Multiobjective Optimization: Improved FPTAS for Shortest Paths and Non-Linear Objectives with Applications

Tsaggouris, George; Zaroliagis, Christos

doi:10.1007/s00224-007-9096-4

Cited by 79 publications

(87 citation statements)

References 19 publications

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“…Comparing the upper bound for the optimization time of the EA (see Theorem 2) with the upper bound O n · m · n · log (n · w max ) ε k-1 for the runtime of the FPTAS provided in Tsaggouris and Zaroliagis (2006), which is the most time-efficient FPTAS available, shows that both bounds coincide up to a factor of (n 2 /m). For dense graphs the difference reduces to (1).…”

Section: Discussionmentioning

confidence: 84%

“…We show that the runtime of the investigated EA is competitive with the best known problem-specific algorithm from Tsaggouris and Zaroliagis (2006).…”

Section: Introductionmentioning

confidence: 88%

“…Furthermore, the authors show how to construct for several multi-objective optimization problems (including the shortest path problem) an FPTAS. An FPTAS with an improved runtime for the single-source multi-objective shortest path problem is presented in Tsaggouris and Zaroliagis (2006). This paper actually motivated the runtime analysis of a simple EA for this problem since such algorithms can "simulate" the FPTAS, which relies on dynamic programming in combination with scaling and rounding.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Horoba

2010

Evolutionary Computation

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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.

show abstract

Section: Discussionmentioning

confidence: 84%

“…We show that the runtime of the investigated EA is competitive with the best known problem-specific algorithm from Tsaggouris and Zaroliagis (2006).…”

Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

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

Horoba

2010

Evolutionary Computation

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“…MOSP algorithms in single-layer networks can be restricted to four following species: exact, heuristic, approximate, and meta-heuristic 41–44 . Many of these algorithms (especially heuristic and approximate ones) assume that the weights are nonzero.…”

Section: Methodsmentioning

confidence: 99%

Shortest Paths in Multiplex Networks

Ghariblou

Salehi

Magnani

et al. 2017

Sci Rep

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The shortest path problem is one of the most fundamental networks optimization problems. Nowadays, individuals interact in extraordinarily numerous ways through their offline and online life (e.g., co-authorship, co-workership, or retweet relation in Twitter). These interactions have two key features. First, they have a heterogeneous nature, and second, they have different strengths that are weighted based on their degree of intimacy, trustworthiness, service exchange or influence among individuals. These networks are known as multiplex networks. To our knowledge, none of the previous shortest path definitions on social interactions have properly reflected these features. In this work, we introduce a new distance measure in multiplex networks based on the concept of Pareto efficiency taking both heterogeneity and weighted nature of relations into account. We then model the problem of finding the whole set of paths as a form of multiple objective decision making and propose an exact algorithm for that. The method is evaluated on five real-world datasets to test the impact of considering weights and multiplexity in the resulting shortest paths. As an application to find the most influential nodes, we redefine the concept of betweenness centrality based on the proposed shortest paths and evaluate it on a real-world dataset from two-layer trade relation among countries between years 2000 and 2015.

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“…In the same context, a lexicographic weighted Chebyshev metric method was developed by Erbas and Erbas () to solve the MPLS routing problem. More multiobjective studies can be found in transportation problems; in particular, we can cite the shortest path (Tsaggouris and Zaroliagis, ), traffic assignment problems , and vehicle‐routing problems (Jozefowiez et al., ). In telecommunication networks, in the context of multiple QoS routing and multiservice networks, a multiobjective modeling is requisite and has potential advantages.…”

Section: Introductionmentioning

confidence: 99%

Metaheuristics for solving the biobjective single‐path multicommodity communication flow problem

Masri¹,

Krichen

Guitouni

2017

Int Trans Operational Res

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Single‐path multicommodity flow problem (SMCFP) is a well‐known combinatorial optimization problem, in which the flow of each commodity can be transmitted using only one path linking its destination to an appropriate origin within the addressed network. In this paper, we study the SMCFP in a multiobjective context by considering the simultaneous optimization of paths' delay and average reliability. The network is modeled as a finite set of nodes that can communicate using preestablished connections where each connection is characterized by a capacity, a lead time, and a reliability. A node can be an information producer or/and information consumer. The contention problem is solved by assigning a path and a dedicated bandwidth to each flow. The problem is formulated as a biobjective nonlinear optimization problem. This biobjective problem has not been considered in the literature. We design three alternative procedures for approximating the Pareto front. We proposed an MGA based on NSGA‐II, a multiobjective variable neighborhood search and a new distance‐based hybrid metaheuristic. The hybridization integrates a local search into the framework of genetic algorithm to effectively drive the search toward a better approximating of the Pareto front. The propounded algorithms' efficiencies are experimentally investigated on a test bed of instances applied to a planar and a grid network. A comparative study is conducted based on different multiobjective performance indicators.

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Multiobjective Optimization: Improved FPTAS for Shortest Paths and Non-Linear Objectives with Applications

Cited by 79 publications

References 19 publications

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

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

Shortest Paths in Multiplex Networks

Metaheuristics for solving the biobjective single‐path multicommodity communication flow problem

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