Single Depot Research Articles

Ultra-Long-Term Delivery of Hydrophilic Drugs Using Injectable In Situ Cross-Linked Depots.

Achieving ultra-long-term release of hydrophilic drugs over several months remains a significant challenge for existing long-acting injectables (LAIs). Existing platforms, such as in situ forming implants (ISFI), exhibit high burst release due to solvent efflux and microsphere-based approaches lead to rapid drug diffusion due to significant water exchange and large pores. Addressing these challenges, we have developed an injectable platform that, for the first time, achieves ultra-long-term release of hydrophilic drugs for over six months. This system employs a methacrylated ultra-low molecular weight pre-polymer (polycaprolactone) to create in situ cross-linked depots (ISCD). The ISCD's solvent-free design and dense mesh network, both attributed to the ultra-low molecular weight of the pre-polymer, effectively minimizes burst release and water influx/efflux. In vivo studies in rats demonstrate that ISCD outperforms ISFI by achieving lower burst release and prolonged drug release. We demonstrated the versatility of ISCD by showcasing ultra-long-term delivery of several hydrophilic drugs, including antiretrovirals (tenofovir alafenamide, emtricitabine, abacavir, and lamivudine), antibiotics (vancomycin and amoxicillin) and an opioid antagonist naltrexone. Additionally, ISCD achieved ultra-long-term release of the hydrophobic drug tacrolimus and enabled co-delivery of hydrophilic drug combinations encapsulated in a single depot. We also identified design parameters to tailor the polymer network, tuning drug release kinetics and ISCD degradation. Pharmacokinetic modeling predicted over six months of drug release in humans, significantly surpassing the one-month standard achievable for hydrophilic drugs with existing LAIs. The platform's biodegradability, retrievability, and biocompatibility further underscore its potential for improving treatment adherence in chronic conditions.

Scalable Multi-Robot Task Allocation Using Graph Deep Reinforcement Learning with Graph Normalization

Task allocation plays an important role in multi-robot systems regarding team efficiency. Conventional heuristic or meta-heuristic methods face difficulties in generating satisfactory solutions in a reasonable computational time, particularly for large-scale multi-robot task allocation problems. This paper proposes a novel graph deep-reinforcement-learning-based approach, which solves the problem through learning. The framework leverages the graph sample and aggregate concept as the encoder to extract the node features in the context of the graph, followed by a cross-attention decoder to output the probability that each task is allocated to each robot. A graph normalization technique is also proposed prior to the input, enabling an easy adaption to real-world applications, and a deterministic solution can be guaranteed. The most important advantage of this architecture is the scalability and quick feed-forward character; regardless of whether cases have a varying number of robots or tasks, single depots, multiple depots, or even mixed single and multiple depots, solutions can be output with little computational effort. The high efficiency and robustness of the proposed method are confirmed by extensive experiments in this paper, and various multi-robot task allocation scenarios demonstrate its advantage.

Modification of the Clarke and Wright Algorithm with a Dynamic Savings Matrix

The goods collection and delivery process often relates to distribution logistics problems. The task is to deliver goods from warehouses to customers under specific circumstances. Efforts to optimize the process are largely aimed at reducing overall costs of goods transportation. Among the prominent algorithms for solving the basic type of the delivery (or collection) problem, which includes a single depot and a homogeneous vehicle fleet, is the algorithm developed by Clarke and Wright in 1964. This algorithm minimizes transportation costs by maximizing the savings achieved through merging multiple routes into one. This paper primarily aims to solve the pickup and delivery problem where the goods must be delivered and empty packaging collected in a single process. The request of a customer can be routed from the depot or from another customer. Similarly, the destination of the request may be the depot or another customer. Unlike the original version of the Clarke and Wright algorithm, the initial routes are created to satisfy delivery orders, and therefore, the same customer can occur in multiple routes. Consequently, a situation may arise in which two routes containing one or more common vertices must be combined during the calculation. Furthermore, these vertices need not be the outermost vertices of the routes. This situation cannot be addressed by using the original version of the Clarke and Wright algorithm, and that is why we propose its modification. Merging routes through inner vertices means that the cost savings depend on the configurations of the routes, and therefore, they cannot be calculated a priori. Instead, the dynamic savings matrix must be used.

