Savings Algorithm Research Articles

A new VRPPD model and a hybrid heuristic solution approach for e-tailing

We analyze a business model for e-supermarkets to enable multi-product sourcing capacity through co-opetition (collaborative competition). The logistics aspect of our approach is to design and execute a network system where “premium” goods are acquired from vendors at multiple locations in the supply network and delivered to customers. Our specific goals are to: (i) investigate the role of premium product offerings in creating critical mass and profit; (ii) develop a model for the multiple-pickup single-delivery vehicle routing problem in the presence of multiple vendors; and (iii) propose a hybrid solution approach. To solve the problem introduced in this paper, we develop a hybrid metaheuristic approach that uses a Genetic Algorithm for vendor selection and allocation, and a modified savings algorithm for the capacitated VRP with multiple pickup, single delivery and time windows (CVRPMPDTW). The proposed Genetic Algorithm guides the search for optimal vendor pickup location decisions, and for each generated solution in the genetic population, a corresponding CVRPMPDTW is solved using the savings algorithm. We validate our solution approach against published VRPTW solutions and also test our algorithm with Solomon instances modified for CVRPMPDTW.

Enhanced savings calculation and its applications for solving capacitated vehicle routing problem

The vehicle routing problem (VRP) is one of the most explored combinatorial problems in operations research. A very fast and simple algorithm that solves the VRP is the well known Clarke–Wright savings algorithm. In this paper we introduce a new way of merging routes and the corresponding formula for calculating savings. We also apply the enhanced merging to develop a new heuristic – Extended Savings Algorithm (ESA) that dynamically recalculates savings during iterations. Computational results show that, on average ESA gives better solutions than the original savings algorithm. Implementing randomization of some steps of our heuristic we obtained even better results which competes with more complex and well known heuristics. The ESA is further used to generate good routes as part of a set-covering-based algorithm for the Capacitated VRP (CVRP). The numerical results of our experiments are reported.

A Smooth Tour Construction Approach for a Mobile Robot with Kinematic Constraints

Mobile robots are increasingly used for service-like applications in which the service points are known and the mobile robot starts from a starting location, visits all the service points requested and returns to the starting location. The tour construction problem in these applications can be treated as a Travelling Salesman Problem (TSP). Classical tour construction algorithms that are proposed for the TSP find tours do not consider robot kinematic constraints. These tours may have sharp turns at some service points. When a mobile robot follows such a tour, it stops, turns and speeds up again. Therefore, the robots waste a considerable amount of power and time. In these cases, tour smoothing can be used to overcome this problem. However, smoothing an existing tour may result in unnecessarily long tours. In this study, a Smooth Tour Construction (STC) approach is proposed for mobile robots with kinematic constraints. The STC approach considers tour construction and tour smoothing concurrently. The logic behind the tour construction part of the approach is based on the Savings Algorithm (SA). The tour smoothing is based on Dubins' arc-line approach. Experiments are conducted for P3-DX robots in a laboratory environment. Comparisons are also drawn with various tour smoothing algorithms in simulation environments to demonstrate the effectiveness of the proposed STC approach.

MILP Formulations for the Order Batching Problem in Low-Level Picker-to-Part Warehouse Systems

In this work we introduce Mixed Integer Linear Programming (MILP) formulations for the Order Batching Problem considering traversal and return routing policies. The proposed MILP formulations have been tested on randomly generated instances and compared with the well-known savings algorithm. According to our extensive computational experiments we can say that the proposed MILP formulations are quite useful to yield good upper bounds and hence, they can be used for benchmarking purposes.

A heuristic for the inventory management of smart vending machine systems

Purpose: The purpose of this paper is to propose a heuristic for the inventory management of smart vending machine systems with product substitution under the replenishment point, order-up-to level policy and to evaluate its performance. Design/methodology/approach: The heuristic is developed on the basis of the decoupled approach. An integer linear mathematical model is built to determine the number of product storage compartments and replenishment threshold for each smart vending machine in the system and the Clarke and Wright’s savings algorithm is applied to route vehicles for inventory replenishments of smart vending machines that share the same delivery days. Computational experiments are conducted on several small-size test problems to compare the proposed heuristic with the integrated optimization mathematical model with respect to system profit. Furthermore, a sensitivity analysis is carried out on a medium-size test problem to evaluate the effect of the customer service level on system profit using a computer simulation. Findings: The results show that the proposed heuristic yielded pretty good solutions with 5.7% error rate on average compared to the optimal solutions. The proposed heuristic took about 3 CPU minutes on average in the test problems being consisted of 10 five-product smart vending machines. It was confirmed that the system profit is significantly affected by the customer service level.

