A new algorithm for finding the k shortest transport paths in dynamic stochastic networks

The static K shortest paths (KSP) problem has been resolved. In reality, however, most of the networks are actually dynamic stochastic networks. The state of the arcs and nodes are not only uncertain in dynamic stochastic networks but also interrelated. Furthermore, the cost of the arcs and nodes are subject to a certain probability distribution. The KSP problem is generally regarded as a dynamic stochastic optimization problem. The dynamic stochastic characteristics of the network and the relationships between the arcs and nodes of the network are analyzed in this paper, and the probabilistic shortest path concept is defined. The mathematical optimization model of the dynamic stochastic KSP and a genetic algorithm for solving the dynamic stochastic KSP problem are proposed. A heuristic population initialization algorithm is designed to avoid loops and dead points due to the topological characteristics of the network. The reasonable crossover and mutation operators are designed to avoid the illegal individuals according to the sparsity characteristic of the network. Results show that the proposed model and algorithm can effectively solve the dynamic stochastic KSP problem. The proposed model can also solve the network flow stochastic optimization problems in transportation, communication networks, and other networks

Finding kk Simple Shortest Paths and Cycles

The problem of finding multiple simple shortest paths in a weighted directed graph $G=(V,E)$ has many applications, and is considerably more difficult than the corresponding problem when cycles are allowed in the paths. Even for a single source-sink pair, it is known that two simple shortest paths cannot be found in time polynomially smaller than $n^3$ (where $n=|V|$) unless the All-Pairs Shortest Paths problem can be solved in a similar time bound. The latter is a well-known open problem in algorithm design. We consider the all-pairs version of the problem, and we give a new algorithm to find $k$ simple shortest paths for all pairs of vertices. For $k=2$, our algorithm runs in $O(mn + n^2 \log n)$ time (where $m=|E|$), which is almost the same bound as for the single pair case, and for $k=3$ we improve earlier bounds. Our approach is based on forming suitable path extensions to find simple shortest paths; this method is different from the `detour finding' technique used in most of the prior work on simple shortest paths, replacement paths, and distance sensitivity oracles. Enumerating simple cycles is a well-studied classical problem. We present new algorithms for generating simple cycles and simple paths in $G$ in non-decreasing order of their weights; the algorithm for generating simple paths is much faster, and uses another variant of path extensions. We also give hardness results for sparse graphs, relative to the complexity of computing a minimum weight cycle in a graph, for several variants of problems related to finding $k$ simple paths and cycles.Comment: The current version includes new results for undirected graphs. In Section 4, the notion of an (m,n) reduction is generalized to an f(m,n) reductio

Mining Relational Paths in Integrated Biomedical Data

Much life science and biology research requires an understanding of complex relationships between biological entities (genes, compounds, pathways, diseases, and so on). There is a wealth of data on such relationships in publicly available datasets and publications, but these sources are overlapped and distributed so that finding pertinent relational data is increasingly difficult. Whilst most public datasets have associated tools for searching, there is a lack of searching methods that can cross data sources and that in particular search not only based on the biological entities themselves but also on the relationships between them. In this paper, we demonstrate how graph-theoretic algorithms for mining relational paths can be used together with a previous integrative data resource we developed called Chem2Bio2RDF to extract new biological insights about the relationships between such entities. In particular, we use these methods to investigate the genetic basis of side-effects of thiazolinedione drugs, and in particular make a hypothesis for the recently discovered cardiac side-effects of Rosiglitazone (Avandia) and a prediction for Pioglitazone which is backed up by recent clinical studies

An Alternative Fuel Refueling Station Location Model considering Detour Traffic Flows on a Highway Road System

With the development of alternative fuel (AF) vehicle technologies, studies on finding the potential location of AF refueling stations in transportation networks have received considerable attention. Due to the strong limited driving range, AF vehicles for long-distance intercity trips may require multiple refueling stops at different locations on the way to their destination, which makes the AF refueling station location problem more challenging. In this paper, we consider that AF vehicles requiring multiple refueling stops at different locations during their long-distance intercity trips are capable of making detours from their preplanned paths and selecting return paths that may be different from original paths for their round trips whenever AF refueling stations are not available along the preplanned paths. These options mostly need to be considered when an AF refueling infrastructure is not fully developed on a highway system. To this end, we first propose an algorithm to generate alternative paths that may provide the multiple AF refueling stops between all origin/destination (OD) vertices. Then, a new mixed-integer programming model is proposed to locate AF refueling stations within a preselected set of candidate sites on a directed transportation network by maximizing the coverage of traffic flows along multiple paths. We first test our mathematical model with the proposed algorithm on a classical 25-vertex network with 25 candidate sites through various scenarios that consider a different number of paths for each OD pair, deviation factors, and limited driving ranges of vehicles. Then, we apply our proposed model to locate liquefied natural gas refueling stations in the state of Pennsylvania considering the construction budget. Our results show that the number of alternative paths and deviation distance available significantly affect the coverage of traffic flows at the stations as well as computational time