General VNS for asymmetric vehicle routing problem with time and capacity constraints

We consider a real-life transportation problem from a hypermarket company in Serbia that consists of delivering online ordered and possibly perishable goods from a single depot to multiple customers. It can be modeled as an asymmetric vehicle routing problem that requires visiting and serving all customers using a limited number of homogeneous vehicles and taking into account time and capacity constraints. The objective function to be minimized is the total distance traveled. We provide a mixed-integer programming (MIP) formulation of the problem and develop several Local Search based metaheuristic methods exploring combinatorial formulation of the considered problem: Multistart Local Search (MLS), Greedy Randomized Adaptive Search Procedure (GRASP), and several variants of General Variable Neighborhood Search (GVNS) methods. All methods are compared on real-life instances provided by the hypermarket company and benchmark instances from the relevant literature. The obtained results show the superiority of GVNS-based methods with respect to both solution quality and running time, confirming that systematic search procedures have more success when dealing with hard optimization problems.

Single Depot Multiple Travelling Salesman Problem Solved With Preference-Based Stepping Ahead Firefly Algorithm

Single Depot Multiple Travelling Salesman Problem Solved With Preference-Based Stepping Ahead Firefly Algorithm

Solving the single depot open close multiple travelling salesman problem through a multi-chromosome based genetic algorithm

The multiple travelling salesman problem (MTSP) extends the classical travelling salesman problem (TSP) by involving multiple salesman in the solution. MTSP has found widespread applications in various domains, such as transportation, robotics, and networking. Despite extensive research on MTSP and its variants, there has been limited attention given to the open close multiple travelling salesman problem (OCMTSP) and its variants in the literature. To the best of the author's knowledge, only one study has addressed OCMTSP, introducing an exact algorithm designed for optimal solutions. However, the efficiency of this existing algorithm diminishes for larger instances due to computational complexity. Therefore, there is a crucial need for a high-level metaheuristic to provide optimal/best solutions within a reasonable timeframe. Addressing this gap, this study proposes a first meta-heuristic called multi-chromosome-based Genetic Algorithm (GA) for solving OCMTSP. The effectiveness of the developed algorithm is demonstrated through a comparative study on distinct asymmetric benchmark instances sourced from the TSPLIB dataset. Additionally, results from comprehensive experiments conducted on 90 OCMTSP symmetric instances, generated from the renowned TSPLIB benchmark dataset, highlight the efficiency of the proposed GA in addressing the OCMTSP. Notably, the proposed multi-chromosome-based GA stands out as the top-performing approach in terms of overall performance. Further, solutions to symmetric TSPLIB benchmark instances are also reported, which will be used as a basis for future studies.

Cost minimizing decisions on equipment and charging schedule for electric buses in a single depot

Combined decisions on equipment and charging schedule for electric buses (e-buses) are studied in this paper. The most representative day is considered, in which each e-bus fulfills a transfer task composed of a series of passenger transportation trips. Each trip starts and terminates at given times in the same single depot where e-buses re-charge their batteries. The problem is to determine battery variants for the e-buses, number of chargers of different types and daily cyclic charging schedule of e-buses such that a linear combination of (a) the total daily cost of the charging equipment, batteries wear and consumed energy, and (b) the total number of e-bus charging interruptions (switchings) is minimized. The constraints include an upper bound on the supplied electric power, restoration of the initial battery energy state before the next day transfer task for each e-bus and an upper bound on the maximal number of switchings for each e-bus in each depot visit over all e-buses and visits. A bi-level decomposition approach is proposed, in which decisions and constraints related to the detailed charging schedule and the number of switchings are moved to the lower-level problem. The lower level problem is formulated as Mixed Integer Linear Programming (MILP) problem. The upper-level problem is reduced to a MILP problem using linearization techniques. An exact decomposition scheme is developed for the upper-level MILP problem. A case study and comprehensive computer experiments are provided.

An exact algorithm for Two-Echelon Location-Routing problem with simultaneous pickup and delivery

This study considers an extension of the two-Echelon Location-Routing Problem (2E-LRP) namely two-Echelon Location-Routing Problem with Simultaneous Pickup and Delivery (2E-LRPSPD). A Mixed Integer Programming (MIP) formulation is developed and strengthened by the use of valid inequalities to solve the 2E-LRPSPD, and then a Branch and Cut-based exact algorithm (B&C) is presented. To improve the upper bounds, Iterated Local Search and Variable Neighborhood Search-based metaheuristic algorithms, namely, ILS-VNS and VNS, are developed and embedded into the B&C. Computational results, conducted on instances produced from the literature, demonstrate that the B&C yields tight lower and upper bounds, and also is capable of solving some instances optimally with up to 50 customers and 10 satellites in a reasonable time. Furthermore, sensitivity analysis reveals that the heuristic approaches and an increase in the runtime limit assist the algorithm to reach tight the upper bounds, whereas the number of potential depots does not have any effect on the performance of the algorithm. Besides, further computational analysis on the 2E-LRPSPD with a single depot, which is studied in the literature, shows that the B&C improves some best-known solutions while proving the optimality of some instances. Finally, the B&C is applied to a two-echelon supermarket distribution system in Türkiye. The computational results show that simultaneous pickup and delivery operations, as well as depot location decisions are critical elements to consider in the design of cost-effective distribution networks.

