Multi-directional Local Search Research Articles

A Bi-Objective Home Health Care Routing and Scheduling Problem under Uncertainty.

Home health care companies provide health care services to patients in their homes. Due to increasing demand, the provision of home health care services requires effective management of operational costs while satisfying both patients and caregivers. In practice, uncertain service times might lead to considerable delays that adversely affect service quality. To this end, this paper proposes a new bi-objective optimization problem to model the routing and scheduling problems under uncertainty in home health care, considering the qualification and workload of caregivers. A mixed-integer linear programming formulation is developed. Motivated by the challenge of computational time, we propose the Adaptive Large Neighborhood Search embedded in an Enhanced Multi-Directional Local Search framework (ALNS-EMDLS). A stochastic ALNS-EMDLS is introduced to handle uncertain service times for patients. Three kinds of metrics for evaluating the Pareto fronts highlight the efficiency of our proposed method. The sensitivity analysis validates the robustness of the proposed model and method. Finally, we apply the method to a real-life case and provide managerial recommendations.

Pareto and decomposition based approaches for the multi-objective home health care routing and scheduling problem with lunch breaks

Home health care (HHC) is a fast-growing area of research that has received increasing attention in recent years due to the rise in life expectancy and the fall in birth rates. It is expected to reduce length of stay in hospital as well as to allow patients to receive care and assistance in their home. Several models and algorithms have been proposed to manage the various constraints and criteria. However, multi-objectives HHC routing and scheduling problems (HHCRSP) with practical and complicated constraints as well as Pareto dominance based approaches are still scarce in the literature. In this paper, we focus on modeling and solving the multi-objectives HHCRSP with lunch breaks, multiple time windows, duty length, skill requirement and a mix of soft and hard services. A mixed integer linear programming (MILP) model with three objectives is proposed, which aims to minimize tardiness of soft services and caregivers’ waiting times and also to balance their workload. Two approaches, Pareto and decomposition based, with multi-objective evolutionary algorithms are proposed to solve the multi-objective HHCRSP. We developed a memetic algorithm (NSGA-LS), resulting from the hybridization of non-dominated sorting genetic algorithm II (NSGA-II) with multidirectional local search (MDLS), to trade-off between exploration and exploitation. Computational results and performance measures inferred that NSGA-LS has a better performance compared to other algorithms. According to the hyper-volume indicator, NSGA-LS obtained 93.75% better solutions for the tested instances in a pairwise comparison between algorithms while multiobjective evolutionary algorithm based on decomposition (MOEA/D) has a better complexity. Sensitivity analysis of the percentage of soft/flexible services and the maximum allowed tardiness showed that increasing them significantly improved the quality and trade-off of solutions.

Two-Phase Model for Demand-Responsive Transit Considering the Cancellation Behavior of Boundedly Rational Passengers

The resurgence of demand-responsive transit (DRT) has been pushed toward a more sharable and user-friendly mobility service to reshape the urban mobility ecosystem. Nevertheless, to fulfill the swiftly growing diversified and personalized demand, how to depict the cancellation behavior of passengers remains an often overlooked but extremely significant challenge. This paper attempts to discuss the cancellation behavior in the two-phase optimization process. With regard to the unconfirmed reservation cancellation, bounded rationality is incorporated to portray the decision-making process of passengers. Bernoulli random variable is utilized to discuss the stochastic possibility of order cancellation. Simultaneously, a two-phase biobjective model considering the cancellation behavior is constructed to balance the inherent trade-off between passengers and operators. In addition, the algorithm based on multidirectional local search is constructed to achieve the Pareto front for the proposed model. Small-scale experiments in the Nguyen-Dupuis network are illustrated to validate the effectiveness of the algorithm. Subsequently, the Beijing case is further exemplified to evaluate the performance of DRT service considering the cancellation behavior. A reasonable penalty mechanism contributes to ensuring operating profit while substantially diminishing the penalty cost. Therefore, this paper facilitates not only capturing the cancellation behavior of passengers but also developing a more flexible and cost-effective DRT service.

An improved multi-directional local search algorithm for vehicle routing problem with time windows and route balance

An improved multi-directional local search algorithm for vehicle routing problem with time windows and route balance

A lexicographic maximin approach to the selective assessment routing problem

Max-min approaches have been widely applied to address equity as an essential consideration in humanitarian operations. These approaches, however, have a significant drawback of being neutral when it comes to solutions with the same minimum values. These equivalent solutions, from a max-min point of view, might be significantly different. We address this problem using the lexicographic maximin approach, a refinement of the classic max-min approach. We apply this approach in the rapid needs assessment process, which is carried out immediately after the onset of a disaster, to investigate the disaster’s impact on the affected community groups through field visits. We construct routes for an assessment plan to cover community groups, each carrying a distinct characteristic, such that the vector of coverage ratios are maximized. We define the leximin selective assessment problem, which considers the bi-objective optimization of total assessment time and coverage ratio vector maximization. We solve the bi-objective problem by a heuristic approach based on the multi-directional local search framework.

