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Coarse-grained multicomputer parallel algorithm using the four-splitting technique for the minimum cost parenthesizing problem 用四分法求解最小代价圆括号问题的粗粒度多机并行算法

ARIMA Pub Date : 2023-11-06 DOI: 10.46298/arima.11217

Jerry Lacmou Zeutouo, Vianney Kengne Tchendji, Jean-Frédéric Myoupo

{"title":"Coarse-grained multicomputer parallel algorithm using the four-splitting technique for the minimum cost parenthesizing problem","authors":"Jerry Lacmou Zeutouo, Vianney Kengne Tchendji, Jean-Frédéric Myoupo","doi":"10.46298/arima.11217","DOIUrl":"https://doi.org/10.46298/arima.11217","url":null,"abstract":"Dynamic programming is a technique widely used to solve several combinatory optimization problems. A well-known example is the minimum cost parenthesizing problem (MPP), which is usually used to represent a class of non-serial polyadic dynamic-programming problems. These problems are characterized by a strong dependency between subproblems. This paper outlines a coarse-grained multicomputer parallel solution using the four-splitting technique to solve the MPP. It is a partitioning technique consisting of subdividing the dependency graph into subgraphs (or blocks) of variable size and splitting large-size blocks into four subblocks to avoid communication overhead caused by a similar partitioning technique in the literature. Our solution consists in evaluating a block by computing and communicating each subblock of this block to reduce the latency time of processors which accounts for most of the global communication time. It requires O(n^3/p) execution time with O(k * sqrt{p}) communication rounds. n is the input data size, p is the number of processors, and k is the number of times the size of blocks is subdivided.","PeriodicalId":495604,"journal":{"name":"ARIMA","volume":"23 22","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135545542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Hybrid Algorithm Based on Multi-colony Ant Optimization and Lin-Kernighan for solving the Traveling Salesman Problem 基于多群蚁群优化和Lin-Kernighan的旅行商问题混合算法

ARIMA Pub Date : 2023-10-28 DOI: 10.46298/arima.8660

Mathurin Soh, Baudoin Nguimeya Tsofack, Clémentin Tayou Djamegni

{"title":"A Hybrid Algorithm Based on Multi-colony Ant Optimization and Lin-Kernighan for solving the Traveling Salesman Problem","authors":"Mathurin Soh, Baudoin Nguimeya Tsofack, Clémentin Tayou Djamegni","doi":"10.46298/arima.8660","DOIUrl":"https://doi.org/10.46298/arima.8660","url":null,"abstract":"In this article, a hybrid heuristic algorithm is proposed to solve the Traveling Salesman Problem (TSP). This algorithm combines two main metaheuristics: optimization of multi-colony ant colonies (MACO) and Lin-Kernighan-Helsgaun (LKH). The proposed hybrid approach (MACO-LKH) is a so-called insertion and relay hybridization. It brings two major innovations: The first consists in replacing the static visibility function used in the MACO heuristic by the dynamic visibility function used in LKH. This has the consequence of avoiding long paths and favoring the choice of the shortest paths more quickly. Hence the term insertion hybridization. The second innovation consists in modifying the pheromone update strategy of MACO by that of the dynamic λ-opt mechanisms of LKH in order to optimize the solutions generated and save in execution time, hence the relay hybridization. The significance of the hybridization, is examined and validated on benchmark instances including small, medium, and large instance problems taken from the TSPlib library. The results are compared to four other state-of-the-art metaheuristic approaches. It results in that they are significantly outperformed by the proposed algorithm in terms of the quality of solutions obtained and execution time.","PeriodicalId":495604,"journal":{"name":"ARIMA","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136157448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0