Modeling and analysis of air campaign resource allocation: a spatio-temporal decomposition approach

Abstract—In this paper, we address the modeling and analysis issues associated with a generic theater level campaign where two adversaries pit their military resources against each other over a sequence of multiple engagements. In particular, we consider the scenario of an air raid campaign where one adversary uses suppression of enemy air defense (SEAD) aircraft and bombers (BMBs) against the other adversary’s invading ground troops (GTs) that are defended by their mobile air defense (AD) units. The original problem is decomposed into a temporal and a spatial resource allocation problem. The temporal resource allocation problem is formulated and solved in a game-theoretical framework as a multiple resource interaction problem with linear attrition functions. The spatial resource allocation problem is posed as a risk minimization problem in which the optimal corridor of ingress and optimal movement of the GTs and AD units are decided by the adversaries. These two solutions are integrated using an aggregation/deaggregation approach to evaluate resource strengths and distribute losses. Several simulation experiments were carried out to demonstrate the main ideas. Index Terms—Air campaign modeling, applied game theory, military campaigns, resource allocation, resource interaction models. I

Planering av väginvesteringar

The problems around and the planning of wood flow is some of the most complex issues in the forest-sector. The experience and overview of the single employees is crucial for the possibility of correct tactical and economical decision-making. The increasing demand of savings and shorter reaction-times with greater flexibility in the wood-supply-chain, makes solutions and aids for improved effectiveness in the work and processes according to wood-flow urgent. Holmen Skog is starting to develop a new forest-road-management-system. The system will facilitate the work according to construction, improvements and updating the standard of roads. The aim of this study was to investigate the tactical and economical functionality of the decision-support tool Vägrust. The goal was to establish a plan for road improvements with 4, 6 and 8 weeks of thaw, running on 10 year at Holmen Skog district Bredbyn. Road-data, stand-data and the coming need of wood at the district founded the base which the optimization was performed. The location of the wood-volumes, conditions of the road-network with respect of accessibility and the yearly procurement-need of the industries was recorded in Vägrust. One optimization was run for each thaw-period of 4, 6 and 8 weeks by Mathias Henningsson at Linköpings universitet. The optimizations shows, in this context, a very low improvement-cost ranging between 5,6-9,7 kr/m³fub for the planning-period depending on the length of the thaw period. Vägrust, that today is a prototype decision-tool, generated useful and reliable plans of road improvements at district Bredbyn. The costs of road management at Holmen Skog AB is supposed to decrease through the use of an optimization-model for road-improvements.Problematiken runt och planering av virkesflödet är något av det mest komplexa i skogsnäringen. Idag är den enskilde tjänstemannens erfarenhet och överblick helt avgörande för att korrekta beslut kan tas, såväl ur ett taktiskt som ekonomiskt perspektiv. Med ökande besparingskrav samt krav på en allt kortare reaktionstid och högre flexibilitet i flödeskedjan är det hög tid att hitta lösningar och hjälpmedel som kan effektivisera arbetet och processerna runt virkesflödet. Holmen Skog ligger i startgroparna med att utveckla ett nytt vägförvaltningssystem. Systemet ska underlätta arbetet med vägar, dels nybyggnation och upprustning men också ajourhållning. Syftet med denna studie var att undersöka funktionaliteten i beslutsstödet Vägrust, såväl ur ett ekonomiskt som ett praktiskt perspektiv. Målet har varit att upprätta en vägupprustningsplan för 4, 6 och 8 veckors tjällossning, löpande på 10 år för Holmen Skog, distrikt Bredbyn. Väg och beståndsdata för distriktet samt för distriktet i dagsläget aktuella mottagares kommande råvarubehov utgjorde grunden för optimeringen. I Vägrust angavs virkesvolymernas geografiska läge, vägnätets beskaffenhet med avseende på tillgänglighet samt respektive industris försörjningsbehov under året. En optimering för respektive förfallsperiod 4, 6 och 8 veckor genomfördes sedan av Mathias Henningsson vid Linköpings universitet. Optimeringarna visade på i sammanhanget mycket låga upprustningskostnader för planperioden, mellan 5,6 och 9,7 kr/m³fub beroende på förfallperiodens längd. Vägrust som idag är en prototyp av ett beslutsstöd för vägupprustningar genererade användbara och trovärdiga upprustningsplaner för distrikt Bredbyn. Holmen Skog AB antas sänka kostnaden för väghållning genom att använda en optimeringsmodell för vägupprustning

Surrogate dual search in nonlinear integer programming.