The effects of triangle inequality on the vehicle routing problem

Routing problems often utilize experimental networks to represent real world scenarios. However most ignore the inclusion of triangle inequality violations, a phenomenon resulting from delays or rounding errors within a network. This work evaluates the effect of both frequency – the number of violations – and severity – the degree of intensity of a violation – of triangle inequality and evaluates both solution quality and solution time based on Simulated Annealing, Ant Colony Optimization and Savings Algorithm methods. Findings indicate that while both frequency and severity degrade solution quality, increased levels of frequency and severity together result in significant adverse affects to solution quality. Solution time, however, is not impacted by the presence of triangle inequality violations within the network. This information should encourage practitioners to identify delays and maintain the presence of triangle inequality violations in a network to ensure accuracy of solution quality.

Some experiments with a savings heuristic and a tabu search approach for the vehicle routing problem with multiple deliverymen

In this work we consider a variant of the vehicle routing problem that allows the assignment of multiple deliverymen to one or more routes. A practical motivation for this variant arises, for example, in the distribution of beverages in highly dense urban areas, characterized by the difficulty in serving daily requests within regular working day hours with a single deliveryman per vehicle. We present a mathematical model and a savings algorithm in order to generate low cost routes that maximize the number of requests served in compliance with the maximum route time. The impact of the extra deliverymen on the solutions provided by the proposed heuristic is assessed by means of sets of generated examples based on classical instances of literature. It is also presented the results obtained by an adaptation of a tabu search approach from the literature.

A hybrid GRASP-tabu search metaheuristic for a Four-Layer Location-Routing Problem

The location-routing problem simultaneously considers location, allocation, and vehicle routing decisions to design optimal distribution networks. In this paper, a hybrid GRASP-tabu search metaheuristic developed for a complex four-layer LRP is presented. The LRP integrates location, allocation, vehicle routing, and transshipment problems. The metaheuristic decomposes the problem into two sub-problems, a location-allocationtransshipment problem and a routing problem. Two metaheuristics of GRASP and tabu search are combined to solve the first sub-problem in which the routing cost is considered implicitly. The Clarke-Wright Savings algorithm and a node ejection chains algorithm are used to solve the second sub-problem.

The Study on Communication Energy Saving Algorithm of Wireless Sensor Network

Wireless transceiver’s energy consumption takes a high proportion of sensors’ whole energy consumption. Saving wireless transceiver’s energy consumption is significant because of limited energy of wireless sensor network nodes. This paper is based on the model of wireless transceiver’s energy consumption which works in a long distance. Predicted on proving real-time character, this paper poses a long distance low energy consumption scheduling algorithm which adopts dynamic modulation scaling technology combined heuristic algorithm. First, dispatching the modulation level off-line, allocating task and solidifying dispatch result into dispatcher manager. Then, according to the practical transmission time during transmission, adjust the modulation levels again. The simulation experiment proves the algorithm’s effective.

The Study on Communication Energy Saving Algorithm of Wireless Sensor Network

Wireless transceiver’s energy consumption takes a high proportion of sensors’ whole energy consumption. Saving wireless transceiver’s energy consumption is significant because of limited energy of wireless sensor network nodes. This paper is based on the model of wireless transceiver’s energy consumption which works in a long distance. Predicted on proving real-time character, this paper poses a long distance low energy consumption scheduling algorithm which adopts dynamic modulation scaling technology combined heuristic algorithm. First, dispatching the modulation level off-line, allocating task and solidifying dispatch result into dispatcher manager. Then, according to the practical transmission time during transmission, adjust the modulation levels again. The simulation experiment proves the algorithm’s effective.

An improved Clarke and Wright savings algorithm for the capacitated vehicle routing problem

In this paper, we have proposed an algorithm that has been improved from the classical Clarke and Wright savings algorithm (CW) to solve the capacitated vehicle routing problem. The main concept of our proposed algorithm is to hybridize the CW with tournament and roulette wheel selections to determine a new and efficient algorithm. The objective is to find the feasible solutions (or routes) to minimize travelling distances and number of routes. We have tested the proposed algorithm with 84 problem instances and the numerical results indicate that our algorithm outperforms CW and the optimal solution is obtained in 81% of all tested instances (68 out of 84). The average deviation between our solution and the optimal one is always very low (0.14%).