Live birth rate following endometrial preparation with daily versus depot GnRH agonist

Background Gonadotrophin-releasing hormone agonist (GnRHa) downregulates gonadotropin secretion in the pituitary gland. It is used both in ovulation induction protocols and in artificial endometrium preparation. Frozen—thawed embryo transfer to artificially prepared endometrium (FET-APE) is a frequent procedure in vitro fertilization (IVF) which requires GnRHa. It can be used either as a daily low-dose injection or as a single depot injection. It is unclear which of these two regimens is superior for artificial endometrium preparation. Methods We evaluated the data of 72 patients who had undergone frozen embryo transfer following the 5th day Preimplantation Genetic Test-aneuploidy (PGT-A) between 2018–2021. All embryos were genetically screened, and euploid single embryos were transferred. Group 1 (n: 36) used depot GnRHa, and Group 2 (n: 36) used single daily injections for artificial endometrial preparation. The outcomes for Beta Human Chorionic Gonadotrophin (BHCG) positivity and live birth rates (LBR) was compared. Results The BHCG positivity for Group 1 and Group 2 was 75% and 80.6%, respectively. The LBR for Group 1 and Group 2 were found to be 58.3% and 63.9%, respectively. There was no statistically significant differences between the two groups. Conclusions In artificial endometrium preparation, depot GnRHa offers cheaper and more convenient alternative to single daily dose injections, particularly in busy clinical settings.

Uncertainty in vulnerability of metro transit networks: A global perspective

This study measures the “uncertainty in vulnerability” of 50 metro transit networks in the most populated cities across the globe under benign and malicious attack scenarios. Uncertainty in vulnerability delineates the gap between the performance loss trajectory formed by link percolation under benign and malicious attacks. Three observations are discerned. First, vulnerability and uncertainty in vulnerability are a function of both size and physics of the network explained by connectivity measures. A 1% increase in the ratio of links to nodes increases the vulnerability by 0.50% and increases the uncertainty in vulnerability by 2.24%. A 1% increase in the ratio of the number of links to the maximum possible number of links decreases vulnerability by 0.03% and the uncertainty in vulnerability by 0.12%. Second, the topology of metro transit networks with <100 nodes follows one of the three analogous forms of tree-shaped networks, networks with one undirected cycle, or single depot networks, while the topology of metro transit networks with ≥100 nodes is closer to grid and matching pairs. Third, metro transit networks (i) are less likely to resume the operation under malicious attacks, (ii) are more likely to resume the operation under benign attacks, and (iii) are susceptible to both severe and non-severe degradations under random attacks. Overall, it is shown that the most vulnerable transit networks experience the maximal uncertainty in vulnerability and own a topology analogous to a single depot. New York, Delhi, and London metro transit networks have the most vulnerable topology. Ahmedabad, Mumbai, and Sydney metro transit networks have the least vulnerable topology.

ELECTRIC VEHICLE ROUTING PROBLEM USING ADAPTIVE SIMULATED ANNEALING

Road transport is a major CO2 emission contributor globally. To tackle the challenge of reducing world carbon emissions, alternative technologies for the automobile industry are widely researched. The automotive industry has started to shift from Internal combustion engine (ICE) vehicles to electric vehicles (EVs), where EVs are the future of the automotive industry in terms of reducing greenhouse gas emissions and air pollution. EV manufacturers are continuously looking for opportunities to optimize the supply chain processes, aiming for supply chain resilience. In this study, we present an Electric Vehicle Routing Problem (EVRP) to achieve the best decision, which is an extension of the traditional Vehicle routing problem (VRP) which in particular finding the shortest route for electric vehicles. The objective function is to find the best travel route that minimizes travel distance. Each route serves a set of customer nodes that starts and ends at a given depot node. We take battery capacity and charging stations as the constraints. In addition, the use of homogenous fleets and single depot are considered in this paper. A hybrid metaheuristic approach is used to find the best solution with the Adaptive Simulated Annealing algorithm. The use of adaptive in simulated annealing generates a higher probability of finding the best operators, which results in better solutions. A comparison of results from various metaheuristic methods is also presented in this paper to get the best method for the EVRP based on a benchmark dataset. This paper ends with recommendations for creating a routing plan that is resilient to disruptions to distribution.

