To evaluate the amount of speed up and the amount of solution quality degradation we imple- mented our algorithm and used a state of the art solver Indigo to route the macro nodes. We executed it over a well recognized benchmark set. This benchmark set consists of three classes of problems: a class of clustered problems whose requests form geographical clusters; a class of random problems, whose requests are randomly scattered; a class that combines both clustered and random locations. All classes have two versions of the problems, one with large capacity and another with small capacity vehicles. Using the problems from the benchmark set, we combined several instances to create new instances of 10x size, and confirmed that the results obtained with 1000 request instances carry over to 10000 request instances.
This study presents a genetic algorithm that uses an optimized crossover operator to solve the vehiclerouting problem withtimewindows. The proposed algorithm has been tested against the best known solutions reported in the literature, using 56 Solomon's problemswith 100 customers. The computational results showed that the proposed algorithm is competitive in terms of the quality of the solutions found (in terms of total travel distance). As for future work, it may be interesting to test OCGA with additional benchmarks of VRPTW.
More recently, a variant of the classical VRP, called the open vehiclerouting problem (OVRP), attracted the attention of practitioners and researchers. In this case, vehicles are not required to return to the depot after serving the last customer on a route . This usually arises in real-world problems, like the planning of train services or bus routes (see ), or when industries do not own a vehicle fleet or their private fleet is inadequate to fully satisfy customer demand, and distribution services (or part of them) are either entrusted to external contractors or assigned to a hired vehicle fleet. In these cases, vehicles are not required to return to the central depot after their deliveries have been satisfied. The main difference between VRP and OVRP is that in VRP, the routes are Hamiltonian cycles, and in the OVRP, the routes are Hamiltonian paths originated at the depot and ending at one of the customers, so the shortest Hamiltonian path problem with a fixed source node has to be solved for each vehicle in the OVRP. The traveling salesperson problem, known to be NP-hard, consists of finding the Hamiltonian cycle with the lowest cost. This, together with the fact that the Hamiltonian cycle problem (HCP) is NP-hard and can be reduced to the Hamiltonian path problem (HPP) , allows us to conclude that the shortest HPP is NP-hard. Consequently, the OVRP is also an NP-hard problem, justifying the development of heuristics and meta-heuristics (see , where a new swarm intelligence approach is proposed). The vehicleroutingwith backup provisioning, under discussion here, can be seen as a variant of the OVRP applied to the transportation of persons, considering multiple depots and having the possibility of backup provision to certain critical stops. Therefore, the vehicleroutingwith backup provisioning is NP-hard.
With the aim of accelerating the occurrence of high quality solutions in the population, we propose the incorporation of a DM module in the GA. This module aims to discover patterns (subroutes) which are commonly found in the best solutions of the population. This approach signiﬁcantly differs from current applications that combine GAs and DM because, until now, most of the efforts deal with the development of GAs as optimization methods to solve DM problems [14,10], such as the discovery of association, classiﬁcation and clustering rules, which is not our case. The process starts with the creation of an elite set of solutions (ES), which will keep the s best solutions generated in the search process. Initially, the ﬁrst s solutions generated are inserted in the ES. Afterwards, this set is updated whenever a solution which is better than the worst solution in ES and different from all others ES solutions is generated. The ES will be the database in which we will try to discover relevant patterns. In order to do this, we implemented an Apriori like algorithm [1,2], which discovers frequent contiguous sequences in the ES. Although there are very efﬁcient algorithms for mining sequential patterns, we chose to implement a simpler one, for two reasons: at ﬁrst, our ES size will be signiﬁcantly
A network is normally represented by a graph that is composed of a set of nodes and edges. The task of network clustering is to divide a network into different clusters based on certain principles. Each cluster is called a community. The LRP combines two classical planning tasks in logistics, that is, optimally locating depots and planning vehicle routes from these depots to geographically scattered customers . These two interdependent problems have been addressed separately for a long time, which often leads to suboptimal planning results. The idea of LRP started in the 1960s, when the interdependence of the two problems was pointed out [9,10]. The variants of the LRP have been frequently studied in recent years. Such variants include the capacitated LRP (CLRP) with constraints on depots and vehicles [20,21], the LRP with multi-echelon of networks [11,12], the LRP with inventory management [13,14], and the LRP with service timewindows [15–17]. For the variant problem withtimewindows, Semet and Taillard incorporated the time window constraint to the LRP for a special case of the road–train- routing problem . Zarandi et al. studied the CLRP with fuzzy travel time and customer timewindows, in which a fuzzy chance-constrained mathematical program was used to model the problem . Later, they extended the problem by adding the fuzzy demands of customers and developed a cluster-first route-second heuristic to solve the problem . A detailed review of the LRP variants can be found in two recent surveys [18,19].
