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We present a theoretical framework that links Fermat's principle of least time to optimal transport theory via a cost function that enforces local transport. The proposed cost function captures the physical constraints inherent in wave propagation; when paired with specific mass distributions, it yields shortest paths in the considered media through the optimal transport plans. In the discrete setting, our formulation results in physically significant optimal couplings, whose off-diagonal entries identify shortest paths in both directed and undirected graphs. For undirected graphs with positive edge weights, commonly used to parameterize seismic media, our method provides solutions to the Eikonal equation consistent with those from the Dijkstra algorithm. For directed negative-weight graphs, corresponding to transportation cost matrices with negative entries, our approach aligns with the Bellman–Ford algorithm but offers considerable computational advantages. We also highlight potential research directions. These include the use of sparse cost matrices to reduce the number of unknowns and constraints in the considered transportation problem, and solving specific classes of optimal transport problems through the Dijkstra algorithm to enhance computational efficiency. [ABSTRACT FROM AUTHOR]

Many spatial applications benefit from the fast answering to a seemingly simple spatial query: "Is a point of interest (POI) 'in-path' to the shortest path between a source and a destination?" In this context, an in-path POI is one that is either on the shortest path or can be reached within a bounded yet small detour from the shortest path. The fast answering of the in-path queries is contingent on being able to determine without having to actually compute the shortest paths during runtime. Thus, this requires a precomputation solution. The key contribution of the paper is the development of an in-path oracle that is based on precomputation of which pairs of sources and destinations are in-path with respect to the given POI. For a given road network with n nodes and m POIs, an O (m × n) -sized oracle is envisioned based on the reduction of the well-separated pairs (WSP) decomposition of the road network. Furthermore, an oracle can be indexed in a database using a B-tree that can answer queries at very high throughput. Experimental results on the real road network POI dataset illustrate the superiority of this technique compared to a baseline algorithm. The proposed approach can answer ≈ 1.5 million in-path queries per second compared to a few hundred per second using a suitable baseline approach. [ABSTRACT FROM AUTHOR]

Changeability analysis methods primarily assist with formulating a response to uncertain and new requirements from various system stakeholders and include asset management issues such as modelling lifecycle path dependency. Epoch-era networks proved to be an effective tool for managing the evolving requirements of a capability system, ensuring sustained value through life. Over the life of a system, stakeholders are faced with countless options to change their capability systems to sustain value, which is path dependent and can greatly impact the scope of decisions available later in life. This paper introduces and demonstrates the application of a revised epoch-era network approach to explore many potential lifecycle paths, along with utility vs. expense strategies, demonstrated through an example of a military frigate subject to evolving requirements. Results indicated the future limitations to sustaining value if the largest and most capable technology upgrades are selected too early in life. The two best lifecycle paths from different strategies were compared to understand the utility/expense trade-offs for the most optimal frigate upgrade trajectory. [ABSTRACT FROM AUTHOR]

This paper presents a new heuristic algorithm tailored to solve large instances of an NP-hard variant of the shortest path problem, denoted the cost-balanced path problem, recently proposed in the literature. The problem consists in finding the origin–destination path in a direct graph, having both negative and positive weights associated with the arcs, such that the total sum of the weights of the selected arcs is as close to zero as possible. At least to the authors' knowledge, there are no solution algorithms for facing this problem. The proposed algorithm integrates a constructive procedure and an improvement procedure, and it is validated thanks to the implementation of an iterated neighborhood search procedure. The reported numerical experimentation shows that the proposed algorithm is computationally very efficient. In particular, the proposed algorithm is most suitable in the case of large instances where it is possible to prove the existence of a perfectly balanced path and thus the optimality of the solution by finding a good percentage of optimal solutions in negligible computational time. [ABSTRACT FROM AUTHOR]