Addendum to “FPBH: A feasibility pump based heuristic for multi-objective mixed integer linear programming” [Comput. Oper. Res. 112 (2019) 104760

This is an addendum to the article ’Pal, A. and Charkhgard, H, “A feasibility pump based heuristic for multi-objective mixed integer linear programming”, Computers & Operations Research 112:104760, 2019. In that work, a comparison was made to another method – a multi-directional local search. This was done using a pre-existing code. After the above work was published, evidence emerged that the mentioned pre-existing code contained a bug. In this addendum note, that bug is corrected and updated comparative results are provided.

Multi-directional local search for sustainable supply chain network design

In this paper, we propose a bi-objective MILP formulation to minimise logistics costs as well as emissions in a supply chain network design problem with multiple layers of facilities, technology levels and transportation mode decisions. The proposed model aims at investigating the trade-off between cost and emissions through supply chain activities (i.e. raw material supply, manufacturing, warehousing, and transportation). To this end, a multi-directional local search (MDLS) metaheuristic is developed. The proposed method provides a limited set of non-dominated solutions ranging from a purely cost effective solution to a purely environmentally effective one. Each iteration of the MDLS consists in performing local searches from all non-dominated solutions. To do so, a Large Neighborhood Search (LNS) algorithm is used. Extensive experiments based on randomly generated instances of various sizes and features are described. Three classic performance measures are used to compare the set of non-dominated solutions obtained by the MDLS algorithm and by directly solving the MILP model with the epsilon-constraint approach. This paper is concluded by managerial insights about the impact of using greener technology on the supply chain topology.

Multi-objective simulation optimization for complex urban mass rapid transit systems

In this paper, we present a multi-objective simulation-based headway optimization for complex urban mass rapid transit systems. Real-world applications often confront conflicting goals of cost versus service level. We propose a two-phase algorithm that combines the single-objective covariance matrix adaptation evolution strategy with a problem-specific multi-directional local search. With a computational study, we compare our proposed method against both a multi-objective covariance matrix adaptation evolution strategy and a non-dominated sorting genetic algorithm. The integrated discrete event simulation model has several stochastic elements. Fluctuating demand (i.e., creation of passengers) is driven by hourly origin-destination-matrices based on mobile phone and infrared count data. We also consider the passenger distribution along waiting platforms and within vehicles. Our two-phase optimization scheme outperforms the comparative approaches, in terms of both spread and the accuracy of the resulting Pareto front approximation.

A lexicographic minimax approach to the vehicle routing problem with route balancing

Vehicle routing problems generally aim at designing routes that minimize transportation costs. However, in practical settings, many companies also pay attention at how the workload is distributed among its drivers. Accordingly, two main approaches for balancing the workload have been proposed in the literature. They are based on minimizing the duration of the longest route, or the difference between the longest and the shortest routes, respectively. Recently, it has been shown on several occasions that both approaches have some flaws. In order to model equity we investigate the lexicographic minimax approach, which is rooted in social choice theory. We define the leximax vehicle routing problem which considers the bi-objective optimization of transportation costs and of workload balancing. This problem is solved by a heuristic based on the multi-directional local search framework. It involves dedicated large neighborhood search operators. Several LNS operators are proposed and compared in experimentations.

Multiobjective memetic algorithm based on adaptive local search chains for vehicle routing problem with time windows

This paper presents a multiobjective memetic algorithm based on adaptive local search chains (MMA-ALSC) for vehicle routing problem with time window (VRPTW) which is an important research area in logistics. As shown in most previous studies, VRPTW is essentially a multiobjective optimization problem and can be solved effectively by the multiobjective algorithms with various local search operators. We have observed, however, that the promising solutions obtained during the process of evolution are not fully utilized to guide the search together with different local search operators. This will lead to the discontinuous and insufficient search in the regions showing promise. To alleviate this drawback, MMA-ALSC is proposed and characterized by combining a multi-directional local search strategy (MD-LS) with an enhanced local search chain technique (eLS-Chain). In MMA-ALSC, on the one hand, with MD-LS, different local search operators are designed to perform the search towards multiple directions with distinct problem-specific knowledge of multiobjective VRPTW (MOVRPTW). On the other hand, with eLS-Chain, the promising solutions obtained during the process of evolution are adaptively selected for the subsequent local search operators. In this way, MMA-ALSC can not only effectively explore the search space in multiple directions, but also fully exploit the promising solutions in a chain-based way. Experimental results on two suites of benchmark instances have demonstrated the competitive performance of MMA-ALSC when compared with other representative algorithms.

