Abstract: A phenomenon-inspired meta-heuristic algorithm, harmonysearch, imitating music improvisation process, is introduced and applied tovehiclerouting problem, then compared with one of the popular evolutionary algorithms, genetic algorithm. The harmonysearch algorithm conceptualized a group of musicians together trying tosearch for better state ofharmony. This algorithm was applied to a test traffic network composed of one bus depot, one school and ten bus stops with demand by commuting students. This school bus routing example is a multi-objective problem to minimize both the number of operating buses and the total travel time of all buses while satisfying bus capacity and time window constraints. Harmonysearch could find good solution within the reasonable amount of time and computation.
extension is done by adding a parameter for setting a minimum value of the tabu list size tls called Threshold. The variation of this parameter improves the exploration of the search space by varying the compromise between intensification and diversification. It allows us to get a dynamic compromise between intensification and diversification. In summary, the more the same solutions found are repeated, the more the tabu list size increases, and vice versa; conversely, the more the solutions are different, the more the tabu list size decreases. This mechanism whereby the number of tabu solutions is increased when reaching local optima allows us to avoid the local optima trap by exploring other solutions in this case because all neighbors have become tabu. The optimization technique for the Reactive tabu with a variable threshold aimed at improving the initial solution (improvement) is developed (Fig. 3) in order to find the best compromise (optimal) solution of the problem. It can quickly check the feasibility of the movement suggested, and then react to the repetition to guide the search. This algorithm is performed via a tabu list size (tls) update mechanism elaborated in five steps, as shown in Fig. 3. The counters and parameters used in Reactive tabu with a variable threshold are defined as follows, and initialized to the following values.
The vehiclerouting problem with backhauls and soft time windows contains two disjoint sets of customers: those that receive goods from the depot, who are called linehauls, and those that send goods to the depot, named backhauls. To each customer is associated an interval of time (time window), during which each one should be served. If a time window can be violated it is called soft, but this violation implies an additional cost. In this paper, only the upper limit of the interval can be exceeded. For solving this problem we created deterministic iterated local search algorithm, which was tested using a large set of benchmark problems taken from the literature. These computational tests have proven that this algorithm competes with best known algorithms in terms of the quality of the solutions andcomputing time. So far as we know, there is no published paper for this problem dealing with soft time windows, and, therefore, this comparison is only with the algorithms that do not allow time windows violation.
At the initiation of each search block the customer move frequency data – used by the Tabu Search – are adjusted to 100 as a starting number. In RE procedure TS and the route elimination are sequentially running. If a successful insertion occurs at depth-first search also the customer move frequency of Tabu Search is modified in order to move those customers that are not successful at the insertion. This way the Tabu Search finds their move cheaper and prefers their move to reveal new regions for the depth-first search. As it is known the TS penalises frequently moving customers. This is the basic idea of this route elimination concept. This process must be controlled because after a while the graph would turn into an expensive state that would be disadvantageous for the search – according to the MB model. The Search management checks regularly the total cost and compares it to the initial cost. If the relative cost increment is higher then 1.1 – or the user defined value – then the customer move frequency data of TS are readjusted to 100. The 100 value of the adjusted move frequency must be in accordance with the block cycle to get reasonable cost and diversification ratio. See Figure (4).
13.1 The VehicleRouting Problem 177 The contribution of this work is then to define a powerful yet simple cMA capable of competing with the best known approaches for solving CVRP in terms of accuracy (final cost) and computational effort (the number of evalua- tions made). For that purpose, we test our algorithm over the mentioned large selection of instances (160), which will allow us to guarantee deep and mean- ingful conclusions. Besides, we compare our results against the best existing ones in the literature, some of which we even improve. In  the reader can find a seminal work with a comparison between our algorithm and some other known heuristics for a reduced set of 8 instances. In that work, we showed the advantages of embedding local search techniques into a cGA for solving CVRP, since our hybrid cGA was the best algorithm out of all those compared in terms of accuracy and time. Cellular GAs represent a paradigm much simpler to comprehend and customize than others such as tabu search (TS) [97, 249] and similar (very specialized or very abstract) algorithms [37, 207]. This is an important point too, since the greatest emphasis on simplicity and flexibility is nowadays a must in research to achieve widely useful contributions .
