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

Horoba, Christian

doi:10.1162/evco_a_00014

Cited by 18 publications

(11 citation statements)

References 28 publications

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“…Also results for NP-hard multi-objective shortest path problems have been obtained. Horoba (2010) proved that a simple multiobjective evolutionary algorithm using only mutation and a mechanism to maintain diversity in the population represents a fully polynomial randomized approximation scheme (FPRAS). Neumann and Theile (2010) extended this result towards the use of crossover, showing that crossover leads to improved running times.…”

Section: Related Workmentioning

confidence: 99%

A Simple Ant Colony Optimizer for Stochastic Shortest Path Problems

Sudholt

Thyssen

2011

Algorithmica

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Ant Colony Optimization (ACO) is a popular optimization paradigm inspired by the capabilities of natural ant colonies of finding shortest paths between their nest and a food source. This has led to many successful applications for various combinatorial problems. The reason for the success of ACO, however, is not well understood and there is a need for a rigorous theoretical foundation.We analyze the running time of a simple ant colony optimizer for stochastic shortest path problems where edge weights are subject to noise that reflects delays and uncertainty. In particular, we consider various noise models, ranging from general, arbitrary noise with possible dependencies to more specific models such as independent gamma-distributed noise. The question is whether the ants can find or approximate shortest paths in the presence of noise. We characterize instances where the ants can discover the real shortest paths efficiently. For general instances we prove upper bounds for the time until the algorithm finds reasonable approximations. Contrariwise, for independent gamma-distributed noise we present a graph where the ant system needs exponential time to find a good approximation. The behavior of the ant system changes dramatically when the noise is perfectly correlated as then the ants find shortest paths efficiently. Our results shed light on trade-offs between the noise strength, approximation guarantees, and expected running times.

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Section: Related Workmentioning

confidence: 99%

A Simple Ant Colony Optimizer for Stochastic Shortest Path Problems

Sudholt

Thyssen

2011

Algorithmica

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“…In order to optimize the material distribution paths for reducing cost of production, and improving market competitiveness of enterprises, some researchers have established different multi-objective model of material distribution path based on the different objectives and impact factors [16]. For example, Mohammad Rahimi [17] posed a new idea about inventory path, based on the level of service in the distribution of perishable products-considered by determining the specific expiration date, and established a multi-objective mathematical model to maximize profit, minimize delay rate, and minimize the number of vehicles.…”

Section: Research Concerning Materials Distribution Optimizationmentioning

confidence: 99%

Carbon Emission Reduction of Apparel Material Distribution Based on Multi-Objective Genetic Algorithm (NSGA-II)

2019

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Low-carbon production has become one of the top management objectives for every industry. In garment manufacturing, the material distribution process always generates high carbon emissions. In order to reduce carbon emissions and the number of operators to meet enterprises’ requirements to control the cost of production and protect the environment, the paths of material distribution were analyzed to find the optimal solution. In this paper, the model of material distribution to obtain minimum carbon emissions and vehicles (operators) was established to optimize the multi-target management in three different production lines (multi-line, U-shape two-line, and U-shape three-line), while the workstations were organized in three ways: in the order of processes, in the type of machines, and in the components of garment. The NSGA-II algorithm (non-dominated sorting genetic algorithm-II) was applied to obtain the results of this model. The feasibility of the model and algorithm was verified by the practice of men’s shirts manufacture. It could be found that material distribution of multi-line layout produced the least carbon emissions when the machines were arranged in the group of type.

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“…Then we add another N TNIU +1 new nodes, representing different resource allocations to NPDP i+1. Then we establish directed links from NPDP i nodes to NPDP i+1 nodes subjected to Constraint (21) or (24). In the route network for g 1 , the length of the link which connects to the node of x n∆ allocation to NPDP i+1 (i.e., x(i+1)= x n∆ ) is set as…”

Section: Bespoke Rsa For Monpdmentioning

confidence: 99%

“…With the constructed route network for g j , we can develop a ripple relay race to calculate the k best solutions in terms of objective g j for MONPD. Basically, the new race process is similar to that in [44], which aims to resolve the k shortest paths problem, and the major modifications are: (i) a new ripple at a node needs to select out feasible links from established links according to Constraint (21) or (24); (ii) the length l n,NP needs to be dynamically reset according to the resource allocations of NPDP1 to NPDP N P -1.…”

Section: Bespoke Rsa For Monpdmentioning

confidence: 99%