scholarly journals Multiple Hungarian Method for k-Assignment Problem

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2050
Author(s):  
Boštjan Gabrovšek ◽  
Tina Novak ◽  
Janez Povh ◽  
Darja Rupnik Poklukar ◽  
Janez Žerovnik
Keyword(s):  
Relative Error ◽  
Assignment Problem ◽  
Search Algorithm ◽  
Computation Time ◽  
Average Relative Error ◽  
Matching Problem ◽  
Solution Quality ◽  
Optimum Algorithm ◽  
Optimal Values

The k-assignment problem (or, the k-matching problem) on k-partite graphs is an NP-hard problem for k≥3. In this paper we introduce five new heuristics. Two algorithms, Bm and Cm, arise as natural improvements of Algorithm Am from (He et al., in: Graph Algorithms And Applications 2, World Scientific, 2004). The other three algorithms, Dm, Em, and Fm, incorporate randomization. Algorithm Dm can be considered as a greedy version of Bm, whereas Em and Fm are versions of local search algorithm, specialized for the k-matching problem. The algorithms are implemented in Python and are run on three datasets. On the datasets available, all the algorithms clearly outperform Algorithm Am in terms of solution quality. On the first dataset with known optimal values the average relative error ranges from 1.47% over optimum (algorithm Am) to 0.08% over optimum (algorithm Em). On the second dataset with known optimal values the average relative error ranges from 4.41% over optimum (algorithm Am) to 0.45% over optimum (algorithm Fm). Better quality of solutions demands higher computation times, thus the new algorithms provide a good compromise between quality of solutions and computation time.

scholarly journals Space-time clustering-based method to optimize shareability in real-time ride-sharing

PLoS ONE ◽  
2022 ◽  
Vol 17 (1) ◽  
pp. e0262499
Author(s):  
Negin Alisoltani ◽  
Mostafa Ameli ◽  
Mahdi Zargayouna ◽  
Ludovic Leclercq
Keyword(s):  
Real Time ◽  
Large Scale ◽  
Computation Time ◽  
Clustering Method ◽  
Matching Problem ◽  
Solution Quality ◽  
Mobility Service ◽  
Ride Sharing ◽  
Large Scale Problems ◽  
Spatio Temporal

Real-time ride-sharing has become popular in recent years. However, the underlying optimization problem for this service is highly complex. One of the most critical challenges when solving the problem is solution quality and computation time, especially in large-scale problems where the number of received requests is huge. In this paper, we rely on an exact solving method to ensure the quality of the solution, while using AI-based techniques to limit the number of requests that we feed to the solver. More precisely, we propose a clustering method based on a new shareability function to put the most shareable trips inside separate clusters. Previous studies only consider Spatio-temporal dependencies to do clustering on the mobility service requests, which is not efficient in finding the shareable trips. Here, we define the shareability function to consider all the different sharing states for each pair of trips. Each cluster is then managed with a proposed heuristic framework in order to solve the matching problem inside each cluster. As the method favors sharing, we present the number of sharing constraints to allow the service to choose the number of shared trips. To validate our proposal, we employ the proposed method on the network of Lyon city in France, with half-million requests in the morning peak from 6 to 10 AM. The results demonstrate that the algorithm can provide high-quality solutions in a short time for large-scale problems. The proposed clustering method can also be used for different mobility service problems such as car-sharing, bike-sharing, etc.

Neural Network-Based Metaheuristic Parameterization with Application to the Vehicle Matching Problem in Ride-Hailing Services

2019 ◽  
Vol 2673 (10) ◽  
pp. 311-320
Author(s):  
Arslan Ali Syed ◽  
Irina Gaponova ◽  
Klaus Bogenberger
Keyword(s):  
Neural Network ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Computation Time ◽  
Problem Instance ◽  
Neighborhood Search ◽  
Matching Problem ◽  
Solution Quality ◽  
Actual Problem ◽  
Parameter Values