Wang, Chongyu.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (leaves 74-78).Abstract also in Chinese.Abstract --- p.1Abstract in Chinese --- p.3Acknowledgement --- p.4Contents --- p.5List of Tables --- p.7List of Figures --- p.8Chapter 1. --- Introduction --- p.9Chapter 2. --- Conventional Dynamic Programming --- p.15Chapter 2.1. --- Principle of optimality and decomposition --- p.15Chapter 2.2. --- Backward dynamic programming --- p.17Chapter 2.3. --- Forward dynamic programming --- p.20Chapter 2.4. --- Curse of dimensionality --- p.23Chapter 3. --- Surrogate Constraint Formulation --- p.26Chapter 3.1. --- Surrogate constraint formulation --- p.26Chapter 3.2. --- Singly constrained dynamic programming --- p.28Chapter 3.3. --- Surrogate dual search --- p.29Chapter 4. --- Distance Confined Path Algorithm --- p.34Chapter 4.1. --- Yen´ةs algorithm for the kth shortest path problem --- p.35Chapter 4.2. --- Application of Yen´ةs method to integer programming --- p.36Chapter 4.3. --- Distance confined path problem --- p.42Chapter 4.4. --- Application of distance confined path formulation to integer programming --- p.50Chapter 5. --- Convergent Surrogate Dual Search --- p.59Chapter 5.1. --- Algorithm for convergent surrogate dual search --- p.62Chapter 5.2. --- "Solution schemes for (Pμ{αk,αβ)) and f(x) = αk" --- p.63Chapter 5.3. --- Computational Results and Analysis --- p.68Chapter 6. --- Conclusions --- p.72Bibliography --- p.7

Optimization Models and Algorithms for Truckload Relay Network Design

Driver turnover is a significant problem for full truckload (TL) carriers that operate using point-to-point (PtP) dispatching. The low quality of life of drivers due to the long periods of time they spend away from home is usually identified as one of the main reasons for the high turnover. In contrast, driver turnover is not as significant for less-than-truckload (LTL) carriers that use hub-and-spoke transportation networks which allow drivers to return home more frequently. Based on the differences between TL and LTL, the use of a relay network (RN) has been proposed as an alternative dispatching method for TL transportation in order to improve driver retention. In a RN, a truckload visits one or more relay points (RPs) where drivers and trailers are exchanged while the truckload continues its movement to the final destination. In this research, we propose a new composite variable model (CVM) to address the strategic TL relay network design (TLRND) problem. With this approach, we capture operational considerations implicitly within the variable definition instead of adding them as constraints in our model. Our composites represent feasible routes for the truckloads through the RN that satisfy limitations on circuity, number of RPs visited, and distances between RPs and between a RP and origin-destination nodes. Given a strict limitation on the number of RPs allowed to be visited, we developed a methodology to generate feasible routes using predefined templates. This methodology was preferred over an exact feasible path enumeration algorithm that was also developed to generate valid routes. The proposed approach was successfully used to obtain high quality solutions to largely-sized problem instances of TLRND. Furthermore extending the original CVM formulation, we incorporate mixed fleet dispatching decisions into the design of the RN. This alternative system allows routing some truckloads through the RN while the remaining truckloads are dispatched PtP. We analyze the performance of our models and the solutions obtained for TLRND problems through extensive computational testing. Finally, we conclude with a description of directions for future research

Analisi comportamentale della scelta del percorso attraverso l'utilizzo di nuove tecnologie di acquisizione delle informazioni

