Pub Date : 2023-12-21DOI: 10.1007/s10732-023-09523-w
Giuseppe Lancia, Marcello Dalpasso
We describe an effective algorithm for exploring the (4)-OPT neighborhood for the Traveling Salesman Problem. (4)-OPT moves change a tour into another by replacing four of its edges. The best move can be found by a (Theta (n^4)) algorithm by complete enumeration, but a (Theta (n^3)) dynamic programming algorithm exists in the literature. Furthermore a (Theta (n^2)) algorithm also exists for a particular subset of symmetric (4)-OPT moves. In this work we describe a new procedure which behaves, on average, slightly worse than a quadratic algorithm over all moves (estimated at (O(n^{2.5}))) and like a quadratic algorithm on the symmetric moves. Computational results are reported which show the effectiveness of our strategy compared to other algorithms for finding the best (4)-OPT move, and discuss the strength of the (4)-OPT neighborhood compared to 2- and (3)-OPT.
{"title":"Algorithmic strategies for a fast exploration of the TSP $$4$$ -OPT neighborhood","authors":"Giuseppe Lancia, Marcello Dalpasso","doi":"10.1007/s10732-023-09523-w","DOIUrl":"https://doi.org/10.1007/s10732-023-09523-w","url":null,"abstract":"<p>We describe an effective algorithm for exploring the <span>(4)</span>-OPT neighborhood for the Traveling Salesman Problem. <span>(4)</span>-OPT moves change a tour into another by replacing four of its edges. The best move can be found by a <span>(Theta (n^4))</span> algorithm by complete enumeration, but a <span>(Theta (n^3))</span> dynamic programming algorithm exists in the literature. Furthermore a <span>(Theta (n^2))</span> algorithm also exists for a particular subset of symmetric <span>(4)</span>-OPT moves. In this work we describe a new procedure which behaves, on average, slightly worse than a quadratic algorithm over all moves (estimated at <span>(O(n^{2.5}))</span>) and like a quadratic algorithm on the symmetric moves. Computational results are reported which show the effectiveness of our strategy compared to other algorithms for finding the best <span>(4)</span>-OPT move, and discuss the strength of the <span>(4)</span>-OPT neighborhood compared to 2- and <span>(3)</span>-OPT.</p>","PeriodicalId":54810,"journal":{"name":"Journal of Heuristics","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139029515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-15DOI: 10.1007/s10732-023-09522-x
Louis Carpentier, Jorik Jooken, Jan Goedgebeur
We propose a new methodology to develop heuristic algorithms using tree decompositions. Traditionally, such algorithms construct an optimal solution of the given problem instance through a dynamic programming approach. We modify this procedure by introducing a parameter W that dictates the number of dynamic programming states to consider. We drop the exactness guarantee in favour of a shorter running time. However, if W is large enough such that all valid states are considered, our heuristic algorithm proves optimality of the constructed solution. In particular, we implement a heuristic algorithm for the Maximum Happy Vertices problem using this approach. Our algorithm more efficiently constructs optimal solutions compared to the exact algorithm for graphs of bounded treewidth. Furthermore, our algorithm constructs higher quality solutions than state-of-the-art heuristic algorithms Greedy-MHV and Growth-MHV for instances of which at least 40% of the vertices are initially coloured, at the cost of a larger running time.