The majority of transportation problems include optimizing some sort of cost function. These optimization problems are often NP-hard and have an exponential increase in computation time with the increase in the model size. The problem of matching vehicles to passenger requests in ride hailing (RH) contexts typically falls into this category.Metaheuristics are often utilized for such problems with the aim of finding a global optimal solution. However, such algorithms usually include lots of parameters that need to be tuned to obtain a good performance. Typically multiple simulations are run on diverse small size problems and the parameters values that perform the best on average are chosen for subsequent larger simulations.In contrast to the above approach, we propose training a neural network to predict the parameter values that work the best for an instance of the given problem. We show that various features, based on the problem instance and shareability graph statistics, can be used to predict the solution quality of a matching problem in RH services. Consequently, the values corresponding to the best predicted solution can be selected for the actual problem. We study the effectiveness of above described approach for the static assignment of vehicles to passengers in RH services. We utilized the DriveNow data from Bavarian Motor Works (BMW) for generating passenger requests inside Munich, and for the metaheuristic, we used a large neighborhood search (LNS) algorithm combined with a shareability graph.

scholarly journals Buffer Allocation via Bottleneck-Based Variable Neighborhood Search

2020 ◽  
Vol 10 (23) ◽  
pp. 8569
Author(s):  
Sixiao Gao ◽  
Toshimitsu Higashi ◽  
Toyokazu Kobayashi ◽  
Kosuke Taneda ◽  
Jose I. U. Rubrico ◽  
...  
Keyword(s):  
Variable Neighborhood Search ◽  
Search Algorithm ◽  
Computation Time ◽  
State Probability ◽  
Neighborhood Search ◽  
Buffer Allocation ◽  
Neighborhood Structure ◽  
Production Lines ◽  
Solution Quality ◽  
Acceptable Solution

This study addresses the challenging problem of efficient buffer allocation in production lines. Suitable locations for buffer allocation are determined to satisfy the desired throughput, while a suitable balance between solution quality and computation time is achieved. A throughput calculation approach that yields the state probability of production lines is adopted to evaluate the effectiveness of candidate buffer allocation solutions. To generate candidate buffer allocation solutions, an active probability index based on state probability is proposed to rapidly detect suitable locations of buffer allocations. A variable neighborhood search algorithm is used to maintain acceptable solution quality; an additional neighborhood structure is used in the case where no satisfactory solution is generated in the initial neighborhood structure. Extensive numerical experiments demonstrate the efficacy of the proposed approach. The proposed approach can facilitate agile design of production lines in industry by rapidly estimating production line topologies.

Parallel Scatter Search Approach for the MinMax Regret Location Problem

2018 ◽  
Vol 9 (2) ◽  
pp. 1-17
Author(s):  
Sarah Ibri ◽  
Mohammed EL Amin Cherabrab ◽  
Nasreddine Abdoune
Keyword(s):  
Location Problem ◽  
Search Algorithm ◽  
Discrete Event ◽  
Scatter Search ◽  
Search Time ◽  
Computation Time ◽  
Minmax Regret ◽  
Search Approach ◽  
Two Stages

In this paper we propose an efficient solving method based on a parallel scatter search algorithm that accelerates the search time to solve the minmax regret location problem. The algorithm was applied in the context of emergency management to locate emergency vehicles stations. A discrete event simulator was used to test the quality of the obtained solutions on the operational level. We compared the performance of the algorithm to an existing two stages method, and experiments show the efficiency of the proposed method in terms of quality of solution as well as the gain in computation time that could be obtained by parallelizing the proposed algorithm.

A Study on Facility Layout Using Evolution Strategies in Case of Different Shapes and Areas of Facilities

2012 ◽  
Author(s):  
Naoki Hirabayashi ◽  
Kazuko Morizawa
Keyword(s):  
Relative Error ◽  
Numerical Experiments ◽  
Facility Layout ◽  
Computation Time ◽  
Adaptive Strategy ◽  
The Other ◽  
Evolution Strategies ◽  
Average Relative Error ◽  
Different Shapes ◽  
Excellent Property

Evolution Strategies have more excellent property than the other existing metaheuristics in a sense of easiness of coding and its manageability of self-adaptive strategy, Hirabayashi et al. proposed a facility layout method using Evolution Strategies for obtaining near optimum solutions efficiently. The shapes of all facilities were, however, assumed to be square. This paper proposes a facility layout method using Evolution Strategies for the case of different shapes and areas of facilities. Some numerical experiments made it clear that the proposed method provides solutions whose average relative error to the optimum or near-optimum solutions obtained by CPLEX are less than 2%, reducing computation time drastically.

