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Comparison between ACO+CP (dark, solid lines) and CP (light, thin lines) on a problem instance with 30 stations. The columns of the graph matrix represent the vehicle time budget and the rows represent the number of available vehicles.
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Balancing bike sharing systems is an increasingly important problem, because of the rising popularity of this mean of transportation. Bike sharing systems need to be balanced so that bikes (and empty slots for returning bikes) are available to the customers, thus ensuring an adequate level of service.
In this paper, we tackle the problem of balanci...
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Context 1
... main goal of this comparison is to understand if a dynamic branching strategy based on ACO can indeed outperform a static branching strategy. Figure 3 shows the results on an instance from the Citybike Vienna benchmark set featuring 30 stations. The choice of this instance has been driven by the fact that a time budget of 2 minutes was too low for CP to obtain even a single solution on larger instances. ...
Context 2
... fact, the CP solver is declared significantly inferior by the F-Race procedure after just 15 iterations. The superior behavior of ACO+CP is confirmed also from the analysis reported in Figure 3, for the variants of a single problem instance with 30 stations. Note that the ACO+CP data is based on 5 repetitions of the same experiment, as the process is intrinsically stochastic. ...
Citations
... Various heuristic algorithms have also been developed or applied to address these NP-hard optimization problems. These include (hybrid) genetic algorithm [48,71], ant colony optimization with CP (ACO-CP) [77], discrete-continuous hybrid model [38], CA [35], extended particle swarm optimization [52,53], greedygenetic heuristic [46], tabu search [49], neighborhood search [50], and neighborhood search-variable neighborhood descent [51]. Other algorithms can be found tabulated in the references [46][47][48]50]. ...
... To ensure scalability, this study proposed a hybrid heuristic algorithm, named ACO-ILP algorithm, which combines ant colony optimization (ACO) with an ILP solver to solve the rebalancing optimization tasks of shared dockless e-scooters. A similar hybrid algorithm, ACO-CP, was developed for the deterministic rebalancing of bike sharing [77]. However, in this study, ACO was utilized to generate a population of route sequences in each iteration, while the ILP solver was employed to optimize the pickup and drop-off operations specifically for each of these predefined route sequences. ...
... As reviewed in Section II, previous studies have designed rebalancing problems with various objective functions, predominantly focused on total driving distance [55] and generalized cost [47,65,67,68,77]. These generalized cost functions often share common terms, such as driving distance or duration, as well as constraints like vehicle capacity, pickup and drop-off constraints, among others. ...
The emergence of dockless shared e-scooters as a new form of shared micromobility offers a viable solution to specific urban transportation problems, including the first-mile–last-mile issue, parking constraints, and environmental emissions. However, this sharing service faces several challenges in daily operation, particularly related to demand volatility, battery recharging, maintenance, and regulation, owing to their trip and physical characteristics. Therefore, this study proposed a new data-driven rebalancing framework for dockless shared e-scooters that incorporates demand and variance prediction and uses Monte Carlo sampling to represent stochastic demand. Thus, demand uncertainty and the collection of low-battery and broken e-scooters were included in the rebalancing formulation to minimize user dissatisfaction and operating costs. Rebalancing optimization is an NP-hard problem, so small-size problems were solved using the integer linear programming (ILP) solver GNU Linear Programming Kit, and large-size problems were solved using a hybrid ant colony optimization–ILP algorithm (ACO–ILP). This framework was evaluated on a real-world dataset from Minneapolis, Minnesota, which demonstrated that the demand and variance prediction efficiently allocated the uncertainty while reducing the overall uncertainty, leading to shorter driving distances and lower rebalancing costs relative to baseline cases.
... Static rebalancing is usually based on the demand forecast for the next day [11][12][13][14]. Gaspero et al. [15] minimize a weighted sum of the deviation from target inventory levels and total work time. ...
