Systematic Literature Review of GPS-based Multi-Objective Environmentally Friendly Shortest Path with a Proposed Lexicographic Framework

Finding a shortest path is one of the most studied problems in computational geometry. There are many variants of the problem. One such variant is the Weighted Region Problem (WRP), i.e., finding a shortest path when the underlying domain is weighted. The difficulty of finding exact weighted shortest paths motivates the study of approximation algorithms for the problem. One alternative that is often encountered is to discretize the continuous space by considering a weighted mesh. Then, optimal shortest paths in this subdivision are approximated. We present two methods that discretize the space based on the placement of Steiner points in the cells of an equilateral-triangle tessellation. Using such a discretization, we can use algorithms for shortest paths in graphs for computing a shortest path in the geometric graph obtained. This will lead us to two approximation algorithms for solving the WRP. In addition, we study how well a weighted mesh approximates the space, with respect to shortest paths. We consider a shortest path~$ \mathit{SP_w}(s,t) $ from~$ s $ to $ t $ in the continuous 2-dimensional space, a shortest vertex path~$ \mathit{SVP_w}(s,t) $ (or any-angle path), which is a shortest path where the vertices of the path are vertices of the mesh, and a shortest grid path $ \mathit{SGP_w}(s,t) $, which is a shortest path in a graph associated to the weighted mesh. We provide upper and lower bounds on the ratios $ \frac{\lVert \mathit{SGP_w}(s,t)\rVert}{\lVert \mathit{SP_w}(s,t)\rVert} $, $ \frac{\lVert \mathit{SVP_w}(s,t)\rVert}{\lVert \mathit{SP_w}(s,t)\rVert} $, $ \frac{\lVert \mathit{SGP_w}(s,t)\rVert}{\lVert \mathit{SVP_w}(s,t)\rVert} $ in equilateral-triangle, square and regular-hexagon meshes. Finally, we explore an application of shortest paths applied to a robotics problem. We study the problem of determining minimum-length coordinated motions for two axis-aligned square robots translating in an obstacle-free plane: Given feasible start and goal configurations, find a continuous motion for the two squares from start to goal, comprising only robot-robot collision-free configurations, such that the Euclidean distance traveled by the two squares is minimal among all possible such motions.

In fields where fault tolerance is critical, such as aerospace and autonomous driving, the Triple Modular Redundancy (TMR) is widely utilized due to its high reliability, yet it comes with significant overhead. To mitigate this issue, Approximate TMR (ATMR) has emerged as a promising solution. However, few studies have addressed the multi-objective optimization problem between hardware saving and fault tolerance caused by approximation. This paper presents two pioneering multi-objective optimization frameworks tailored for fault-tolerant circuit design that leverage approximate redundancy to achieve this delicate balance. The first framework, Dynamic Adjustment Multi-Objective Optimization (DA-MOO), proposes a Dynamic Adjustment Optimized NSGA-II (DAON) algorithm utilizing parity expansion and dynamic probability adjustment to generate ATMR solutions. This method surpasses traditional TMR by halving area and power overhead while still achieving over 70% of fault coverage. Considering the computational intensity of DA-MOO, we further propose the Pre-Encoding Multi-Objective Bayesian Optimization (PE-MOBO) framework, achieving a 198x improvement in computational time over traditional methods. In summary, DA-MOO is well-suited for scenarios requiring a premium on reliability alongside cost-efficiency, such as in the commercial aerospace industry, while PE-MOBO is particularly advantageous for applications demanding rapid design cycles, like consumer electronics.