{"title":"A heuristic algorithm using tree decompositions for the maximum happy vertices problem","authors":"Louis Carpentier, Jorik Jooken, Jan Goedgebeur","doi":"10.1007/s10732-023-09522-x","DOIUrl":"https://doi.org/10.1007/s10732-023-09522-x","url":null,"abstract":"<p>We propose a new methodology to develop heuristic algorithms using tree decompositions. Traditionally, such algorithms construct an optimal solution of the given problem instance through a dynamic programming approach. We modify this procedure by introducing a parameter <i>W</i> that dictates the number of dynamic programming states to consider. We drop the exactness guarantee in favour of a shorter running time. However, if <i>W</i> is large enough such that all valid states are considered, our heuristic algorithm proves optimality of the constructed solution. In particular, we implement a heuristic algorithm for the Maximum Happy Vertices problem using this approach. Our algorithm more efficiently constructs optimal solutions compared to the exact algorithm for graphs of bounded treewidth. Furthermore, our algorithm constructs higher quality solutions than state-of-the-art heuristic algorithms Greedy-MHV and Growth-MHV for instances of which at least 40% of the vertices are initially coloured, at the cost of a larger running time.</p>","PeriodicalId":54810,"journal":{"name":"Journal of Heuristics","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"DSLS: a simple and efficient local search algorithm for the maximum bisection problem","authors":"Xinliang Tian, Dantong Ouyang, Huisi Zhou, Rui Sun, Liming Zhang","doi":"10.1007/s10732-023-09521-y","DOIUrl":"https://doi.org/10.1007/s10732-023-09521-y","url":null,"abstract":"","PeriodicalId":54810,"journal":{"name":"Journal of Heuristics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136282419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-11DOI: 10.1007/s10732-023-09520-z
Ebrahim Teimoury, Reza Rashid
{"title":"A hybrid variable neighborhood search heuristic for the sustainable time-dependent truck-drone routing problem with rendezvous locations","authors":"Ebrahim Teimoury, Reza Rashid","doi":"10.1007/s10732-023-09520-z","DOIUrl":"https://doi.org/10.1007/s10732-023-09520-z","url":null,"abstract":"","PeriodicalId":54810,"journal":{"name":"Journal of Heuristics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135041837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-13DOI: 10.1007/s10732-023-09519-6
Mohamed-Amine Ouberkouk, Jean-Paul Boufflet, Aziz Moukrim
{"title":"Effective adaptive large neighborhood search for a firefighters timetabling problem","authors":"Mohamed-Amine Ouberkouk, Jean-Paul Boufflet, Aziz Moukrim","doi":"10.1007/s10732-023-09519-6","DOIUrl":"https://doi.org/10.1007/s10732-023-09519-6","url":null,"abstract":"","PeriodicalId":54810,"journal":{"name":"Journal of Heuristics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135854749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-09DOI: 10.1007/s10732-023-09518-7
Majid Namazi, M. A. Hakim Newton, Conrad Sanderson, Abdul Sattar
A travelling thief problem (TTP) is a proxy to real-life problems such as postal collection. TTP comprises an entanglement of a travelling salesman problem (TSP) and a knapsack problem (KP) since items of KP are scattered over cities of TSP, and a thief has to visit cities to collect items. In TTP, city selection and item selection decisions need close coordination since the thief's travelling speed depends on the knapsack's weight and the order of visiting cities affects the order of item collection. Existing TTP solvers deal with city selection and item selection separately, keeping decisions for one type unchanged while dealing with the other type. This separation essentially means very poor coordination between two types of decision. In this paper, we first show that a simple local search based coordination approach does not work in TTP. Then, to address the aforementioned problems, we propose a human designed coordination heuristic that makes changes to collection plans during exploration of cyclic tours. We further propose another human designed coordination heuristic that explicitly exploits the cyclic tours in item selections during collection plan exploration. Lastly, we propose a machine learning based coordination heuristic that captures characteristics of the two human designed coordination heuristics. Our proposed coordination based approaches help our TTP solver significantly outperform existing state-of-the-art TTP solvers on a set of benchmark problems. Our solver is named Cooperation Coordination (CoCo) and its source code is available from https://github.com/majid75/CoCo
