to the maximum row value. The proposed method was tested on 20 small and 11 large-scale problems, recommended by Hougardy and Zhong, which are difficult to solve optimally. The same problems were also solved by Greedy, Boruvka, Quick-Boruvka, Nearest-Neighborhood and Lin-Kernighan heuristics working on the Concorde software. Based on the comparisons, it is seen that the recommended maxS heuristic performance was better than that of Greedy and Nearest-Neighborhood heuristics and it showed a similar performance with Boruvka in small-scale problems. When the same comparisons were made for large-scale problems, maxS showed better performance than Quick Boruvka and Nearest-Neighborhood heuristics, on average. The maxS heuristic, which is very effective in terms of solution times, can be proposed as a promising initial solution method.

Keywords

• Traveling Salesman Problem
• maxS
• Boruvka
• Nearest-Neighborhood
• Lin-Kernighan
• Initial Solutions

Gezgin Satici Problemi Için Yeni Bir Sezgisel:maxS

Abstract

Bu çalışmada, gezgin satıcı problemi için yeni bir başlangıç çözüm sezgiseli önerilmiştir. Önerilen maxS metodu, üzerinde çalışılan problemin mesafe matrisinin maksimum satır değerine göre normalize edilmesiyle elde edilen yeni mesafe matrisi ile çalışır. Önerilen metot, Hougardy ve Zhong tarafından tavsiye edilen ve optimal çözümü zor olan 20 küçük ve 11 büyük ölçekte problem üzerinde test edilmiştir. Aynı problemler, Concorde yazılımı üzerinde çalışan Greedy, Boruvka, Quick-Boruvka, Nearest-Neighborhood and Lin-Kernighan sezgiselleri ile de çözülmüştür. Çözümler karşılaştırıldığında küçük ölçekli problemler için maxS sezgiselinin performansının Greedy ve Nearest-Neighborhood sezgisellerinden daha iyi olduğu ve Boruvka ile benzer performansta olduğu gözlenmiştir. Benzer karşılaştırmalar büyük ölçekli problemler için yapıldığında maxS, Quick Boruvka ve Nearest-Neighborhood sezgisellerinden ortalama olarak daha iyi performans göstermiştir. Çözüm zamanları açısından çok etkili olan maxS sezgiseli, gelecek vaadeden başlangıç çözüm yöntemi olarak önerilebilir.

Keywords

• Gezgin Satıcı Problemi
• maxS
• Boruvka
• Nearest-Neighbourhood
• Lin-Kernighan
• başlangıç çözümü

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