Palavras-chave: Roteamento de veículos; Múltiplos entregadores; Busca Local Iterada; Busca em Vizinhança Grande. Abstract: This paper addresses the vehiclerouting problem with time windows and multiple deliverymen, a variant of the vehiclerouting problem which includes the decision of the crew size of each delivery vehicle, besides the usual scheduling and routing decisions. This problem arises in the distribution of goods in congested urban areas where, due to the relatively long service times, it may be dificult to serve all customers within regular working hours. Given this dificulty, an alternative consists in resorting to additional deliverymen to reduce the service times, which typically leads to extra costs in addition to travel and vehicle usage costs. The objective is to deine routes for serving clusters of customers, while minimizing the number of routes, the total number of assigned deliverymen, and the distance traveled. Two metaheuristic approaches based on Iterated Local Search and Large Neighborhood Search are proposed to solve this problem. The performance of the approaches is evaluated using sets of instances from the literature.
The algorithms developed to detect distributed predicates can be online or offline. Online detection works during the execution of the application, and hence it may change the behavior of the application in unexpected manner. However, it has the advantage of avoiding the need to keep very large trace files as it is the case in offline detection. Offline detection collects the necessary information at runtime and later analyzes it to decide whether a given predicate has been satisfied during the execution or not. Offline detection does not have a strong impact on the behavior of the application under consideration. However, it requires the collection of very large trace files.
oisy optimization problems arise in many real life application domains. One of the most common problems is the attempt to optimize a performance index for a complex procedure that is captured through a simulation model, giving rise to what is known as simulation- optimization -. In the field of logistic systems and operations research, Discrete Event Systems (DES) are among the most prominent members for simulating complex logistic systems. Their main drawback is that in most cases their execution is quite slow combined with the need to run multiple replications for a specific design due to “simulation noise”.
The VehicleRouting Problem is a well studied combinatorial optimization problem with many real practical applications. The variant of VRP that we considered is the VRPs with hard time windows. Literature is full with different methods for solving this type of VRPs. Exact methods for solving VRPs with optimalitty are based on Mixed Integer Programming (MIP) and are only capable of solving instances with no more than 100 requests. Approximation methods do not provide any guaranties on the solution quality, but are more efficient computationally. Empirical results show that approximation methods are capable of achieving solutions with quality within 1% of optimalitty. However, even approximation methods are computationally expensive due to the large search neighborhoods.
847 by the real life behavior of ants foraging for food. During the search for food from their nest to the food source, it was found that a moving ant will lay a chemical substance called pheromone on the trail. The pheromone trail is a form of communication among the ants which will attract the other ants to use the same path to travel. Thus, higher amount of pheromone will enhance the probability of the next ant selecting that path to travel. With times, as more ants are able to complete the shorter path, the pheromone will accumulate faster on shorter path compared to the longer path. Consequently, majority of the ants would have travelled on the shortest path. Detailed descriptions of the ACO can be found in the book by Dorigo and Stutzle (2004). Recent applications of ACO can be found in Naganathan and Rajagopalan (2011) and Yap et al. (2012).
