The Traveling Tournament Problem with Maximum Tour Length Two: A Practical Algorithm with An Improved Approximation Bound

The Traveling Tournament Problem is a well-known benchmark problem in tournament timetabling, which asks us to design a schedule of home/away games of n teams (n is even) under some feasibility requirements such that the total traveling distance of all the n teams is minimized. In this paper, we study TTP-2, the traveling tournament problem where at most two consecutive home games or away games are allowed, and give an effective algorithm for n/2 being odd. Experiments on the well-known benchmark sets show that we can beat previously known solutions for all instances with n/2 being odd by an average improvement of 2.66%. Furthermore, we improve the theoretical approximation ratio from 3/2+O(1/n) to 1+O(1/n) for n/2 being odd, answering a challenging open problem in this area.

Angle Bisector Algorithm and Modified Dynamic Programming Algorithm for Dubins Traveling Salesman Problem

A Dubin's Travelling Salesman Problem (DTSP) of finding a minimum length tour through a given set of points is considered. DTSP has a Dubins vehicle, which is capable of moving only forward with constant speed. In this paper, first, a worst case upper bound is obtained on DTSP tour length by assuming DTSP tour sequence same as Euclidean Travelling Salesman Problem (ETSP) tour sequence. It is noted that, in the worst case, \emph{any algorithm that uses of ETSP tour sequence} is a constant factor approximation algorithm for DTSP. Next, two new algorithms are introduced, viz., Angle Bisector Algorithm (ABA) and Modified Dynamic Programming Algorithm (MDPA). In ABA, ETSP tour sequence is used as DTSP tour sequence and orientation angle at each point $i_k$ are calculated by using angle bisector of the relative angle formed between the rays $i_{k}i_{k-1}$ and $i_ki_{k+1}$. In MDPA, tour sequence and orientation angles are computed in an integrated manner. It is shown that the ABA and MDPA are constant factor approximation algorithms and ABA provides an improved upper bound as compared to Alternating Algorithm (AA) \cite{savla2008traveling}. Through numerical simulations, we show that ABA provides an improved tour length compared to AA, Single Vehicle Algorithm (SVA) \cite{rathinam2007resource} and Optimized Heading Algorithm (OHA) \cite{babel2020new,manyam2018tightly} when the Euclidean distance between any two points in the given set of points is at least $4\rho$ where $\rho$ is the minimum turning radius. The time complexity of ABA is comparable with AA and SVA and is better than OHA. Also we show that MDPA provides an improved tour length compared to AA and SVA and is comparable with OHA when there is no constraint on Euclidean distance between the points. In particular, ABA gives a tour length which is at most $4\%$ more than the ETSP tour length when the Euclidean distance between any two points in the given set of points is at least $4\rho$.

Angle Bisector Algorithm and Modified Dynamic Programming Algorithm for Dubins Traveling Salesman Problem

A Dubin's Travelling Salesman Problem (DTSP) of finding a minimum length tour through a given set of points is considered. DTSP has a Dubins vehicle, which is capable of moving only forward with constant speed. In this paper, first, a worst case upper bound is obtained on DTSP tour length by assuming DTSP tour sequence same as Euclidean Travelling Salesman Problem (ETSP) tour sequence. It is noted that, in the worst case, \emph{any algorithm that uses of ETSP tour sequence} is a constant factor approximation algorithm for DTSP. Next, two new algorithms are introduced, viz., Angle Bisector Algorithm (ABA) and Modified Dynamic Programming Algorithm (MDPA). In ABA, ETSP tour sequence is used as DTSP tour sequence and orientation angle at each point $i_k$ are calculated by using angle bisector of the relative angle formed between the rays $i_{k}i_{k-1}$ and $i_ki_{k+1}$. In MDPA, tour sequence and orientation angles are computed in an integrated manner. It is shown that the ABA and MDPA are constant factor approximation algorithms and ABA provides an improved upper bound as compared to Alternating Algorithm (AA) \cite{savla2008traveling}. Through numerical simulations, we show that ABA provides an improved tour length compared to AA, Single Vehicle Algorithm (SVA) \cite{rathinam2007resource} and Optimized Heading Algorithm (OHA) \cite{babel2020new,manyam2018tightly} when the Euclidean distance between any two points in the given set of points is at least $4\rho$ where $\rho$ is the minimum turning radius. The time complexity of ABA is comparable with AA and SVA and is better than OHA. Also we show that MDPA provides an improved tour length compared to AA and SVA and is comparable with OHA when there is no constraint on Euclidean distance between the points. In particular, ABA gives a tour length which is at most $4\%$ more than the ETSP tour length when the Euclidean distance between any two points in the given set of points is at least $4\rho$.