Radiation therapy treatment planning is inherently a multiobjective problem, aiming to obtain the best tradeoffs between irradiating the tumor with the prescribed dose and sparing as much as possible the surrounding healthy organs. Many different multiobjective approaches have been proposed for the optimization of radiation intensities for fixed beam irradiation directions. However, multiobjective beam angle optimization is seldom considered. The purpose of this paper is to introduce a new multiobjective optimization framework that explicitly and simultaneously considers the optimization of intensities and also beam directions. Whilst multiobjective optimization of radiation intensities considering a fixed set of beam directions gives rise to a single Pareto front, beam angle optimization gives rise to the appearance of multiple Pareto fronts, each one associated with a given beam angle set. Our framework proposes a beam angle set choice based on the evaluation of non-dominated solutions belonging to different Pareto fronts, using a tree-based approach and a performance indicator to assess the quality of each Pareto front. The proposed approach, illustrated by head-and-neck cancer cases, allows for more flexibility in the calculation of solutions and a better understanding of the existing compromises between different objectives.

Geographic information systems (GISs) are becoming the most popular field in recent years. A GIS is an application or system which is designed for capture, storage, manipulation, analysis, and presentation of spatial or geographic information. Geographic location is the key term or information for the geographic information without which the data can’t be said to be spatial or geographic. The approach mentioned in this paper explores two famous problems, i.e., GIS and graph theory algorithms to find out the shortest path between the two nodes. This paper explores the working of “shortest path analyzer” plugin developed for QGIS [1, 2] to find out the shortest path between two nodes (source and destination) in road network (geospatial data) using various algorithm approaches of PgRouting [3, 4] extension of PostgreSQL [5] database. A detailed overview of this plugin is presented in this paper. PgRouting provides some methods by which the cost parameter of distance from the source node to the destination node can be calculated dynamically. In this research, various algorithms (provided in PgRouting) are implemented to calculate the best and an optimal shortest path between two nodes and the comparison of various shortest path algorithms [6] is made to calculate the shortest path with minimum cost. This paper is a comprehensive compilation of theory as well as an implementation of PgRouting library functions in the form of the plugin of QGIS in the spatial network analysis domain. This research is implementing a geospatial database at the backend and PyQGIS plugin at the front end to calculate and visualize the shortest path between two nodes of the road network using various combinations.

Computing the shortest path between two vertices in a given graph finds out vast applications. Currently most state-of-the-art research studies the shortest path computation problem in single-weight graphs, i.e., each edge in the graph has only one weight. In some applications, there are multiple weights on an edge, and those weights need to be considered when computing the shortest path. However, the sub-path property that any sub-path on a shortest path is also a shortest path, is violated in multi-weight graphs, and hence those state-of-the-arts could not be directly applied. This paper proposes a Bidirectional Best-First Search (BBFS) method with heuristic optimizations to find an optimal shortest path in multi-weight graphs. Experiments show that compared to the single search Best-First Search (BFS), BBFS has higher performance. Meanwhile, BBFS has high accuracy especially for long paths search.

This paper addresses one of the potential graphbased problems that arises when an optimal shortest path solution, or near optimal solution is acceptable, namely the Single Source Shortest Path (SSSP) problem. The single source shortest path problem is an NP-hard combinatorial optimization problem that has long challenged researchers. The objective of the SSSP is to find the path between two nodes with shortest length (weight). For solving this problem, a new technique Modified Shuffled Frog Leaping algorithm (MSFLA) with GA cross-over is developed and evaluated. SFLA is a meta-heuristic search method inspired by natural memetics. It combines the benefits of both meme-based Memetic Algorithm (MA) and social behaviour based Particle Swarm Optimization (PSO). In this paper some modification of SFLA is done and also GA Cross-over is implemented and applied it to SSSP problem. Some problems from references are solved using the proposed algorithm and an implementation study is presented. The implementation study shows the efficiency of the proposed algorithm.

Multi-objective optimization control for tunnel boring machine performance improvement under uncertainty

Due to the tremendous development in the field of computer and software sciences, the theory of graphics has spread widely and quickly, even becoming one of the most important sciences that played a large role in solving many problems of many diverse applications. These applications include computer protocols, Google Maps, games and more. Many researches have discussed shortest path algorithms to solve the shortest path problem in these applications. In this study, a very popular algorithms called Dijkstra algorithm and Bellman-Ford algorithm are used to make a comparison between them on the basis of complexity and performance in terms of shortest path optimization. Our results show that Dijkstra is better than the Bellman-Ford interms of execution time and more efficient for solving the shortest path issue, but the algorithm of Dijkstra work with non-negative edge weights.