The proposed model is validated by solving some test problems. The detail of the parameters’ distribution functions is listed in Table 1. To solve large-sized test problems, SA and GA are used. The performance of proposed meta-heuristic algorithms is compared with each other and LINGO software. Both of SA and GA algorithms are compiled in MATLAB 7.1 on the personal computer including, Intel Core 2 Duo 2.6 GHz processors and 2 GB RAM. In this section, the performance of the proposed SA and GA in terms of solution quality and computational time is evaluated in some randomly generated problems. Each algorithm runs for five times and the best result is reported. The parameter setting of meta-heuristic algorithms have considerable effect on their performance. In this paper, the parameter settings of the proposed meta-heuristics is tuned by the response surface methodology (RSM). The optimum parameter settings of SA and GA algorithms are tabulated in Tables 2 and 3, respectively. The solutions of GA and SA are compared with the optimal solutions obtained from LINGO software in small-sized test problems. Moreover, for large-sized problems that LINGO software cannot reach the optimum solution at the reasonable time. The comparison result between the proposed meta-heuristics in small-sized problems is reported in Table 4. In small-sized problems, a gap between SA and GA with LINGO software is reported through the percentage of relative gap measure that calculated based on [100 × (G LINGO − G Meta )/G Meta ],
A common feature of all previous approaches that have dealt with VRPCD is the assumption that vehicles must stop at the CD after the requests are collected from suppliers. That applies even if the vehicle collects and delivers the same requests. Of course, allowing vehicles to avoid the stop at the CD in such cases may reduce the transportation costs while, at the same time, frees space and resources at the station. For that reason, we propose in this thesis to extend previous works on VR- PCD and introduce a new problem, on which vehicles are allowed to deliver the re- quests immediately after collecting them, avoiding to stop at the CD for consolidation. The proposed approach considers two types of routes: pickup and delivery routes [Savelsbergh and Sol, 1995] (when the vehicle does not stop at the CD) and routes that stop at the CD to implement load changes. We name such a problem as the Pickup and Delivery Problem with Cross-Docking (PDPCD). Therefore, the proposed PDPCD is suitable to consider all the problems between a classical Pickup and De- livery Problem [Savelsbergh and Sol, 1995] and a classical VRPCD [Lee et al., 2006], whether all vehicles stop at the CD.
Basically we use a Data Mining strategy, in which every new individual has its route analyzed to extract patterns (sequence of customers) within a given range [minP atternSize, maxP atternSize]. Each pattern found is stored in a structure called patternsList along with the frequency it has appeared in the solutions already ana- lyzed. In addition to these information, we also keep record of the average cost of the route in which the pattern was found so as to improve the robustness of the eval- uation criteria that decides how good a pattern is. Therefore we have two types of data to evaluate a pattern: frequence and average cost. Good patterns have high frequency and low average cost. Since cost value is usually much higher than the frequency value, this data must be normalized. Lets call nF requency the normal- ized frequency value, nAvgCost the normalized average cost. Therefore we define qualityIndex = (1 − nAvgCost) + nF requency, as the value used to evaluate the pat- terns, since it considers both measures. The closer to 2 the better. This is not the first time an approach combining a heuristic and a data mining algorithm is proposed for a vehiclerouting problem. In , Santos et al proposed 4 approaches for a single vehiclerouting problem, including one that combines a Genetic Algorithm with the data mining algorithm Apriori. Our approach is not based on their approach and is fairly different from the algorithm they developed.