Estimating the Tour Length for the Close Enough Traveling Salesman Problem

We construct empirically based regression models for estimating the tour length in the Close Enough Traveling Salesman Problem (CETSP). In the CETSP, a customer is considered visited when the salesman visits any point in the customer’s service region. We build our models using as many as 14 independent variables on a set of 780 benchmark instances of the CETSP and compare the estimated tour lengths to the results from a Steiner zone heuristic. We validate our results on a new set of 234 instances that are similar to the 780 benchmark instances. We also generate results for a new set of 72 larger instances. Overall, our models fit the data well and do a very good job of estimating the tour length. In addition, we show that our modeling approach can be used to accurately estimate the optimal tour lengths for the CETSP.

HOUSEHOLD/ZONAL SOCIOECONOMIC CHARACTERISTICS AND TOUR MAKING: CASE OF RICHMOND/TRI-CITIES MODEL REGION IN VIRGINIA

This paper statistically assesses the impacts of household/zonal socio economic characteristics on tour making within the Richmond/Tri-Cities Model Region, Virginia, United States, based on the dataset made available through the 2009 Virginia National Household Travel Survey (NHTS) Add-On Program. The tour analysis distinguishes nine tour types (three simple tours and six complex tours) stratified by aggregate tour purposes of work (including school and other subsistence activities), maintenance and discretionary. A series of regression model runs have yielded the following conclusions: First, at aggregate level, the number of drivers, median household income, household size, number of workers, and zonal walking modal share are statistically significant and positively impact tour frequency. Tour length and complexity are positively related to household income and number of vehicles, but negatively related to zonal walking modal share. Second, at an individual tour type level, each tour type’s frequency/length/complexity is impacted by a different set of household/zonal socioeconomic characteristics. Zonal socioeconomic characteristics have little or no impacts on household tour making. It is recognized that many unknown factors may also have impacted tour activities, which require further in-depth studies in order to better explain complex tours.This paper statistically assesses the impacts of household/zonal socio economic characteristics on tour making within the Richmond/Tri-Cities Model Region, Virginia, United States, based on the dataset made available through the 2009 Virginia National Household Travel Survey (NHTS) Add-On Program. The tour analysis distinguishes nine tour types (three simple tours and six complex tours) stratified by aggregate tour purposes of work (including school and other subsistence activities), maintenance and discretionary. A series of regression model runs have yielded the following conclusions: First, at aggregate level, the number of drivers, median household income, household size, number of workers, and zonal walking modal share are statistically significant and positively impact tour frequency. Tour length and complexity are positively related to household income and number of vehicles, but negatively related to zonal walking modal share. Second, at an individual tour type level, each tour type’s frequency/length/complexity is impacted by a different set of household/zonal socioeconomic characteristics. Zonal socioeconomic characteristics have little or no impacts on household tour making. It is recognized that many unknown factors may also have impacted tour activities, which require further in-depth studies in order to better explain complex tours.

A Cluster–based Approach for Minimizing Energy Consumption by Reducing Travel Time of Mobile Element in WSN

Envoy Node Identification (ENI) and Halting Location Identifier (HLI) algorithms have been developed to reduce the travel time of Mobile Element (ME) by determining Optimal Path(OP) in Wireless Sensor Networks. Data generated by cluster members will be aggregated at the Cluster Head (CH) identified by ENI for onward transmission to the ME and it likewise decides an ideal path for ME by interfacing all CH/Envoy Nodes (EN). In order to reduce the tour length (TL) further HLI determines finest number of Halting Locations that cover all ENs by taking transmission range of CH/ENs into consideration. Impact of ENI and HLI on energy consumption and travel time of ME have been examined through simulations.