In order to improve the scheduling ability of urban cold chain multi-series distributed logistics, it is necessary to carry out path optimization planning and design. This paper puts forward the shortest path optimization planning algorithm of urban cold chain multi-series distributed logistics based on particle swarm optimization. The particle swarm optimization method is adopted to sample the environmental information of urban cold chain multi-serial point distributed logistics area, the collected data of urban cold chain multi-serial point distributed logistics area is dynamically weighted and the shortest path optimization control is carried out, and the path space area grid block planning detection model of urban cold chain multi-serial point distributed logistics area is established. According to the task requirements, Particle swarm optimization (PSO) shortest path detection method is used to optimize the shortest path planning and block search of urban cold chain multi-series distributed logistics. The pheromone features of the shortest path planning of urban cold chain multi-series distributed logistics are extracted. The shortest path planning method is used to analyze the characteristics of urban cold chain multi-series distributed logistics, and the global evolution game features of logistics trolley are analyzed. Particle swarm optimization (PSO) algorithm is used to carry out adaptive optimization in the shortest path planning process of urban cold chain multi-series distributed logistics, so as to realize independent planning and shortest optimization of the global path of urban cold chain multi-series distributed logistics. The simulation results show that the shortest path planning of urban cold chain multi-series distributed logistics with this method has good optimization ability, which improves the response ability of urban cold chain multi-series distributed logistics and reduces the cost of distribution time.

Graph-based approaches for simulating pedestrian dynamics in building models

Constructing efficient data structures (distance oracles) for fast computation of shortest paths and other connectivity measures in graphs has been a promising area of study in computer science [23, 24, 28]. In this paper, we propose very efficient algorithms, based on a distance oracle, for computing approximate shortest paths and alternate paths in road networks. Specifically, we adopt a distance oracle construction that exploits the existence of small separators in such networks. In other words, the existence of a small cut in a graph admits a partitioning of the graph into balanced components with a small number of inter-component edges. We demonstrate the efficacy of our algorithm by using it to find near optimal shortest paths and show that it also has the desired properties of well-studied goal-oriented path search algorithms such as ALT [12]. We further demonstrate the use of our distance oracle to produce multiple alternative routes in addition to the shortest path. Finally, we empirically demonstrate that our method, while exploring few edges, produces high quality alternates with respect to metrics such as optimality-loss and diversity of paths.

Dynamic shortest path algorithms modify the existing shortest path tree or graph, taking into account changes in the underlying graph configuration. In the premise of this paper, the dynamic Dijkstra algorithm is specifically considered which is used for the solution of single source shortest path problem in dynamic graphs. Dynamic Single Source Shortest Path (DSSSP) problem is considered from a completely different perspective. For incorporating the dynamic changes into the solution, the retroactive data structure has been used. Dynamics of retroactive data structures provide a natural order for propagating the desired changes in the underlying graph configuration. DSSSP has been solved in efficient way with worst case complexity O(m log n) and also proved the correctness of our proposed algorithm.

An algorithmic framework for the single source shortest path problem with applications to disk graphs

The shortest path problem is a search for the shortest or minimum path between the source and destination under the relevant parameter constraints, and it is an effective method for solving network routing problems. Many good algorithms have been proposed by researchers for single-parameter shortest path problems, but the process of finding shortest paths for multiple parameters is an NP-complete problem, and less research has been done. In this paper, a multi-objective shortest path algorithm MQGASP based on genetic algorithm is proposed, which regards the feasible solution of the nearest ideal solution of partial distance measurement as the solution to be found. Because the priority based coding method can potentially represent all possible paths in the directed graph, it can well represent the paths in the network graph with chromosomes. Simulation experiments show that the MQGASP algorithm has better performance in solving multi-QoS routing and is able to find the shortest transmission path with maximum bandwidth and minimum delay.

Multi-objective optimization framework of a vehicle door design in the slamming event for optimal dynamic performances