A Stochastic Savings Algorithm for Vehicle Routing Problem with a Centralized Distribution Center and Delivery Time Window

The vehicle routing problem (VRP) under study involves managing a fleet of trucks existing to provide transportation services from a centralized distribution center (DC) to a set of geographically dispersed customers. The problem is motivated by a real problem from one of the large chains of high-end retail stores in Thailand. The objective of this study is to develop a simple and effective algorithm that can help the user manage the fleet in order to reduce the total transportation cost. The developed algorithm is based on the parallel savings algorithm but with a stochastic component that has a capability of escaping the local optima. The stochastic component applied a biased random sampling (BRS) and regret based random sampling (RBRS) to the selection of customers to add to delivery routes. Specifically, the selection probabilities are computed proportionally from the savings value of merging customers. The algorithm generates solutions containing delivery routes and schedules for all trucks in the fleet that satisfy daily store demands under limited truck capacity and delivery time window restrictions. Three measures of performance include the total distance, total travel time, and total cost. Computational test of the algorithm was performed on a set of standard problems, and promising results are obtained.

Joint port-cost and power-consumption savings in hybrid hierarchical optical networks

In optical networks, with the number of wavelengths in fibers increasing, the size and cost of Optical Cross-Connects (OXC) have been increased. Waveband merging technology, which groups several wavelength routes into a single waveband tunnel with at least two hops, could perform port-cost savings by reducing the size and cost of OXC since switching one waveband in the All Optical (OOO) domain only consumes two ports at each bypass node. On the other hand, the absence of wavelength conversion restricts the capability of OOO–OXC. Therefore, designing a hybrid hierarchical node to transmit wavebands in an OOO switch and add/drop local requests or perform wavelength conversion in an Optical-Electrical-Optical (OEO) switch has been one of the promising solutions for next-generation optical networks. However, due to the increasing effects of greenhouse gases and the drastic consumption of power, port-cost and power-consumption savings are becoming the new and twin objectives to further develop hybrid hierarchical optical networks. In this paper, we jointly consider port-cost and power-consumption in a hybrid hierarchical optical network and propose efficient approaches including Integer Linear Programming (ILP) models and heuristics. Simulation results of two heuristic approaches, a Cost and Power savings algorithm based on an End-to-End waveband Merging strategy (CPEEM) as well as a Cost and Power savings algorithm based on a Sub-Path waveband Merging strategy (CPSPM), show that the cost of Transmitting Ports (TPs) used in an OOO switch is in contrast to the use of the power consumed by the OEO part of a hybrid hierarchical node. Moreover, comparing with CPEEM, CPSPM has a better performance for port-cost savings but the performance improvement is at the cost of higher power consumption in an OEO switch. On the contrary, CPEEM has a better performance for power-consumption savings but the performance improvement is achieved at the expense of a higher cost of transmitting ports comparing with CPSPM. Based on the parameter, Boundary of Consumed Power (BCP), a New Integrated Algorithm (NIA) that could effectively choose between CPEEM or CPSPM according to the current network state is proposed to obtain the trade-off performances.

A robust enhancement to the Clarke–Wright savings algorithm

We address the Clarke and Wright (CW) savings algorithm proposed for the Capacitated Vehicle Routing Problem. We first consider a recent enhancement that uses the put first larger items idea originally proposed for the bin packing problem and show that the conflicting idea of putting smaller items first has a comparable performance. Next, we propose a robust enhancement to the CW savings formulation. The proposed formulation is normalized to efficiently solve different problems, independent from the measurement units and parameter intervals. To test the performance of the proposed savings function, we conduct an extensive computational study on a large set of well-known instances from the literature. Our results show that the proposed savings function provides shorter distances in the majority of the instances and the average performance is significantly better than previously presented enhancements.

Finding top-k elements in a time-sliding window

Identifying the top-k most frequent elements is one of the many problems associated with data streams analysis. It is a well-known and difficult problem, especially if the analysis is to be performed and maintained up to date in near real time. Analyzing data streams in time sliding window model is of particular interest as only the most recent, more relevant events are considered. Approximate answers are usually adequate when dealing with this problem. This paper presents a new and innovative algorithm, the Filtered Space-Saving with Sliding Window Algorithm (FSW) that addresses this problem by introducing in the Filtered Space Saving (FSS) algorithm an approximated time sliding window counter. The algorithm provides the top-k list of elements, their frequency and an error estimate for each frequency value within the sliding window. It provides strong guarantees on the results, depending on the elements real frequencies. Experimental results detail performance on real life cases.