In travel demand modeling, route choice is one of the most complex decision-making contexts to understand and mathematically represent for several reasons. Firstly, a large number of available paths may exist between the same origin-destination (OD) pair. Secondly, neither the traveler nor the modeler are aware of all the available alternatives. Thirdly, individual choices are dictated by different constraints and preferences that are difficult to capture by modelers who face increasingly larger datasets where retrieving the exact path chosen by travelers is not always straightforward. Last, there is a lot of uncertainty about travelers’ perceptions of route characteristics as well as other characteristics that can influence their choices, such as age, gender, habit, weather conditions and network conditions. This highlights the difficulties encountered for interpreting individual user behavior in greater depth. The rapid advances in GPS devices, has resulted in major benefits for data collection, which now can be recorded automatically and with greater accuracy compared to the techniques used in the past (phone calls, e-mails, face-to-face interviews, laboratory experiments.). On these basis the main objective of the thesis is then to study route choice using a GPS database. The data were acquired during a survey, named "Casteddu Mobility Styles” (CMS), conducted by the University of Cagliari (Italy) in the metropolitan area of Cagliari between February 2011 and June 2012. Each participant was asked to carry a smartphone with builtin GPS in which an application called “Activity Locator” – implemented by CRiMM (Centre for Research on Mobility and Modeling) – had been installed. A total of 8831 trips were recorded by 109 individuals, of which 4791 referring to the car driver mode. Each GPS track (consisting of a sequence of referenced position points) was then treated with map-matching techniques, through which it was possible to associate each “GPS point” to a link of the network, thus creating the observed route database. The first objective of the thesis is to understand which are the characteristics of the data acquired during the CMS survey, doing firstly the same analysis that other authors did in their researches based on GPS data. In almost all the previous researches, the GPS data were collected through in-vehicle surveys that make it possible to gather objective information on trips (travel times and distances). Pre-and post-analysis interviews were conducted to gather information about the subjective characteristics of the individuals and GIS platforms were used to study the routes. In the present study, the data were collected using an integrated system able to also record the activities conducted, along with all the characteristics associated thereto. In this way a complete database was created containing all the information (objective and not) concerning the trips. For comparisons with the objectively most convenient paths, then, was used a static macrosimulation model (implemented in CUBE, Citilabs Ltd.) of the entire study area (Cagliari and its metropolitan area), which reproduces the network characteristics actually encountered by the drivers referring to the data used. From this first analysis it was observed that when more than one route is taken for repetitive trips between the same OD. In order to understand these particular behavior of users, named also intravariability, discrete choice models were estimated. It’s important to note that in the previous GPS-based researches this particular behavior was only identified, without studying it in depth. Several other studies, focused on route switching behavior, tried to understand it applying discrete choice models, but their database were based on data acquired through questionnaires or laboratory experiments, and for the majority the route switching behavior was studied in relation to the trip information provision. The objective of this analysis is then to combine the two fields of the research on route switching, trying to understand it estimating discrete choice models using a GPS based database, closing the gap of the previous researches. The final goal of the model estimations is to understand which are the main attributes of the routes and the characteristics of the users that most influence the choice of an habitual route for the same origin-destination (OD) trip. After these first analysis, the final objective of the thesis is to apply a route choice model to GPS-based data. Modeling route choice behavior is generally framed as a two-stage process: generation of the alternative routes and modeling of the choice from the generated choice set. The focus of this step of the research is on the bias that might be introduced in the model estimation by the choice set generation process. Specifically, although several explicit choice set generation techniques are found in the literature, the focus is on stochastic route generation and the correction for unequal sampling probability of routes when applying this technique that is easily applicable to large-scale networks. Indeed, stochastic route generation is a case of importance sampling where the selection of the path depends on its own properties, so route choice models based on stochastic route generation must include a sampling correction coefficient that accounts for the different selection probability. In this study is proposed a methodology for calculating and considering this correction factor into MNL-based models with choice sets generated by means of stochastic route generation. Specifically, was decided to look at the sampling correction factor proposed for the random walk algorithm and to calculate the route selection probability in order to exploit this expression. Therefore, a procedure is proposed for the computation of the selection probabilities on the basis of the stochastic generation principle, then the correction factor and last the EPS for model estimation. The modeling analysis confirms the functionality of the proposed approach that has great advantages: (i) it provides insight into the application of stochastic generation in route choice modeling, especially in large-scale networks where the only need is a standard random number generator and a Dijkstra algorithm; it proposes a simple and manageable procedure from the computational perspective for the calculation of route selection probabilities and hence the correction factor and EPS for model estimation; it proves the efficiency of the proposed methodology on revealed preference data in a dense urban network by showing an increase in goodness-of-fit of the model and a shift from illogical to logical sign in parameters estimated for key variables such as travel time