Featured Application: Our proposal has application in a real problem, whose objective is to guide a mobile robot to a target point in an environment that changes along time. These changes are characterized by the addition of obstacles that prevent navigation or the inability to follow a previously computed route, for instance scenarios of recent hazards or natural disasters. Robot navigation is still an open research topic, mainly regarding applications that require online planning. In this context, this manuscript presents an implementation of the Lifelong Planning A* (LPA*) search algorithm to guide a mobile robot in an environment that changes along time, by detecting obstacles and updating the current mapping information. Firstly, simulations validate the strategy, and later experiments confirm these results considering a real application. The result is that the LPA* algorithm is able to guide the mobile robot to its target in a changing environment. Obstacles are interactively included in the scene to force the route redesign and the seeking for a new optimal solution connecting the current robot position and its target position. [ABSTRACT FROM AUTHOR]

There is a growing market for electric vehicles (EVs) in recent years. Due to this, many studies on electric vehicles are in progress and research on charging operations for EVs are especially active. Recent research trends on electric vehicle routes rely on the stochastic modelling of various factors such as convenience of a user's point of view, charging station (CS), location, destination, and so on. In this paper, a charging control scheme for electric vehicles is proposed from the point of view of the system operators rather than the user. From a user's point of view, the EV route can be set up directly, but it is difficult for the system operator to directly participate in the route of the EV. In this paper, a method is proposed to indirectly change the route of the EV by changing the charging cost through real-time dynamic pricing, in order to prevent risks in the system operation due to voltage fluctuations in the system. With dynamic pricing, the voltage of the system is kept within a stable range, and the EV user sets the route with an economic benefit. The proposed scheme is verified through Dijkstra's algorithm and a control strategy via a simulation model using MATLAB. [ABSTRACT FROM AUTHOR]

Subnetwork mining is an essential issue in the analysis of biological, social and communication networks. Recent applications require the simultaneous mining of several networks on the same or a similar vertex set. That is, one searches for subnetworks fulfilling different properties in each input network. We study the case that the input consists of a directed graph D and an undirected graph G on the same vertex set, and the sought pattern is a path P in D whose vertex set induces a connected subgraph of G. In this context, three concrete problems arise, depending on whether the existence of P is questioned or whether the length of P is to be optimized: in that case, one can search for a longest path or (maybe less intuitively) a shortest one. These problems have immediate applications in biological networks and predictable applications in social, information and communication networks. We study the classic and parameterized complexity of the problem, thus identifying polynomial and NP-complete cases, as well as fixed-parameter tractable and W[1]-hard cases. We also propose two enumeration algorithms that we evaluate on synthetic and biological data. [ABSTRACT FROM AUTHOR]

This paper introduces a new variant of the Shortest Path Problem ( S P P ) called the Cost-Balanced Path Problem ( C B P P ). Various real problems can either be modeled as B C P P or include B C P P as a sub-problem. We prove several properties related to the complexity of the C B P P problem. In particular, we demonstrate that the problem is NP-hard in its general version, but it becomes solvable in polynomial time in a specific family of instances. Moreover, a mathematical formulation of the C B P P , as a mixed-integer programming model, is proposed, and some additional constraints for modeling real requirements are given. This paper validates the proposed model and its extensions with experimental tests based on random instances. The analysis of the results of the computational experiments shows that the proposed model and its extension can be used to model many real applications. Obviously, due to the problem complexity, the main limitation of the proposed approach is related to the size of the instances. A heuristic solution approach should be required for larger-sized and more complex instances. [ABSTRACT FROM AUTHOR]

The present paper focuses on the development of an algorithm for safely and optimally managing the routing of aircraft on an airport surface in future airport operations. This tool is intended to support air traffic controllers' decision-making in selecting the paths of all aircraft and the engine startup approval time for departing ones. Optimal routes are sought for minimizing the time both arriving and departing aircraft spend on an airport surface with engines on, with benefits in terms of safety, efficiency and costs. The proposed algorithm first computes a standalone, shortest path solution from runway to apron or vice versa, depending on the aircraft being inbound or outbound, respectively. For taking into account the constraints due to other traffic on an airport surface, this solution is amended by a conflict detection and resolution task that attempts to reduce and possibly nullify the number of conflicts generated in the first phase. An example application on a simple Italian airport exemplifies how the algorithm can be applied to true-world applications. Emphasis is given on how to model an airport surface as a weighted and directed graph with non-negative weights, as required for the input to the algorithm. [ABSTRACT FROM AUTHOR]