The second strand of the relevant literature consists of the routing problems that consider the limited driving range of vehicles and the possibility of refueling en route. Conrad and Figliozzi introduced the recharging VRP, in which vehicles with a limited range are allowed to recharge at certain customer stations within a fixed time . Erdogan and Miller-Hookers presented the green VRP (G-VRP) for routing AFVs and solved the problem with two algorithms. In G-VRP, refueling stations are assumed to be independent of customer sites, and an AFV may refuel at these stations within a fixed time . Later, Schneider et al. incorporated the time window constraint into the G-VRP and proposed the EV-routing problem with time windows and recharging station (E-VRPTW) . The charging time in E-VRPTW is not fixed but instead is related to the battery charge of an EV upon arrival at the station. To address the problem, they developed a hybrid heuristic that combines the VNS with the TS algorithm (VNS/TS). Schneider et al. then introduced the VRP with intermediate stops (VRPIS), which generalized the G-VRP, and solved the problem by AVNS . Five route selection methods and three vertex sequence selection methods were utilized in the adaptive shaking phase of AVNS. Felipe et al. proposed several heuristics to address the G-VRP with multiple technologies and partial recharges. The problem extends the G-VRP by incorporating different technologies for battery recharge and the possibility of partial recharges . Goeke and Schneider combined the E- VRPTW with a mixed fleet of EVs and ICVs, and utilized realistic energy consumption functions in their problem . The resulting problem was solved by an ALNS with a local search for intensification. Yang and Sun adopted the simultaneous optimization idea from the LRP to the context of EV and proposed the BSS location-routing problem of EVs . The problem is intended to minimize infrastructure and shipping costs by determining the station location and vehicle-routing plan jointly under a driving range limitation. For the solution method, they employed the concept of solving separate sub-problems iteratively from the LRP and proposed two hybrid heuristics . In detail, one algorithm called TS-modified Clarke–Wright saving (MCWS) combines the TS algorithm for location strategy and the MCWS method for the routing decision. The other approach named SIGALNS includes four main phases: initialization, location sub-problem, routing sub-problem, and improvement. Iterative greedy (IG) is utilized in the location phase, and an ALNS in the routing phase.
are abundant in the literature, the applicationof DM to improve the results of evolutionary algorithms is still scarce. The DM module proposed corresponds to an intensiﬁcation strategy, since it tries to discover good features in the best solutions found so far and to apply them in the generation of new solutions. The addition of the DM module into the GA signiﬁcantly improved this method and the hybrid version with local search (GADMLS), on average, produced the better results. Results could be improved if other interactions between modules and/or a more exhaustive set of experiments were conducted (perhaps, larger running times would beneﬁt the more computationally expensive version—GADMLS). Nonetheless, our proposal looks very promising, specially considering problems in which it is difﬁcult to devise efﬁcient local search algorithms.
Location-Routing problems involve locating a number of facilities among can- didate sites and establishing delivery routes to a set of users in such a way that the total system cost is minimized. A special case of these problems is Hamilto- nian p-Median problem (HpMP). This research applies the metaheuristic method of ant colony optimization (ACO) to solve the HpMP. Modifications are made to the ACO algorithm used to solve the traditional vehiclerouting problem (VRP) in order to allow the searchof the optimal solution of the HpMP. Regarding this metaheuristic algorithm a computational experiment is reported as well.
In this article, a vehiclerouting with backup provisioning approach is proposed for sustainable urban mobility with efficient use of resources. Besides formalizing mathematically the problem, a heuristic is proposed that allows solutions to be obtained more quickly. The vehiclerouting with backup provisioning approach is able to provide higher quality of service, regarding time for the backup vehicleto arrive, and it avoids new schedules/vehicles/drivers for backup provisioning. Although routes become longer, to ensure backup, thresholds on time for backup to arrive can be adequately set to keep such distances acceptable. However, since more stops are being served, the increase of routes should not be seen just as a penalty. Regarding the neighborhood formation approach and local search procedures, incorporated in the heuristic, these have proven to be effective. Route distances reduced by approximately 30%. In summary, the overall perception is that the proposed heuristic is able to effectively solve the vehiclerouting with backup provisioning problem under consideration. As future work, we expect to study fleet planning considering vehicles of different sizes. Acknowledgments: This work was supported by FCT (Foundation for Science and Technology) from Portugal within CEOT (Center for Electronic, Optoelectronic and Telecommunications) and the UID/MULTI/00631/2013 project.
Abstract — We consider a case study on the applicationof techniques for solving assignment problem (AP) and vehicle problem with time window (VRPTW) occurred in cash distribution of bank in Bangkok, Thailand. An intensive review of the literature about AP and VRP is also discussed. The main aims of this research are to cluster all branches into groups belongs to each depot and to produce the routes for each depot. The objective of this research is to improve a cash distribution while using the existing resources. In order to find good solutions, an optimization of assignment problem is used incorporated with heuristics methods for VRP. Sweep Algorithm, Group Sweep Algorithm, and Nearest Neighbor Algorithm are used in this research. Results received by those methods are better than the current operation.