Enhanced multi-directional local search for the bi-objective heterogeneous vehicle routing problem with multiple driving ranges

The transportation sector accounts for a significant amount of greenhouse gas emissions. To mitigate this problem, electric vehicles have been widely recommended as green vehicles with lower emissions. However, the driving range of electric vehicles is limited due to their battery capacity. In this paper, a bi-objective mixed-integer linear programming model is proposed to minimise total costs (fixed plus variable) as well as CO2 emissions caused by the vehicles used in the fleet for a Heterogeneous Vehicle Routing Problem with Multiple Loading Capacities and Driving Ranges (HeVRPMD). To solve the proposed model, an enhanced variant of Multi-Directional Local Search (EMDLS) is developed to approximate the Pareto frontier. The proposed method employs a Large Neighbourhood Search (LNS) framework to find efficient solutions and update the approximated Pareto frontier at each iteration. The LNS algorithm makes use of three routing-oriented destroy operators and a construction heuristic based on a multi-round approach. The performance of EMDLS is compared to MDLS, an Improved MDLS (IMDLS), non-dominated sorting genetic algorithm II (NSGAII), non-dominated sorting genetic algorithm III (NSGAIII), and the weighting and epsilon-constraint methods. Extensive experiments have been conducted using a set of instances generated from the Capacitated Vehicle Routing Problem benchmark tests in the literature. In addition, real data is utilised to estimate fixed and variable costs, CO2 emissions, capacity, and the driving range of each type of vehicle. The results show the effectiveness of the proposed method to find high-quality non-dominated solutions.

A Feasibility Pump and Local Search Based Heuristic for Bi-Objective Pure Integer Linear Programming

We present a new heuristic algorithm to approximately generate the nondominated frontier of bi-objective pure integer linear programs. The proposed algorithm employs a customized version of several existing algorithms in the literature of both single-objective and bi-objective optimization. Our proposed method has two desirable characteristics: (1) there is no parameter to be tuned by users other than the time limit; (2) it can naturally exploit parallelism. An extensive computational study shows the efficacy of the proposed method on some existing standard test instances in which the true frontier is known, and also some large randomly generated instances. We show that even a basic version of our algorithm can significantly outperform the Nondominated Sorting Genetic Algorithm II (Deb et al. 2002), and the sophisticated version of our algorithm is competitive with Multidirectional Local Search (Tricoire 2012). We also show the value of parallelization on the proposed approach.

A multi-objective approach for intermodal train load planning

In intermodal freight transportation, train load planners are confronted with complex practical considerations during the booking and planning process. In order to optimally utilize the available loading space, train capacity is monitored in terms of available length and weight while accounting for the urgency with which load units must be sent. Furthermore, the execution of the load plan by the terminal operator must be performed efficiently to minimize total handling costs. In this paper, a static model with multiple objectives is developed to introduce a number of practical constraints from the viewpoint of the network operator. Numerical experiments are performed using an exact $$\varepsilon $$ -constraint method as well as a multi-directional local search heuristic. It is shown that the multi-objective approach provides train load planners with a set of train load plans, for which the trade-offs between the different objectives can be analyzed. Given this information, the most suitable plan can be determined based on the real-time operational environment.

Multi-directional local search for a bi-objective dial-a-ride problem in patient transportation

This paper considers a generalization of a bi-objective dial-a-ride problem, incorporating real-life characteristics of patient transportation. It studies the impact of combination restrictions, preventing particular user combinations and limiting the set of drivers to which particular users can be assigned. The academic literature currently lacks insights into the effect of these restrictions on the cost structure of a service provider. A multi-directional local search algorithm is developed to solve this problem, taking into account the fundamental tradeoff between operational efficiency and service quality. Local search is integrated into a variable neighborhood descent framework that applies an intelligent candidate list principle to reduce computation time. Moreover, a new scheduling procedure is proposed, constructing time schedules that minimize total user ride time. It proves to be faster and more efficient than existing scheduling procedures. Overall, computational experiments on existing benchmark data extended with combination restrictions reveal a general pattern in the effect of the combination restrictions. Such insights are essential for service providers in order to support policy choices, e.g. related to service quality or medical education of drivers.