In a previous paper by the author, a pathfinding problem for directed trees is studied under the following situation: each edge has a nonnegative integer length, but the length is unknown in advance and should be found by a procedure whose computational cost becomes exponentially larger as the length increases. In this paper, the same problem is studied for a more general class of graphs called fork-join directed acyclic graphs. The problem for the new class of graphs contains the previous one. In addition, the optimality criterion used in this paper is stronger than that in the previous paper and is more appropriate for real applications. [ABSTRACT FROM AUTHOR]

Linear Diophantine fuzzy set (LDFS) theory expands Intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PyFS) theories, widening the space of vague and uncertain information via reference parameters owing to its magnificent feature of a broad depiction area for permissible doublets. We codify the shortest path (SP) problem for linear Diophantine fuzzy graphs. Linear Diophantine fuzzy numbers (LDFNs) are used to represent the weights associated with arcs. The main goal of the presented work is to create a solution technique for directed network graphs by introducing linear Diophantine fuzzy (LDF) optimality constraints. The weights of distinct routes are calculated using an improved score function (SF) with the arc values represented by LDFNs. The conventional Dijkstra method is further modified to find the arc weights of the linear Diophantine fuzzy shortest path (LDFSP) and coterminal LDFSP based on these enhanced score functions and optimality requirements. A comparative analysis was carried out with the current approaches demonstrating the benefits of the new algorithm. Finally, to validate the possible use of the proposed technique, a small-sized telecommunication network is presented. [ABSTRACT FROM AUTHOR]

The aim of each company/industry is to provide a final product to customers at the minimum possible cost, as well as to protect the environment from degradation. Ensuring the shortest travel distance between involved locations plays an important role in achieving the company's/industry's objective as (i) the cost of a final product can be minimized by minimizing the total distance travelled (ii) finding the shortest distance between involved locations will require less fuel than the longest distance between involved locations. This will eventually result in lesser degradation of the environment. Hence, in the last few years, various algorithms have been proposed to solve different types of shortest path problems. A recently proposed algorithm for solving interval-valued Pythagorean fuzzy shortest path problems requires excessive computational efforts. Hence, to reduce the computational efforts, in this paper, firstly, an alternative lexicographic method is proposed for comparing interval-valued Pythagorean fuzzy numbers. Then, using the proposed lexicographic comparing method, a new approach (named as Mehar approach) is proposed to solve interval-valued Pythagorean fuzzy shortest path problems. Furthermore, the superiority of the proposed lexicographic comparing method, as well as the proposed Mehar approach, is discussed. [ABSTRACT FROM AUTHOR]

The time-dependent traveling salesman problem (TDTSP) asks for a shortest Hamiltonian tour in a directed graph where (asymmetric) arc-costs depend on the time the arc is entered. With traffic data abundantly available, methods to optimize routes with respect to time-dependent travel times are widely desired. This holds in particular for the traveling salesman problem, which is a corner stone of logistic planning. In this paper, we devise column-generation-based IP methods to solve the TDTSP in full generality, both for arc- and path-based formulations. The algorithmic key is a time-dependent shortest path problem, which arises from the pricing problem of the column generation and is of independent interest—namely, to find paths in a time-expanded graph that are acyclic in the underlying (non-expanded) graph. As this problem is computationally too costly, we price over the set of paths that contain no cycles of length k. In addition, we devise—tailored for the TDTSP—several families of valid inequalities, primal heuristics, a propagation method, and a branching rule. Combining these with the time-dependent shortest path pricing we provide—to our knowledge—the first elaborate method to solve the TDTSP in general and with fully general time-dependence. We also provide for results on complexity and approximability of the TDTSP. In computational experiments on randomly generated instances, we are able to solve the large majority of small instances (20 nodes) to optimality, while closing about two thirds of the remaining gap of the large instances (40 nodes) after one hour of computation. [ABSTRACT FROM AUTHOR]