Several approaches were made to solve the VRPTW problems. The use of meta-heuristics is a common solution [Mou08, TM08, BG02, LYL11, GTA99, GGLM03]. Other solutions in- clude heuristics like the one for the distribution of fresh vegetables presented in [OS08] in which the perishability represents a critical factor. The problem was formulated as a VRPTW withtime-dependent travel-times, where the travel-times between two locations depend on both the distance and the time of the day. The problem was solved using a heuristic approach based on the Tabu Search and performance was veriﬁed using modiﬁed Solomon’s problems. A somewhat similar work was proposed in [TK02], which deals with distribution problem formulated as an open multi-depot vehiclerouting problem encountered by a fresh meat distributor. To solve the problem, a stochastic search meta-heuristic algorithm, termed as the list-based threshold accepting algorithm, was proposed. In [AS07] a generalization of the asymmetric capacitated vehiclerouting problem with split delivery was considered. The solution determines the dis- tribution plan of two types of products, namely: fresh/dry and frozen food. The problem was solved using a mixed-integer programming model, followed by a two-step heuristic procedure.
Many computation trials were made to check this model on the Solomon problems, although trials were possible only on those problem instances where the initial number of routes were more then the ever found best one. Explanation below supports the concept. Figure 1 shows how the “flexibility” of the graph is changing during the route elimination and increasing after cost reduction. On the vertical axis for instance the numbers of possible insertions are indicated. These numbers can be obtained the following way: select two adjacent nodes and try all possible insertions excluded the selected one and the depot. Summarize these numbers for each possible pairs on the routes. The charts show a strong increment after the cost reduction especially in the insertion numbers.
From a practical point of view, the problem being tackled applies to specific sectors that bene- fit from planning their routes according to the previously defined motivations. Companies that put their focus on customer service level, maintain a close relationship with the customer and operate on a tight delivery lead time have the most benefits to withdraw from using a delivery system with consistent routes. Cases of such companies are fairly common in small package distribution industries facing large competition and highly demanding customers, with pharmaceutical and au- tomobile spare parts distribution being the most well-known examples. Other activities in which consistent routingwith a service level focus is relevant include home care services, better estab- lished home deliveries, which may be a potential development area for e-commerce operations, and also the transportation of children, elderly or handicapped people. These companies seek for a customer focused environment that leads to more complex and strict service level agreements as a way to increase customer loyalty. However, with stricter service level targets, the number of fail- ures and complaints tends to increase, which often leads to frequent changes to the tactical plan in order to quickly solve these problems. Making solid consistent route plans that will perform well in practice while still being efficient is therefore a very hard task that many companies struggle with. Tools that assist decision-making in these conditions and take the business characteristics in consideration are therefore very useful and desired by practitioners.
The VRP is a very important source for problems, since solving it is equiv- alent to solving multiple TSP problems at once . Due to the difficulty of this problem (NP-hard) and because of its many industrial applications, it has been largely studied both theoretically and in practice . There is a large number of extensions to the canonical VRP. One basic extension is known as the capacitated VRP –CVRP–, in which vehicles have fixed capacities of a single commodity. Many different variants can be constructed from CVRP; some of the most important ones  are those including timewindows re- strictions –VRPTW– (customers must be supplied following a certain time schedule), pickups and deliveries –VRPPD– (customers will require goods to be either delivered or picked up), and backhauls –VRPB– (like VRPPD, but deliveries must be completed before any pickups are made).
Harmony Search (HS) algorithm has been recently developed in an analogy with music improvisation process where musicians in an ensemble continue to polish their pitches in order to obtain better harmony  . The HS algorithm has been successfully applied to various real-world combinatorial optimization problems such as truss structure design, pipe network design, pump switching, and hydrologic parameter calibration [10-13] . Especially, for the pump switching problem which has 2 40 ( 1.1× 10 12 ) different combinations, HS found the less energy consuming operation than GA or even than B&B methods which were implemented as an IBM subroutine or MS-Excel Solver. Consequently, the HS algorithm provides a
In the simulation, we compared the performance of our proposed EEAP algorithm and with LEACH protocol in under the continuous delivery model. We simulated the model for the equal initial energy (0.2J) in each node. The size area was considered with small (100x100) situation. Our performance criteria are total residual energy per round in the network and total network lifetime. Network lifetime is the number of round from the start of operation until the death of the last alive node. The network connectivity which depends on the time of the first node failure is a meaningful measurement in the sense that a single node failure can make the network partitioned and further services be interrupted. When a sensor node is depleted of energy, it will die and be disconnected from the network which may impact the performance of the application significantly.