Logistical considerations and challenges in deploying virtual biomethane pipelines to serve on-farm biogas plants

On-farm anaerobic digestion plants served by virtual biomethane pipelines may be used in areas with no gas grid infrastructure access to improve manure (slurry) management and to produce and deliver renewable gas. A modelling analysis of a simulated virtual biomethane pipeline is presented whereby gas is collected from 100 on-farm biogas plants fed with slurry and grass silage feedstocks and delivered to a market entry point (depot). In total, 7 scenarios are presented in the analysis. In scenarios 1–4, the biogas is upgraded on-site by the digester operator, the biomethane is collected by the haulage vehicle(s) and transported to a single depot. The impact of an additional depot on vehicle routing is investigated in scenarios 5 and 6. Scenario 7 investigates the use of a mobile-upgrading and compression unit, which would allow biogas plant operators to forego the installation and operation of biogas upgrading facilities. In scenario 3 (which considers the largest capacity biomethane haulage vehicles and a single delivery depot) all 100 anaerobic digestion plants are visited over the course of one week using 4 routes, with a total aggregated distance travelled of 205 km. Scenario 7 requires a total routing distance in excess of 613 km to visit all 100 biogas plants and requires long routing times and periods of downtime at each site due to the slow upgrading speed of the mobile unit. The weekly greenhouse gas emissions due to vehicle routing from each scenario are calculated. Assuming diesel-fuelled haulage vehicles, scenario 7 routing results in 431 kg CO2-eq week−1, a 167% increase in vehicle route emissions compared to scenario 3 (161 kg CO2-eq week−1). Additionally, whilst the mobile-upgrading unit may alleviate financial challenges, they carry significant logistical challenges, and their resultant higher routing emissions will impact the sustainability of the collected biomethane. Biomethane fuelled haulage vehicles may address this concern if the biomethane is sustainably sourced.

Electric Vehicle Scheduling Problem with Tour Combinations

Vehicle scheduling problem (VSP) has been studied since mid-90s, and yet the emerging electrification technology adoption requires a revisit to the problem since recharging event schedules need to be planned. The single depot electric vehicle scheduling problem (SDEVSP) is NP-hard, and large-scale instances cannot be solved to optimality in reasonable time. Hence, a heuristic solution approach was developed to address the problem. In this approach, we generate short tours that can be served by an electric vehicle (EV) and use a mixed-integer non-linear program to combine tour tuples that maximize EV utilization. The model was demonstrated on a hypothetical case study using a depot of the Chicago Transit Authority.

New approximation algorithms for the rooted Budgeted Cycle Cover problem

The rooted Budgeted Cycle Cover (BCC) problem is a fundamental optimization problem arising in wireless sensor networks and vehicle routing. Given a metric space (V,w) with vertex set V consisting of two parts D (containing depots) and V∖D (containing nodes), and a budget B≥0, the rooted BCC problem asks to find a minimum number of cycles to cover all the nodes in V∖D, satisfying that each cycle has length at most B and each cycle must contain a depot in D. In this paper, we give new approximation algorithms for the rooted BCC problem. For the rooted BCC problem with single depot, we give an O(log⁡Bμ)-approximation algorithm, where μ is the minimum difference of any two different distances between the vertices in V and the root. For the rooted BCC problem with multiple depots, we give an O(log⁡n)-approximation algorithm, where n is the number of vertices. We also test our algorithms on the randomly generated instances. The experimental results show that the algorithms have good performance in practice.

Memetic search for the minmax multiple traveling salesman problem with single and multiple depots

The minmax multiple traveling salesman problem with single depot (the minmax mTSP) or multiple depots (the minmax multidepot mTSP) aims to minimize the longest tour among a set of tours. These two minmax problems are useful for a variety of real-life applications and typically studied separately in the literature. We propose a unified memetic approach to solving both cases of the minmax mTSP and the minmax multidepot mTSP. The proposed algorithm features a generalized edge assembly crossover to generate offspring solutions, an efficient variable neighborhood descent to ensure local optimization as well as an aggressive post-optimization for additional solution improvement. Extensive experimental results on 77 minmax mTSP benchmark instances and 43 minmax multidepot mTSP instances commonly used in the literature indicate a high performance of the algorithm compared to the leading algorithms. Additional experimental investigations are conducted to shed light on the rationality of the key algorithmic ingredients.