The shortest path problem is a topic of increasing interest in various scientific fields. The damage to roads and bridges caused by disasters makes traffic routes that can be accurately expressed become indeterminate. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership of the constituent elements. It has a symmetric form and indeterminacy membership is their axis of symmetry. In uncertain environments, the neutrosophic number can more effectively express the edge distance. The objectives in this study are to solve the shortest path problem of the neutrosophic graph with an edge distance expressed using trapezoidal fuzzy neutrosophic numbers (TrFNN) and resolve the edge distance according to the score and exact functions based on the TrFNN. Accordingly, the use of a circle-breaking algorithm is proposed to solve the shortest path problem and estimate the shortest distance. The feasibility of this method is verified based on two examples, and the rationality and effectiveness of the approach are evaluated by comparing it with the Dijkstra and Bellman algorithms. [ABSTRACT FROM AUTHOR]

In the first part of the review, we observed that there exists a significant gap between the predictive and prescriptive models pertaining to crash risk prediction and minimization, respectively. In this part, we review and categorize the optimization/ prescriptive analytic models that focus on minimizing crash risk. Although the majority of works in this segment of the literature are related to the hazardous materials (hazmat) trucking problems, we show that (with some exceptions) many can also be utilized in non-hazmat scenarios. In an effort to highlight the effect of crash risk prediction model on the accumulated risk obtained from the prescriptive model, we present a simulated example where we utilize four risk indicators (obtained from logistic regression, Poisson regression, XGBoost, and neural network) in the k-shortest path algorithm. From our example, we demonstrate two major designed takeaways: (a) the shortest path may not always result in the lowest crash risk, and (b) a similarity in overall predictive performance may not always translate to similar outcomes from the prescriptive models. Based on the review and example, we highlight several avenues for future research. [ABSTRACT FROM AUTHOR]

This research addresses how the stochasticity and correlation of travel speeds affect the shortest path solutions in sustainable environments. We consider a shortest path problem with the objective function of minimizing a linear combination of the mean and standard deviation of carbon emissions. By adjusting the proportion of the standard deviation in the objective function, the effects of speed stochasticity and correlation are studied under different preferences of the decision-makers on the fluctuations of carbon emissions. Based on 102-day real speed data from the Los Angeles freeway network, this research conducts extensive numerical experiments on 200 randomly chosen origin-destination pairs. Experimental results demonstrate the necessity of considering speed stochasticity and correlation, especially when the standard deviation of carbon emissions takes a large proportion in the objective function. As the weight of the standard deviation in the objective function increases from 0 to 1.5, the reduction of emission objective values increases from 0.03% to 0.13% by considering speed stochasticity, and increases from 0.02% to 0.20% by considering speed correlation. Taking the city Los Angeles with about 2361 taxis and about 525,945 passenger orders in January 2017 as an example, 0.03% and 0.02% reductions respond to about 3156 kg and 2630 kg carbon emission, respectively. [ABSTRACT FROM AUTHOR]

Bird migration is a long studied phenomenon that involves animals moving back and forth from wintering sites and to reproductive grounds. Several studies have focused on identifying the timing, physiology and evolution of migration, but a spatial approach to understand the migratory routes is still an open challenge. Geographic Information Systems (GIS) can provide the tools to explore such a complicated issue. Birds usually move from the wintering sites to spring breeding grounds in multiple flights, stopping at intermediate sites to rest and refuel, being unable to cover the distance in a single travel. The choice of stopover sites by birds depends not only on their ecological features but also on their position and visibility along main migratory flyways. In this work, we calculated the possible migratory routes that minimize the distance covered or the elevation gaps for birds crossing the Southern Alps, simulating the flight within a network connecting potential stopover sites and other relevant point of passage, using the shortest path computation. Subsequently, we performed a visibility analysis along the identified flyways to understand which stopover sites, belonging to the Natura2000 network, were visible for a bird in an area with complex morphology. Data available from ringing stations confirm the selection or avoidance of some stopover sites based on their en route visibility. The knowledge of bird flyways and stopover sites has implications for conservation as well as for planning, especially for wind farms or other infrastructures. [ABSTRACT FROM AUTHOR]