In this context, we first propose a variation of the k-nearest neighbor query, named TD-kNN-OTC, in which the operating time of facilities is taken into account. The problem of finding the k nearest points of interest (POIs), for example, museums or restaurants, in time- dependent road networks has been studied in previous works. However, they have focused only on searching for the POIs that can be reached the quickest, without taking into consideration if it will take a long time for these POIs to open from the moment they are reached. Differently from those works, we aim at minimizing the time for one to be served, which takes into account both the travel time to the POI and the waiting time, if it is closed. Even though this is discussed in details in Chapter 3, let us consider the following example for the sake of motivation. Imagine that we are looking for the closest POI from us at 19:00 and the time it takes to reach the nearest POI is 20 minutes, but it opens at 20:00. However, it takes 25 minutes to reach the second nearest POI, but it opens at 19:30. A regular k-NN query returns the first POI as the answer, since it is the closest in terms of travel-time from our location, but when we get there we have to wait 40 minutes until this POI opens. Even though it takes 5 minutes more to reach the second POI, it is a better answer, since we just need to wait 5 minutes.
set of individuals with the set of variables. Additionally we searched for a reference global cluster- ing structure over the whole sample, able to keep the variability of the groups. Thus in this case the corresponding data base should include not only the two sets of individuals and variables but also the groups set. Moreover, groups might have different dimensions or alternatively be represented by interval data. Therefore such a global cluster analysis should be based on a generalized three- way or complex data representation (H. Bacelar-Nicolau, 2002; H. Bacelar-Nicolau, Nicolau, Sousa, & L. Bacelar-Nicolau, 2009; Souza & De Carvalho, 2004). The present work refers to global cluster analysis. In order to obtain data typologies, hierarchical cluster analysis methods were ap- plied to classify the set of variables/scales, using a suitable extended affinity coefficient (e.g., Matu- sita, 1951, 1955; H. Bacelar-Nicolau, 2002; Nicolau & Bacelar-Nicolau, 1982) as a proximity measure associated with four different aggregation criteria: two empirical ― single link and com- plete link ― and two probabilistic criteria ― Aggregation Validity Link (AVL) and Aggregation Validity B-Link (AVB) (B from Bacelar-Nicolau, 1985, meaning also Brake that is “reducing both chain and symmetry/equicardinality clustering effects”; e.g., Bacelar-Nicolau, 1988; Lerman, 1972, 1981). The single link and the two probabilistic criteria are incorporated into an adaptive family of aggregation criteria similar to Lance and Williams’ well known formula (e.g., H. Bacelar-Nicolau, 2002; Lerman, 1981; Nicolau & Bacelar-Nicolau, 1998). Part of the three-way or complex cluster- ing approach was published and programmed in Bock and Diday (2000) and associated software SODAS, as well as in H. Bacelar-Nicolau (2000, 2002), L. Bacelar-Nicolau (2002), H. Bacelar- Nicolau et al. (2009, 2010), and Sousa (2005). Applications have been reported in those papers as well as, for instance, in H. Bacelar-Nicolau (2002), Nicolau et al. (2007), Sousa, Nicolau, H. Bace- lar-Nicolau, and Silva (2010), Sousa, Tomás, Silva, and H. Bacelar-Nicolau (2013).
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).
In the present era of globalization and competitive market, cellular manufacturing has become a vital tool for meeting the challenges of improving productivity, which is the way to sustain growth. Getting best results of cellular manufacturing depends on the formation of the machine cells and part families. This paper examines advantages of ART method of cell formation over array based clustering algorithms, namely ROC-2 and DCA. The comparison and evaluation of the cell formation methods has been carried out in the study. The most appropriate approach is selected and used to form the cellular manufacturing system. The comparison and evaluation is done on the basis of performance measure as grouping efficiency and improvements over the existing cellular manufacturing system is presented.
The mesh network, as is a special case of Ad-hoc networks and MANET networks. These include a new vision of routing protocols based clusters, whose principle is very simple: divide the whole network into several parts, each party will elect a central node, responsible for coordination of routing information between other adjacent nodes, that node is named CH (Cluster Head), other nodes called its members. Communication in this type of network is simple, any member wishing to transmit, do it through its CH. The latter has a routing table, if the destination is internal (in the same group), then the delivery will be direct, if not the CH sends queries to neighbors to find the right path.