scholarly journals How to start a heuristic? Utilizing lower bounds for solving the quadratic assignment problem

2022 ◽  
Vol 13 (2) ◽  
pp. 151-164 ◽  
Author(s):  
Radomil Matousek ◽  
Ladislav Dobrovsky ◽  
Jakub Kudela
Keyword(s):  
Lower Bounds ◽  
Assignment Problem ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Computation Time ◽  
Quadratic Assignment ◽  
Combinatorial Optimization Problems ◽  
Lower Bounding ◽  
Programming Techniques

The Quadratic Assignment Problem (QAP) is one of the classical combinatorial optimization problems and is known for its diverse applications. The QAP is an NP-hard optimization problem which attracts the use of heuristic or metaheuristic algorithms that can find quality solutions in an acceptable computation time. On the other hand, there is quite a broad spectrum of mathematical programming techniques that were developed for finding the lower bounds for the QAP. This paper presents a fusion of the two approaches whereby the solutions from the computations of the lower bounds are used as the starting points for a metaheuristic, called HC12, which is implemented on a GPU CUDA platform. We perform extensive computational experiments that demonstrate that the use of these lower bounding techniques for the construction of the starting points has a significant impact on the quality of the resulting solutions.

MULTISTAGE MICROSTRIP UHF LOAD

2018 ◽  
pp. 53-57 ◽  
Author(s):  
G. G. Savenkov ◽  
V. P. Razinkin ◽  
A. D. Mekhtiev
Keyword(s):  
Frequency Response ◽  
Frequency Band ◽  
High Power ◽  
Two Stage ◽  
High Power Microwave ◽  
Modelling Method ◽  
Optimal Values ◽  
Inductive Elements ◽  
Power Microwave

Applications of modern terminal loads and its relevant disadvantages are described in this paper. The decomposing method of wideband microwave high power microstrip loads design is proposed in this paper with purpose of matching quality improving. Multiple extension of multistage load bandwidth is provided by using of external matching circuit and internal matching inductive elements. The maximum reachable bandwidth of multistage load is estimated and optimal values of mathing circuit elements are founded on basis of equivalent lumped scheme. The topology of microstrip two-stage high power microwave load is developed and its frequency response, calculated via numeric electrodynamic modelling method is outlined in the paper. Modelling results show good matching quality of considered load at the frequency band below 3,5 GHz.

Analysis of Solution Quality of Multiobjective Evolutionary Algorithms for Service Restoration in Distribution Systems

2017 ◽  
Vol 28 (6) ◽  
pp. 796-805
Author(s):  
Danilo Sipoli Sanches ◽  
Marcelo Favoretto Castoldi ◽  
João Bosco Augusto London ◽  
Alexandre Cláudio Botazzo Delbem
Keyword(s):  
Evolutionary Algorithms ◽  
Distribution Systems ◽  
Multiobjective Evolutionary Algorithms ◽  
Solution Quality ◽  
Service Restoration

scholarly journals A Heuristics-Based Parthenogenetic Algorithm for the VRP with Potential Demands and Time Windows

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Chenghua Shi ◽  
Tonglei Li ◽  
Yu Bai ◽  
Fei Zhao
Keyword(s):  
Genetic Algorithm ◽  
Time Windows ◽  
Computation Time ◽  
Routing Problem ◽  
Split Delivery ◽  
Soft Time Windows ◽  
Comparison Results ◽  
Potential Demand ◽  
The Cost

We present the vehicle routing problem with potential demands and time windows (VRP-PDTW), which is a variation of the classical VRP. A homogenous fleet of vehicles originated in a central depot serves customers with soft time windows and deliveries from/to their locations, and split delivery is considered. Also, besides the initial demand in the order contract, the potential demand caused by conformity consuming behavior is also integrated and modeled in our problem. The objective of minimizing the cost traveled by the vehicles and penalized cost due to violating time windows is then constructed. We propose a heuristics-based parthenogenetic algorithm (HPGA) for successfully solving optimal solutions to the problem, in which heuristics is introduced to generate the initial solution. Computational experiments are reported for instances and the proposed algorithm is compared with genetic algorithm (GA) and heuristics-based genetic algorithm (HGA) from the literature. The comparison results show that our algorithm is quite competitive by considering the quality of solutions and computation time.

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