Abstract: A phenomenon-inspired meta-heuristic algorithm, **harmony** **search**, imitating music improvisation process, is introduced and applied **to** **vehicle** **routing** problem, then compared with one **of** the popular evolutionary algorithms, genetic algorithm. The **harmony** **search** algorithm conceptualized a group **of** musicians together trying **to** **search** for better state **of** **harmony**. 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. **Harmony** **search** could find good solution within the reasonable amount **of** time and computation.

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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.

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The **vehicle** **routing** 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.

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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).

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13.1 The **Vehicle** **Routing** 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 [11] 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 [52].

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Palavras-chave: Roteamento de veículos; Múltiplos entregadores; Busca Local Iterada; Busca em Vizinhança Grande. Abstract: This paper addresses the **vehicle** **routing** problem with time windows and multiple deliverymen, a variant **of** the **vehicle** **routing** 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.

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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.

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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 [1]-[4]. 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”.

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The **Vehicle** **Routing** 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.

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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).

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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 [23]. 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 [24]. 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) [7]. 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 [29]. 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 [25]. Goeke and Schneider combined the E- VRPTW with a mixed fleet **of** EVs and ICVs, and utilized realistic energy consumption functions in their problem [26]. 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 [6]. 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 [22]. 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.

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are abundant in the literature, the **application** **of** 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.

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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 **vehicle** **routing** problem (VRP) in order **to** allow the **search** **of** the optimal solution **of** the HpMP. Regarding this metaheuristic algorithm a computational experiment is reported as well.

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In this article, a **vehicle** **routing** 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 **vehicle** **routing** with backup provisioning approach is able **to** provide higher quality **of** service, regarding time for the backup **vehicle** **to** 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 **vehicle** **routing** 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.

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Abstract — We consider a case study on the **application** **of** 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.

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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.

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OR **vehicle** positioning, global positioning system (GPS) is the most widespread used technology [1],[2]. However, GPS may suffer from signal interruption or multipath [3] 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) [4] or dead reckoning (DR) [5]. 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 [6] 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

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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 **vehicle** **routing** 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).

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RVPSE adapted the mathematical model proposed by Fisher & Jaikumar (1981) developed for a typical **vehicle** **routing** 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.

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A dynamic programming approach is also investigated, using state space relaxation and a penalty method to improve the bound.. comparative study of the computational [r]

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