Because of imbalanced spatial‐temporal user demands, situations with no available bikes or docks often occur. In order to better response to user demands, many researchers are devoted to rebalancing bike sharing systems (BSS). Existing researches focus primarily on rebalancing BSS by trucks or by workers individually, resulting in two issues: (a) the high cost and massive emissions associated with trucks‐based rebalancing; and (b) the low efficiency associated with workers‐based rebalancing. This paper combines two rebalancing methods together and proposes a mixed rebalancing strategy to tackle the aforementioned issues. This strategy rebalances free‐floating BSS (FBSS) by trucks on the eve of peak hours and by workers during peak hours, in which the worker‐based rebalancing plan is given by a worker‐and‐system trade‐off model which simultaneously considers the impact of workers' costs and real‐time inventory of stations. A case study is conducted on two scenarios of the Beijing Mobike dataset: the Beigongdaximen subway station and the Jinyijiayuan residential area. The results show that our mixed rebalancing strategy can effectively rebalance FBSS by improving the following four indices: rebalancing cost, usage rate of shared bikes and docks, survival time of stations, and demand satisfaction.
... vehicle capacity and constrained route length. 13 All instances are solved to optimality with the CP model of Di Gaspero et al. (2013a), which was slightly adjusted to fit our altered objective functions. Figure 2 shows the normalized distributions of bike deviations from the balance targets of their stations, in the three contexts mentioned previously. ...
... We present the CP-based BBSS model of Di Gaspero et al. (2013a), using that notation (an example of a non-CP formulation can be found in Rainer-Harbach et al. (2015)). Let -S = {1, . . . ...
The concept of balance plays an important role in many combinatorial optimization problems. Yet there exist various ways of expressing balance, and it is not always obvious how best to achieve it. In this methodology-focused paper, we study three cases where its integration is deficient and analyze the causes of these inadequacies. We examine the characteristics and performance of the measures of balance used in these cases, and provide general guidelines regarding the choice of a measure.
... In the following, relevant papers that have been conducted in this context are presented. In [17] and [18] CP was hybridized to ACO. In the first work, the objective was to solve a real-world bicycle sharing problem. ...
Constraint satisfaction problem (CSP) has been actively used for modeling and solving a wide range of complex real-world problems. However, it has been proven that developing efficient methods for solving CSP, especially for large problems, is very difficult and challenging. Existing complete methods for problem-solving are in most cases unsuitable. Therefore, proposing hybrid CSP-based methods for problem-solving has been of increasing interest in the last decades. This paper aims at proposing a novel approach that combines incomplete and complete CSP methods for problem-solving. The proposed approach takes advantage of the group search algorithm (GSO) and the constraint propagation (CP) methods to solve problems related to the remote sensing field. To the best of our knowledge, this paper represents the first study that proposes a hybridization between an improved version of GSO and CP in the resolution of complex constraint-based problems. Experiments have been conducted for the resolution of object recognition problems in satellite images. Results show good performances in terms of convergence and running time of the proposed CSP-based method compared to existing state-of-the-art methods.
... This was considered by (Bengio, Lodi, and Prouvost 2018) as an important challenge in learning-based methods for combinatorial optimization. Note also that compared to failure-driven explanation-based learning (Kambhampati 1998), hybridation with ant colony optimization (Meyer 2008;Khichane, Albert, and Solnon 2010;Di Gaspero, Rendl, and Urli 2013), and related mechanisms (Katsirelos and Bacchus 2005;Xia and Yap 2018), where learning is used to improve the search of the solving process for a specific instance, the knowledge learned by our approach can be used to solve new instances. The closest related work we identified is the approach of (Antuori et al. 2020) that has been developed in parallel by another team independently. ...
Combinatorial optimization has found applications in numerous fields, from aerospace to transportation planning and economics. The goal is to find an optimal solution among a finite set of possibilities. The well-known challenge one faces with combinatorial optimization is the state-space explosion problem: the number of possibilities grows exponentially with the problem size, which makes solving intractable for large problems. In the last years, deep reinforcement learning (DRL) has shown its promise for designing good heuristics dedicated to solve NP-hard combinatorial optimization problems. However, current approaches have an important shortcoming: they only provide an approximate solution with no systematic ways to improve it or to prove optimality. In another context, constraint programming (CP) is a generic tool to solve combinatorial optimization problems. Based on a complete search procedure, it will always find the optimal solution if we allow an execution time large enough. A critical design choice, that makes CP non-trivial to use in practice, is the branching decision, directing how the search space is explored. In this work, we propose a general and hybrid approach, based on DRL and CP, for solving combinatorial optimization problems. The core of our approach is based on a dynamic programming formulation, that acts as a bridge between both techniques. We experimentally show that our solver is efficient to solve three challenging problems: the traveling salesman problem with time windows, the 4-moments portfolio optimization problem, and the 0-1 knapsack problem. Results obtained show that the framework introduced outperforms the stand-alone RL and CP solutions, while being competitive with industrial solvers.