An improved multi-directional local search algorithm for the multi-objective consistent vehicle routing problem

ABSTRACTThis article presents a multi-objective variant of the Consistent Vehicle Routing Problem (MoConVRP). Instead of modeling consistency considerations such as driver consistency and time consistency as constraints as in the majority of the ConVRP literature, they are included as objectives. Furthermore, instead of formulating a single weighted objective that relies on specifying relative priorities among objectives, an approach to approximate the Pareto frontier is developed. Specifically, an improved version of multi-directional local search (MDLS) is developed. The updated algorithm, IMDLS, makes use of large neighborhood search to find solutions that are improved according to at least one objective to add to the set of nondominated solutions at each iteration. The performance of IMDLS is compared with MDLS and five other multi-objective algorithms on a set of ConVRP test instances from the literature. The computational study validates the competitive performance of IMDLS. Furthermore, results of the computational study suggest that pursuing the best compromise solution among all three objectives may increase travel costs by about 5% while improving driver and time consistency by approximately 60% and over 75% on average, when compared with a compromise solution having lowest overall travel distance. Supplementary materials are available for this article. Go to the publishe's online edition of IIE Transactions for datasets, additional tables, detailed proofs, etc.

A bi-objective home care scheduling problem: Analyzing the trade-off between costs and client inconvenience

Organizations providing home care services are inclined to optimize their activities in order to meet the constantly increasing demand for home care. In this context, home care providers are confronted with multiple, often conflicting, objectives such as minimizing their operating costs while maximizing the service level offered to their clients by taking into account their preferences. This paper is the first to shed some light on the trade-off relationship between these two objectives by modeling the home care routing and scheduling problem as a bi-objective problem. The proposed model accounts for qualifications, working regulations and overtime costs of the nurses, travel costs depending on the mode of transportation, hard time windows, and client preferences on visit times and nurses. A distinguishing characteristic of the problem is that the scheduling problem for a single route is a bi-objective problem in itself, thereby complicating the problem considerably. A metaheuristic algorithm, embedding a large neighborhood search heuristic in a multi-directional local search framework, is proposed to solve the problem. Computational experiments on a set of benchmark instances based on real-life data are presented. A comparison with exact solutions on small instances shows that the algorithm performs well. An analysis of the results reveals that service providers face a considerable trade-off between costs and client convenience. However, starting from a minimum cost solution, the average service level offered to the clients may already be improved drastically with limited additional costs.

The multi-objective generalized consistent vehicle routing problem

More and more companies in the routing industry are providing consistent service to gain competitive advantage. However, improved service consistency comes at the price of higher routing cost, i.e., routing cost and service consistency are conflicting objectives. In this paper, we extend the generalized consistent vehicle routing problem (GenConVRP) by considering several objective functions: improving driver consistency and arrival time consistency, and minimizing routing cost are independent objectives of the problem. We refer to the problem as the multi-objective generalized consistent vehicle routing problem (MOGenConVRP). A multi-objective optimization approach enables a thorough trade-off analysis between the conflicting objective functions. The results of this paper should help companies in finding adequate consistency goals to aim for. Results are generated for several test instances by two exact solution approaches and one heuristic. The exact approaches are based on the ϵ-constraint framework and are used to solve small test instances to optimality. Large instances with up to 199 customers and a planning horizon of 5 days are solved by multi directional large neighborhood search (MDLNS) that combines the multi directional local search framework and the LNS for the GenConVRP. The solution quality of the heuristic is evaluated by examining five multi-objective quality indicators. We find that MDLNS is an eligible solution approach for performing a meaningful trade-off analysis.Our analysis shows that a 70 percent better arrival time consistency is achieved by increasing travel cost by not more than 3.84 percent, on average; visiting each customer by the same driver each time is significantly more expensive than allowing at least two different drivers per customer; in many cases, arrival time consistency and driver consistency can be improved simultaneously.

Multi-directional local search

This paper introduces multi-directional local search, a metaheuristic for multi-objective optimization. We first motivate the method and present an algorithmic framework for it. We then apply it to several known multi-objective problems such as the multi-objective multi-dimensional knapsack problem, the bi-objective set packing problem and the bi-objective orienteering problem. Experimental results show that our method systematically provides solution sets of comparable quality with state-of-the-art methods applied to benchmark instances of these problems, within reasonable CPU effort. We conclude that the proposed algorithmic framework is a viable option when solving multi-objective optimization problems.