{"title":"Solving travelling thief problems using coordination based methods","authors":"Majid Namazi, M. A. Hakim Newton, Conrad Sanderson, Abdul Sattar","doi":"10.1007/s10732-023-09518-7","DOIUrl":"https://doi.org/10.1007/s10732-023-09518-7","url":null,"abstract":"A travelling thief problem (TTP) is a proxy to real-life problems such as postal collection. TTP comprises an entanglement of a travelling salesman problem (TSP) and a knapsack problem (KP) since items of KP are scattered over cities of TSP, and a thief has to visit cities to collect items. In TTP, city selection and item selection decisions need close coordination since the thief's travelling speed depends on the knapsack's weight and the order of visiting cities affects the order of item collection. Existing TTP solvers deal with city selection and item selection separately, keeping decisions for one type unchanged while dealing with the other type. This separation essentially means very poor coordination between two types of decision. In this paper, we first show that a simple local search based coordination approach does not work in TTP. Then, to address the aforementioned problems, we propose a human designed coordination heuristic that makes changes to collection plans during exploration of cyclic tours. We further propose another human designed coordination heuristic that explicitly exploits the cyclic tours in item selections during collection plan exploration. Lastly, we propose a machine learning based coordination heuristic that captures characteristics of the two human designed coordination heuristics. Our proposed coordination based approaches help our TTP solver significantly outperform existing state-of-the-art TTP solvers on a set of benchmark problems. Our solver is named Cooperation Coordination (CoCo) and its source code is available from https://github.com/majid75/CoCo","PeriodicalId":54810,"journal":{"name":"Journal of Heuristics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135094808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-23DOI: 10.1007/s10732-023-09517-8
Jan Wehner, Michael Sioutis, Diedrich Wolter
{"title":"On robust vs fast solving of qualitative constraints","authors":"Jan Wehner, Michael Sioutis, Diedrich Wolter","doi":"10.1007/s10732-023-09517-8","DOIUrl":"https://doi.org/10.1007/s10732-023-09517-8","url":null,"abstract":"","PeriodicalId":54810,"journal":{"name":"Journal of Heuristics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135967313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-22DOI: 10.1007/s10732-023-09516-9
Abtin Nourmohammadzadeh, Malek Sarhani, Stefan Voß
Abstract In the family traveling salesman problem (FTSP), there is a set of cities which are divided into a number of clusters called families. The salesman has to find a shortest possible tour visiting a specific number of cities from each of the families without any restriction of visiting one family before starting the visit of another one. In this work, the general concept of the Partial OPtimization Metaheuristic Under Special Intensification Conditions is linked with the exact optimization by a classical solver using a mathematical programming formulation for the FTSP to develop a matheuristic. Moreover, a genetic and a simulated annealing algorithm are used as metaheuristics embedded in the approach. The method is examined on a set of benchmark instances and its performance is favorably compared with a state-of-the-art approach from literature. Moreover, a careful analysis of the specific components of the approach is undertaken to provide insights into the impact of their interplay.
{"title":"A matheuristic approach for the family traveling salesman problem","authors":"Abtin Nourmohammadzadeh, Malek Sarhani, Stefan Voß","doi":"10.1007/s10732-023-09516-9","DOIUrl":"https://doi.org/10.1007/s10732-023-09516-9","url":null,"abstract":"Abstract In the family traveling salesman problem (FTSP), there is a set of cities which are divided into a number of clusters called families. The salesman has to find a shortest possible tour visiting a specific number of cities from each of the families without any restriction of visiting one family before starting the visit of another one. In this work, the general concept of the Partial OPtimization Metaheuristic Under Special Intensification Conditions is linked with the exact optimization by a classical solver using a mathematical programming formulation for the FTSP to develop a matheuristic. Moreover, a genetic and a simulated annealing algorithm are used as metaheuristics embedded in the approach. The method is examined on a set of benchmark instances and its performance is favorably compared with a state-of-the-art approach from literature. Moreover, a careful analysis of the specific components of the approach is undertaken to provide insights into the impact of their interplay.","PeriodicalId":54810,"journal":{"name":"Journal of Heuristics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136061003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-09DOI: 10.1007/s10732-023-09515-w
Fatemeh Sarayloo, T. Crainic, W. Rei
{"title":"An integrated learning and progressive hedging matheuristic for stochastic network design problem","authors":"Fatemeh Sarayloo, T. Crainic, W. Rei","doi":"10.1007/s10732-023-09515-w","DOIUrl":"https://doi.org/10.1007/s10732-023-09515-w","url":null,"abstract":"","PeriodicalId":54810,"journal":{"name":"Journal of Heuristics","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42926158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-29DOI: 10.1007/s10732-023-09513-y
Michel Vasquez, Mirsad Buljubasic, S. Hanafi
{"title":"An efficient scenario penalization matheuristic for a stochastic scheduling problem","authors":"Michel Vasquez, Mirsad Buljubasic, S. Hanafi","doi":"10.1007/s10732-023-09513-y","DOIUrl":"https://doi.org/10.1007/s10732-023-09513-y","url":null,"abstract":"","PeriodicalId":54810,"journal":{"name":"Journal of Heuristics","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43968175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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