... Therefore, most researchers prefer to adopt heuristics to solve their problems. The existing heuristics include metaheuristic (e.g., Di Gaspero et al., 2013;Chemla et al., 2013b), neighborhood search algorithm (e.g., Rainer-Harbach et al., 2013;Rainer-Harbach et al., 2015;Cruz et al., 2017;Ho and Szeto, 2017), phase-based method (e.g., Raviv et al., 2013;Forma et al., 2015;Schuijbroek et al., 2017) and metaheuristic (Ho and Szeto, 2014;Szeto et al., 2016;Li et al., 2016;Szeto and Shui, 2018). Mladenovic et al. (1997) introduce a powerful Variable Neighborhood Search (VNS) metaheuristic based on the principle of systematic change of neighborhood. ...
A static bike rebalancing problem with optimal user incentives is investigated. The problem is formulated as a mixed-integer nonlinear and nonconvex programming model to minimize the total cost, including the travel costs, unbalanced penalties, and incentive costs. We reformulate the mixed-integer program and develop a new outer-approximation method to obtain its global ε-optimal solutions. We also propose a bi-level variable neighborhood search algorithm to solve large problems. The results tested on small examples reveal problem properties and the performance of the outer-approximation method. The results tested on large examples show that the bi-level algorithm can provide high-quality solutions with short computational times.
... Papazek et al. set the primary goal to minimize the absolute deviation between target and final fill levels for all stations [16]. Gaspero et al. solve the problem with the aim of minimizing the weighted sum of the total travel time and the total absolute deviation from the target number of bikes [17], while Raviv and Kolka take it as a penalty cost [18]. Faulty bikes are considered by Wang and Szeto with the objective of minimizing the total carbon emission of all vehicles [19]. ...
... Constraints (16) indicate the safe residual charge constraints of EVs. Constraints (17) and (18) show that EVs are fully charged when leaving the depot or a charging station. Constraints (19) guarantee the residual charges of EVs are the same after serving a BSS station. ...
Nowadays, as a low-carbon and sustainable transport mode bike-sharing systems are increasingly popular all over the world, as they can reduce road congestion and decrease greenhouse gas emissions. Aiming at the problem of the mismatch of bike supply and user demand, the operators have to transfer bikes from surplus stations to deficiency stations to redistribute them among stations by vehicles. In this paper, we consider a mixed fleet of electric vehicles and internal combustion vehicles as well as the traffic restrictions to the traditional vehicles in some metropolises. The mixed integer programming model is firstly established with the objective of minimizing the total rebalancing cost of the mixed fleet. Then, a simulated annealing algorithm enhanced with variable neighborhood structures is designed and applied to a set of randomly generated test instances. The computational results and sensitivity analysis indicate that the proposed algorithm can effectively reduce the total cost of rebalancing.
... In terms of the number of trucks used, static BRP studies are mainly divided into two categories: single and multiple vehicle problems. However, compared with multiple-vehicle BRP [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], it is more realistic to consider a single-vehicle BRP for a particular street in the city [22][23][24][25][26][27][28][29][30][31][32]. In this paper, we focuses on the single-vehicle static BRP. ...
... Existing models to SPRP define user dissatisfaction either as the sum of the unmet demand (only consider stations with too few bikes) [4][5][6][7][8][9] or as the sum of the absolute differences between the current inventory and the target inventory at all stations (including stations with too many bikes and stations with too few bikes) [10,11,32]. ey commonly ignore the different level of dissatisfaction caused by different stations. ...