An Adaptive Data Gathering Algorithm for Minimum Travel Route Planning in WSNs Based on Rendezvous Points

A recent trend in wireless sensor network (WSN) research is the deployment of a mobile element (ME) for transporting data from sensor nodes to the base station (BS). This helps to achieve significant energy savings as it minimizes the communications required among nodes. However, a major problem is the large data gathering latency. To address this issue, the ME (i.e., vehicle) should visit certain rendezvous points (i.e., nodes) to collect data before it returns to the BS to minimize the data gathering latency. In view of this, we propose a rendezvous-based approach where some certain nodes serve as rendezvous points (RPs). The RPs gather data using data compression techniques from nearby sources (i.e., affiliated nodes) and transfer them to a mobile element when the ME traverses their paths. This minimizes the number of nodes to be visited, thereby reducing data gathering latency. Furthermore, we propose a minimal constrained rendezvous point (MCRP) algorithm, which ensures the aggregated data are relayed to the RPs based on three constraints: (i) bounded relay hop, (ii) the number of affiliation nodes, and (iii) location of the RP. The algorithm is designed to consider the ME’s tour length and the shortest path tree (SPT) jointly. The effectiveness of the algorithm is validated through extensive simulations against four existing algorithms. Results show that the MCRP algorithm outperforms the compared schemes in terms of the ME’s tour length, data gathering latency, and the number of rendezvous nodes. MCRP exhibits a relatively close performance to other algorithms with respect to power algorithms.

Fleet management for autonomous vehicles: Online PDP under special constraints

The VIPAFLEET project consists in developing models and algorithms for managing a fleet of Individual Public Autonomous Vehicles (VIPA). Hereby, we consider a fleet of cars distributed at specified stations in an industrial area to supply internal transportation, where the cars can be used in different modes of circulation (tram mode, elevator mode, taxi mode). One goal is to develop and implement suitable algorithms for each mode in order to satisfy all the requests under an economic point of view by minimizing the total tour length. The innovative idea and challenge of the project is to develop and install a dynamic fleet management system that allows the operator to switch between the different modes within the different periods of the day according to the dynamic transportation demands of the users. We model the underlying online transportation system and propose a corresponding fleet management framework, to handle modes, demands and commands. We consider two modes of circulation, tram and elevator mode, propose for each mode appropriate online algorithms and evaluate their performance, both in terms of competitive analysis and practical behavior.

Delay Tolerance and Energy Saving in Wireless Sensor Networks with a Mobile Base Station

Recent research shows that significant energy saving can be achieved in wireless sensor networks by using mobile devices. A mobile device roams sensing fields and collects data from sensors through a short transmission range. Multihop communication is used to improve data gathering by reducing the tour length of the mobile device. In this paper we study the trade-off between energy saving and data gathering latency in wireless sensor networks. In particular, we examine the balance between the relay hop count and the tour length of a mobile Base Station (BS). We propose two heuristic algorithms, Adjacent Tree-Bounded Hop Algorithm (AT-BHA) and Farthest Node First-Bounded Hop Algorithm (FNF-BHA), to reduce energy consumption of sensor nodes. The proposed algorithms select groups of Collection Trees (CTs) and a subset of Collection Location (CL) sensor nodes to buffer and forward data to the mobile BS when it arrives. Each CL node receives sensing data from its CT nodes within bounded hop count. Extensive experiments by simulation are conducted to evaluate the performance of the proposed algorithms against another heuristic. We demonstrate that the proposed algorithms outperform the existing work with the mean of the length of mobile BS tour.

Setting the Configuration Parameters of the Algorithm for the Periodic Vehicle Routing Problem by HPC Power

The quality of an opt imal solut ion of the Vehicle Rout ing Problem is st rongly depended on the sett ing of the configurat ion parameters of the algorithm. The paper is focused on the int roduct ion of hyperparameter search for solving the Vehicle Rout ing Problem using a HyperLoom plat form for defining and execut ing scient ific pipelines in a dist ributed environment . To give a concrete example, we focused on Periodic Vehicle Rout ing Problem for the waste collect ion. HyperLoom plat form was used to define and execute the hyperparameters sweep pipeline. The heurist ic algorithm was tested on a real benchmark of the waste collect ion in Ostrava, Czech Republic. The aim of our ca se was to effect ively combine the minimizat ion of the total t ravelled distance and the opt imizat ion of the fairness of the routes in terms of the standard deviat ion of a tour length. The waste collect ion problem was very extensive and computat ionally demanding, so it was necessary to use high performance comput ing architecture for test ing a large number of different sett ings of configurat ion parameters. The experiments were run on the supercomputer Salomon operated by IT4Innovations Nat ional Supercomput ing Center in the Czech Republic.