Despite the advantages of adopting consistent routes, few papers have addressed the conVRP and most approaches resort to approximation methods. Groer et al. (2009) formulate the conVRP as a Mixed-Integer Program (MIP) and improve the algorithm used by Li et al. (2005) to solve very large VRPs. A real-world data set is used to generate instances with up to 700 customers which are solved by the algorithm. The obtained consistent routes are less than 10% longer on average, compared to inconsistent routes. Recently, Ridder (2014) shows that some optimal solu- tions provided by Groer et al. (2009) are not feasible because service times were not considered. The author develops an algorithm that improves solutions provided by the latter paper. Tarantilis et al. (2012) propose a Tabu Search (TS) algorithm to iteratively generate template routes and to improve the daily routes that are derived from the template routes. These routes are used as the basis to construct the vehicle routes and service schedules for both frequent and non-frequent customers over multiple days. The best reported cumulative and mean results over all conVRP- benchmark instances is improved. Kovacs et al. (2014b) construct template routes by means of an Adaptive Large Neighbourhood Search (ALNS), which uses several operators in order to destroy and repair a given solution. It is shown that solving daily VRPs may lead to inconsistent routes whereas consistent long-term solutions can be generated by using historic template routes. Kovacs et al. (2014a) state that assigning one driver to each customer and bound the variation in the arrival times over a given planning horizon may be too restrictive in some applications. They propose the generalized conVRP in which a customer is visited by a limited number of drivers and the vari- ation in the arrival times is penalized in the objective function. A Large Neighbourhood Search (LNS) metaheuristic generates solutions without using template routes. The computational results on different variants of the conVRP prove the efficiency of the algorithm, as it outperforms all published algorithms. Sungur et al. (2010) consider a real-world courier delivery problem where customers appear probabilistically. Although the authors do not call it a conVRP, their assump- tions are completely in line with this type of problem. The proposed approach generates master plans and daily schedules with the objective of maximizing both the coverage of customers and the similarity between the routes performed in each day. In order to deal with uncertain service times, it is assumed that the master plans serves frequent customers with the worst-case service times found in historical data. Once again, a mathematical formulation is proposed but the real-world problem is tackled by means of a two-phase heuristic based on insertion and TS.
OR vehicle positioning, global positioning system (GPS) is the most widespread used technology ,. However, GPS may suffer from signal interruption or multipath  in GPS-denied environments which may decreases the positioning accuracy and reliability. To overcome the signal blockage of GPS, one common solution is that GPS is integrated with an inertial navigation system (INS)  or dead reckoning (DR) . Owing to the measurement biases and integration processes, the INS and DR will accumulate large errors over time. These large errors may cause the rapid performance degradation during GPS outages. Other in-vehicle sensors such as vehicle motion sensors  can be used to compensate for the errors. However, the compensation effect is limited when GPS is in a long-time failure. The main reason is that the lack of the position
The goal of the MDVRPB is to determine the routes to be performed from the selected depots to the customers by a fleet of homogeneous vehicles in order to satisfy the demand of the customers (products to be collected or products to be delivered). The objective functions considered for the multiobjective version of the MDVRPB is to minimize the total traveled distance, the total time and the consumed energy. The first objective is the common function considered in the literature related to the vehiclerouting problems. The second objective is obtained by the allowed speed on each edge. In particular, we have considered a random speed between 30 km /hr to 90 km/hr for the complete graph on the benchmarking set of instances. Finally, the third objective is adopted from the idea of gas emission and consumption of energy introduced by Bektaş and Laporte (2011) and Demir et al. (2014).
RVPSE adapted the mathematical model proposed by Fisher & Jaikumar (1981) developed for a typical vehiclerouting problem. The main changes were regarding (i) specific replacement and maintenance nodes for each good in each period, and (ii) limited replacements avoiding successive exchanges for distinct goods in each period. The sequence of arcs at the lowest cost was chosen by exhaustive enumeration using the branch-and-bound algorithm of integer linear programming, which is also available in the Microsoft Excel Solver optimization software.