Multiobjective Multidepot Capacitated Arc Routing Optimization Based on Hybrid Algorithm

The multidepot capacitated arc routing problem (CARP) is investigated with the hybrid optimization algorithm of the Dijkstra algorithm and genetic algorithm. The complex multidepot CARP is transformed into multiple single depot CARP by systematic clustering analysis. After completing the system clustering, the Dijkstra algorithm is used to adjust the boundary arc locally and merge it to a reasonable depot, while in the genetic algorithm, the structure of the chromosome is reset to use the path as the way of real coding, and the elite selection is used to decode to obtain the optimal path optimization scheme. Finally, Lanzhou road network data as experimental data, through Matlab to achieve the practicability of the algorithm in sprinkler applications. The results show that the improved genetic algorithm can successfully solve the multi-segment CARP with a certain road network scale, ensuring the correctness and feasibility of the algorithm. In addition, the efficiency of the algorithm in the later iteration is basically controlled at about 0.5 seconds, indicating that the efficiency of the algorithm is worth identifying.

Minimization of Sustainable-Cost Using Tabu Search for Single Depot Heterogeneous Vehicle Routing Problem with Time Windows

Minimization of Sustainable-Cost Using Tabu Search for Single Depot Heterogeneous Vehicle Routing Problem with Time Windows

A shortfall modelling-based solution approach for stochastic cyclic inventory routing

This paper studies the cyclic inventory routing problem with stochastic demand. A geographically dispersed set of retailers with stochastic demand rates is replenished from a single depot using vehicles with limited capacity. For an infinite horizon, a fixed-partition policy is adopted that partitions the retailers into subsets that are always replenished together in the same route being cyclically repeated. The objective is to provide cost efficient buffering of the demand variability within a cyclic distribution plan by providing carefully calibrated safety stock levels at the retailers. In doing so, the vehicle capacity needs to be taken into account, since cumulative demand during a cycle of the retailers in a route may exceed this capacity. In that case, shortfall remains at the retailer inventories because they are not fully replenished, which affects the service level (and cost balance) in the consecutive cycle(s). An approximate method is presented for determining the safety stock levels and is integrated into a state-of-the-art metaheuristic solution approach for cyclic inventory routing. An illustrative example and experiments on benchmark instances show (i) the effect of the vehicle capacity on the cost balance in a route, (ii) the accuracy of the approximation, and (iii) the added value of taking demand variability and shortfall due to limited vehicle capacity into account during the route design.

A two-phase ant colony optimization based approach for single depot multiple travelling salesman problem in Type-2 fuzzy environment

A two-phase ant colony optimization based approach for single depot multiple travelling salesman problem in Type-2 fuzzy environment

A bio-inspired approach: Firefly algorithm for Multi-Depot Vehicle Routing Problem with Time Windows

In this research, an improved bio-inspired metaheuristic named firefly is utilized to solve the Multi-Depot Vehicle Routing Problem with Time Windows (MDVRP-TW) and it is a generalization of Vehicle Routing Problem with Time Windows. This paper discusses the use of biological intelligence in analysis and optimization on MDVRP-TW. The objective of the MDVRP-TW is to minimize the overall distance, means of transportation within a specified time gap, along with other constraints such as limitation of vehicle capacity, restrictions of route duration length to satisfy the customer’s requirements. The routes must be designed where each customer is visited only once in a particular time gap with one vehicle and all the routes must originate and end at the same depot. The overall demand should not go beyond the vehicle’s capacity on each route. Multi-objective problems have attracted the attentions of many researchers in recent years, as they are more closely related to real-world situations. However, transportation is a significant factor for the current society, exhibiting and planning a complicated transport system was a very thought-provoking task. Many research studies have shown several successful metaheuristics and heuristic methodologies to solve MDVRP-TW in which, instead of a single depot, numerous depots with varying locations. In this work considered both the earliest time and latest arrival time window (double-sided time window). It is assumed that if an arrival time is more significant than the latest time, it will lead to an infeasible solution whereas, if an arrival time is lesser than the earliest time, then it will lead to a waiting time. However, due to its challenging task and multi-objective and limitations, there is still a space to solve it. In this work, a novel technique that combines an improved firefly algorithm (IFA), which uses different mechanisms, namely, inter-depot approach in assignment phase, Clarke & wright algorithm, and local search method in routing and scheduling phase were applied. The suggested technique has been evaluated using Cordeau standard benchmark instances and proved the technique’s novelty and feasibility. In a few circumstances, the modified firefly algorithm outperforms other algorithms, and optimal benchmark solution in terms of results and competence.