GRACE: A Generational Randomized ACO for the Multi-objective Shortest Path Problem

2011 ◽  
pp. 535-549
Author(s):  
Leonardo C. T. Bezerra ◽  
Elizabeth F. G. Goldbarg ◽  
Luciana S. Buriol ◽  
Marco C. Goldbarg
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Multi Objective

scholarly journals A Comparison of Genetic Representations and Initialisation Methods for the Multi-objective Shortest Path Problem on Multigraphs

2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Lilla Beke ◽  
Michal Weiszer ◽  
Jun Chen
Keyword(s):  
Shortest Path ◽  
Time Budget ◽  
Exact Algorithm ◽  
Simple Graph ◽  
Shortest Path Problem ◽  
Future Application ◽  
Multi Objective ◽  
Trade Offs ◽  
Conflicting Objectives ◽  
Problem Instances

AbstractThis paper compares different solution approaches for the multi-objective shortest path problem (MSPP) on multigraphs. Multigraphs as a modelling tool are able to capture different available trade-offs between objectives for a given section of a route. For this reason, they are increasingly popular in modelling transportation problems with multiple conflicting objectives (e.g., travel time and fuel consumption), such as time-dependent vehicle routing, multi-modal transportation planning, energy-efficient driving, and airport operations. The multigraph MSPP is more complex than the NP-hard simple graph MSPP. Therefore, approximate solution methods are often needed to find a good approximation of the true Pareto front in a given time budget. Evolutionary algorithms have been successfully applied for the simple graph MSPP. However, there has been limited investigation of their applications to the multigraph MSPP. Here, we extend the most popular genetic representations to the multigraph case and compare the achieved solution qualities. Two heuristic initialisation methods are also considered to improve the convergence properties of the algorithms. The comparison is based on a diverse set of problem instances, including both bi-objective and triple objective problems. We found that the metaheuristic approach with heuristic initialisation provides good solutions in shorter running times compared to an exact algorithm. The representations were all found to be competitive. The results are encouraging for future application to the time-constrained multigraph MSPP.

New Algorithms For Multi Objective Shortest Path Problem

OPSEARCH ◽  
2003 ◽  
Vol 40 (4) ◽  
pp. 278-298 ◽  
Author(s):  
V. N. Sastry ◽  
T. N. Janakiraman ◽  
S. Ismail Mohideen
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Multi Objective ◽  
New Algorithms

A memory efficient stochastic evolution based algorithm for the multi-objective shortest path problem

2014 ◽  
Vol 14 ◽  
pp. 653-662 ◽  
Author(s):  
Umair F. Siddiqi ◽  
Yoichi Shiraishi ◽  
Mona Dahb ◽  
Sadiq M. Sait
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Stochastic Evolution ◽  
Multi Objective ◽  
Memory Efficient

Exploring the Runtime of an Evolutionary Algorithm for the Multi-Objective Shortest Path Problem

2010 ◽  
Vol 18 (3) ◽  
pp. 357-381 ◽  
Author(s):  
Christian Horoba
Keyword(s):  
Evolutionary Algorithm ◽  
Shortest Path ◽  
Fitness Function ◽  
Approximate Solutions ◽  
Shortest Path Problem ◽  
Worst Case ◽  
Multi Objective ◽  
Natural Vector ◽  
Hard Problems ◽  
Vector Valued

We present a natural vector-valued fitness function f for the multi-objective shortest path problem, which is a fundamental multi-objective combinatorial optimization problem known to be NP-hard. Thereafter, we conduct a rigorous runtime analysis of a simple evolutionary algorithm (EA) optimizing f. Interestingly, this simple general algorithm is a fully polynomial-time randomized approximation scheme (FPRAS) for the problem under consideration, which exemplifies how EAs are able to find good approximate solutions for hard problems. Furthermore, we present lower bounds for the worst-case optimization time.

A multi-objective shortest path problem

2001 ◽  
Vol 54 (3) ◽  
pp. 445-454 ◽  
Author(s):  
Kazuyoshi Wakuta
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Multi Objective

An Approach for the Fast Calculation Method of Pareto Solutions of a Two-objective Network

2015 ◽  
Vol 22 (01) ◽  
pp. 1550005 ◽  
Author(s):  
Natsumi Takahashi ◽  
Tomoaki Akiba ◽  
Shuhei Nomura ◽  
Hisashi Yamamoto
Keyword(s):  
Shortest Path ◽  
Optimization Problem ◽  
Computing Time ◽  
Search Space ◽  
Shortest Path Problem ◽  
Objective Functions ◽  
Pareto Solutions ◽  
Fast Calculation ◽  
Multi Objective ◽  
Other Information

The shortest path problem is a kind of optimization problem and its aim is to find the shortest path connecting two specific nodes in a network, where each edge has its distance. When considering not only the distances between the nodes but also some other information, the problem is formulated as a multi-objective shortest path problem that involves multiple conflicting objective functions. The multi-objective shortest path problem is a kind of optimization problem of multi-objective network. In the general cases, multi-objectives are rarely optimized by a solution. So, to solve the multi-objective shortest path problem leads to obtaining Pareto solutions. An algorithm for this problem has been proposed by using the extended Dijkstra's algorithm. However, this algorithm for obtaining Pareto solutions has many useless searches for paths. In this study, we consider two-objective shortest path problem and propose efficient algorithms for obtaining the Pareto solutions. Our proposed algorithm can reduce more search space than existing algorithms, by solving a single-objective shortest path problem. The results of the numerical experiments suggest that our proposed algorithms reduce the computing time and the memory size for obtaining the Pareto solutions.

Facing robustness as a multi-objective problem: A bi-objective shortest path problem in smart regions

2019 ◽  
Vol 503 ◽  
pp. 255-273 ◽  
Author(s):  
C. Cintrano ◽  
F. Chicano ◽  
E. Alba
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Multi Objective

The fuzzy inference approach to solve multi-objective constrained shortest path problem

2020 ◽  
Vol 38 (4) ◽  
pp. 4711-4720 ◽  
Author(s):  
Ali Abbaszadeh Sori ◽  
Ali Ebrahimnejad ◽  
Homayun Motameni
Keyword(s):  
Shortest Path ◽  
Fuzzy Inference ◽  
Shortest Path Problem ◽  
Multi Objective ◽  
Constrained Shortest Path
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