... e goal of these problems is not only to pursue the minimum transportation cost by determining routing decisions, but also to minimize user dissatisfaction by determining loading and unloading decisions at each station. User dissatisfaction is commonly measured by the penalty costs [3,12,19,28,29], the absolute deviation from the target number of bikes [4][5][6][7][8][9], and the unmet demand [10,11,32]. ...
In this paper, a single-vehicle static partial repositioning problem (SPRP) is investigated, which distinguishes the user dissatisfaction generated by different stations. The overall objective of the SPRP is to minimize the weighted sum of the total operational time and the total absolute deviation from the target number of bikes at all stations. An iterated local search is developed to solve this problem. A novel loading and unloading quantity adjustment operator is proposed to further improve the quality of the solution. Experiments are conducted on a set of instances from 30 to 300 stations to demonstrate the effectiveness of the proposed customized solution algorithm as well as the adjustment operator. Using a small example, this paper also reveals that the unit penalty cost has an effect on the repositioning strategies.
... Rainer-Harbach et al. (2013) proposed a competitive station-binding neighborhood structure used the VNS algorithm that is combined with the Optimal Loading Operations strategy. A number of hybrid algorithms have also achieved promising results, including the hybrid ant colony algorithm with constraint programming ( Di Gaspero et al., 2013 ), the hybrid VNS and VND ( Rainer-Harbach et al., 2013 ), and the hybrid branch-and-cut and tabu search ( Haider et al., 2018 ). In addition, branch and cut, destroy and repair, and stochastic programming were proposed by Dell Amico et al. to solve BSRP ( Amico et al., 2014;. ...
This paper studies the bike-sharing re-positioning problem (BSRP) frequently encountered in modern bike-sharing systems that are widely deployed around the world. To cope with customer demand fluctuations and improve service level, BSRP aims to identify the optimal vehicle routes to visit bike-sharing stations in order to balance their inventories, picking up excess bikes from surplus stations and adding needed bikes to insufficient stations, with the objective of minimizing total traveling cost and inventory cost. The mathematical model of the studied problem is first given, detailing the considerations of multiple depots available for re-positioning vehicles and the extra objective of inventory cost minimization. An effective clustering strategy is then proposed to put bike-sharing stations into self-sufficient groups, which is shown to be able to greatly decompose the problem complexity for large-scale instances. A destroy-and-repair algorithm is developed to improve the clusters, and an adaptive variable neighborhood search algorithm is designed to conduct intra-cluster and inter-cluster vehicle routing optimization. Performance of the hybrid algorithm is validated on three sets of benchmark instances, and compared with CPLEX as well as state-of-the-art algorithms from the literature, which demonstrates that the proposed algorithm is highly competitive in solving BSRPs.
... Papazek et al. [13] set the primary goal to minimize the absolute deviation between target and final fill levels for all stations. Gaspero et al. [14] solve the problem with the aim of minimizing the weighted sum of the total travel time and the total absolute deviation from the target number of bikes, while Raviv and Kolka [15] take it as a penalty cost. Szeto et al. [16] and Espegren et al. [17] also consider the same factors, but the objective is to minimize the weighted sum of unmet customer demand and operational time. ...
The bike-sharing system (BSS), as a sustainable way to deal with the “last mile” problem of mass transit systems, is increasingly popular in recent years. Despite its success, the BSS tends to suffer from the mismatch of bike supply and user demand. BSS operators have to transfer bikes from surplus stations to deficit stations to redistribute them among stations by means of trucks. In this paper, we deal with the bike-sharing rebalancing problem with balance intervals (BRP-BIs), which is a variant of the static bike-sharing rebalancing problem. In this problem, the equilibrium of station is characterized by a balance interval instead of a balance point in the literature. We formulate the BRP-BI as a biobjective mixed-integer programming model with the aim of determining both the minimum cost route for a single capacitated vehicle and the maximum average rebalance utility, an index for the balanced degree of station. Then, a multistart multiobjective particle swarm optimization (MS-MOPSO) algorithm is proposed to solve the model such that the Pareto optimal solutions can be derived. The proposed algorithm is extended with crossover operator and variable neighbourhood search to enhance its exploratory capability. Compared with Hybrid NSGA-II and MOPSO, the computational experimental results demonstrate that our MS-MOPSO can obtain Pareto optimal solutions with higher quality.