SWARM INTELLIGENCE: APPLICATION OF THE ANT COLONY OPTIMIZATION ALGORITHM TO LOGISTICS‐ORIENTED VEHICLE ROUTING PROBLEMS

This research evaluates a set of logistics‐oriented vehicle routing problems (VRP) taken from the logistics and supply chain literature under the widely used Clark‐Wright Savings algorithm and the newer metaheuristic method employing a type of swarm intelligence called Ant Colony Optimization (ACO). ACO simulates the decision‐making processes of colonies of ants as they forage for food and is related to other artificial intelligence techniques such as Tabu Search, Simulated Annealing and Genetic Algorithms. Experimentation shows that ACO is successful in finding solutions near the best‐known solutions for problems with up to 20 demand locations. In addition, testing for the affect of spatial patterns suggested by the logistics literature for facility locations appears to make a difference in the quality of the solutions for the two algorithms. Finally, ACO is shown to be superior to the savings algorithm found in software packages and as a result should be tested on even larger, more complex logistics‐oriented vehicle routing problems, representative of those encountered in larger industrial and retail settings.

Efficacy of an aspheric treatment algorithm in decreasing induced spherical aberration after laser in situ keratomileusis

To determine the effectiveness of an aspheric laser in situ keratomileusis (LASIK) algorithm for myopia with and without astigmatism in minimizing postoperative induction of spherical aberration. Four sites in Asia. Patients with -1.00 to -10.00 diopters (D) of spherical myopia with -4.00 D or less of astigmatism were recruited. Patients randomly had bilateral Zyoptix aspheric algorithm (aspheric group) or bilateral conventional Zyoptix Tissue Saving algorithm (control group). A Technolas 217z100 excimer system was used for LASIK ablation. Visual effectiveness, safety, higher-order aberrations, and corneal asphericity (Q value) were evaluated postoperatively. The aspheric group comprised 86 eyes and the control group, 84 eyes. At 3 months, the high-contrast uncorrected distance visual acuity was 20/20 or better in 78% of eyes in the aspheric group and 83% of eyes in the control group. The control treatment induced 0.22 microm of spherical aberration, which was significantly higher than the 0.04 microm induced with the aspheric treatment (6.0 mm pupil) (P<.0001). The aspheric treatment induced significantly less vertical coma and trefoil (P = .02). Eyes in the aspheric group had significantly lower Q values (P<.0001). There was no statistically significant difference in the manifest refraction spherical equivalent between the 2 groups (P >.05). Although high- and low-contrast corrected distance visual acuity (CDVA) was similar between the groups, the aspheric group gained more lines of low-contrast CDVA. The aspheric algorithm was more effective than the conventional algorithm in reducing induced spherical aberration and maintaining corneal asphericity after myopic LASIK.

Fast and effective algorithms for the liquid crystal display module (LCM) scheduling problem with sequence-dependent setup time

The liquid crystal display module scheduling problem (LCMSP) is a variation of the classical parallel machines scheduling problem, which has many real-world applications, particular, in the thin film transistor liquid crystal display (TFT-LCD) manufacturing industry. In this paper, we present a case study on the LCMSP, which is taken from a final liquid crystal display module (LCM) shop floor in a TFT-LCD industry. For the case we investigated, the jobs are clustered by their product types and the machine setup time is sequentially dependent on the product types of the jobs processed on the machine. In LCMSP, the objective is to maximize the total profit subject to fulfilling contracted quantities without violating the due date and machine capacity restrictions. The LCMSP can be modelled as a multi-level optimization problem. The sub-problem of LCMSP can be transformed into the vehicle routing problem with time window (VRPTW). One can therefore solve the LCMSP efficiently using existing VRPTW algorithms. We present two new algorithms based on the savings algorithms with some modifications to accommodate the LCMSP. Based on the characteristics of the LCM process, a set of test problems is generated covering most of the real-world applications for test purposes. Computational results and performance comparisons show that the proposed algorithms solved the LCMSP efficiently and near-optimally.

Heuristic-Based Dynamic Route Planning Method for a Homogeneous Multi-robot Team

Multi-robot systems have recently received a great deal of attention due to the ability to perform an assigned task in a more reliable, faster and cheaper way beyond what is possible with a single robot. However, they may have some drawbacks, such as obstruction among robots during a task. Non-intersecting tours are preferable for the robots to prevent obstruction. Moreover, after an initial plan, the environment (open roads may be closed) and/or task requests (active/deactive) may change dynamically, which may require a fast tour construction for the members of the mobile robot group. In this study, a novel heuristic method is proposed to construct non-intersecting tours for the members of a mobile robot group in dynamic and/or partially unknown environments considering the energy capacities of the robots. It is an aggregate algorithm consisting of the Savings algorithm and the Sweep algorithm, and is applicable to the problems that are modeled using complete, sparse, directed or undirected networks. Simulations are offered to show the effectiveness of the proposed algorithm.

Energy Saving Algorithms for Wireless Sensor Communications: The Aeronautical Case Study

Energy Saving Algorithms for Wireless Sensor Communications: The Aeronautical Case Study