Two-phase Algorithm Research Articles

A two-phase algorithm for the dynamic time-dependent green vehicle routing problem in decoration waste collection

Transportation activities associated with construction waste generate substantial carbon emissions, an issue that is attracting increasing environmental concern. To raise construction waste transportation efficiency and reduce carbon emission, we address the dynamic time-dependent green vehicle routing problem for decoration waste collection (DTDGVRP-DWC). In the existing literature, many deterministic approaches to the dynamic vehicle routing problem are myopic, as they only react to already arrived requests. In this paper, we propose a stochastic sampling method to tackle with uncertain customer request in the real world. The DTDGVRP-DWC is formulated as an 0-1 programming. In the new model, we consider urban traffic congestion and variable speeds over time, and factors that significantly influence both carbon emissions and fuel costs. To quickly solve the complicated optimization problem, we develop a two-phase algorithm. In the first phase, we embed a competitive simulated annealing algorithm to determine visitation schedules for anticipated and early-request customers. In the second phase, we propose an event-trigger mechanism to decompose the dynamic problem into a series of static sub-problems, and an effective heuristic to solve each sub-problem. Computational results show that as long as the prediction accuracy exceeds a threshold, the forecast routing method consistently performs better than reactive routing. A real-world case demonstrates that an early commitment waiting time strategy benefits timely service requirements, whereas a late or hybrid waiting time strategy takes overall efficiency and customer satisfaction into account.

A Two-Phase Algorithm for Reliable and Energy-Efficient Heterogeneous Embedded Systems

A Two-Phase Algorithm for Reliable and Energy-Efficient Heterogeneous Embedded Systems

Dual step hybrid routing protocol for network lifetime enhancement in WSN-IoT environment

Recent development in internet of things (IoT) has been generating huge data due to the large number of nodes deployed and utilized for different applications. In addition, these applications utilize big data and require a more efficient mechanism for data sensing and data transmission. This research work proposes dual step hybrid routing (DSHR) protocol for efficient cluster-based routing. It comprises a two-phase algorithm, which aims at finding the optimal path considering clustering. It further comprises several processes such as cluster head selection, optimal path construction, integrating of nodes to cluster head and sensing range optimization. DSHR is evaluated considering the network lifetime; thereafter model is compared with the existing low energy adaptive clustering hierarchy (LEACH) protocol to prove the efficiency.

Time-dependent hydrogen fuel cell vehicle routing problem with drones and variable drone speeds

This paper proposes a novel problem called the time-dependent hydrogen fuel cell vehicle routing problem with drones and variable drone speeds (TDHFCVRP-D-VDS). In this problem, a fleet of hydrogen fuel cell vehicles (HFCVs) are equipped with multiple unmanned aerial vehicles (UAVs) to perform delivery and pickup services within the customers’ time windows. The UAV is capable of performing pickup operations after the delivery service, as long as it does not exceed its energy capacity. The HFCV can launch and retrieve the UAV multiple times as needed throughout the routing process. We establish a mixed integer programming model to simultaneously minimize the total cost and makespan, and verify its accuracy by Gurobi. To tackle larger-scale instances, we propose a non-dominated sorting genetic algorithm III with intelligent selection (NSGA-III-IS). The initial population is generated using four distinct approaches aimed at enhancing both diversity and quality. Considering the customers’ time windows, we factor in the temporal-spatial distances between customers when generating the initial population. Our approach employs a two-phase algorithm for developing initial solutions. In the first phase, the algorithm focuses on generating UAV trips, while in the second phase, it creates joint delivery routes for both the HFCV and the UAV. To enhance the optimization process, we have developed four strategies for optimizing UAV speed. These strategies dynamically adjust the UAV’s speed in response to the customers’ time windows and the HFCVs’ arrival times. Additionally, we have integrated an intelligent selection mechanism to optimize the execution probabilities of both general and problem-specific operators. The experimental results demonstrate the following: (1) The proposed NSGA-III-IS outperforms other variant algorithms and two benchmark algorithms; (2) UAVs significantly benefit from variable flight speeds, resulting in reduced costs and improved efficiency; (3) The HFCV with UAV joint delivery pattern is superior for reducing carbon emissions compared to other joint delivery patterns; (4) Longer customer time windows and optimized UAV speed strategies are effective in reducing the total cost, makespan, and total UAV hover waiting time; (5) Finally, a method that combines multi-attribute decision-making with principal component analysis is utilized to aid decision-makers in selecting satisfactory solutions.

Battery swapping, vehicle rebalancing, and staff routing for electric scooter sharing systems

Electric scooter (e-scooter) sharing systems provide on-demand electric scooter rental services. E-scooters are equipped with swappable batteries managed by staff who visit each scooter and replace depleted batteries with charged ones. The e-scooters in this system are free-floating; they can be located anywhere without having to be returned to designated stations. Due to this characteristic of the scattered location of e-scooters, operation decisions with associated staff routing are more challenging than station-based services. Thus, it is critical to implement the efficient management of e-scooter redistribution and charging decisions with proper staff routing to successfully prepare for user demand within a limited operation time while minimizing the total operating cost. To this end, we introduce a battery swapping and vehicle rebalancing problem with staff routing for e-scooter sharing systems, formulated as a mixed integer programming (MIP) model. To derive solutions efficiently for a large-scale instance in practice, we propose a clustered iterative construction approach where the problem is decomposed into two phases. The first phase clusters regions using an approximation of intra-region and inter-region operation costs with the minimum spanning tree approach. The second phase efficiently derives multiple candidate regional sequences by our partial permutation procedure and following the sequences, iteratively solves a significantly reduced size of the problem to construct operation assignments. Our numerical experiments on the generated instances and real-world instances demonstrate that the proposed two-phase algorithm shows significantly superior performance in practically large scale instances than the benchmarks without clustering or the iterative procedures of our algorithm.

Federated deep reinforcement learning for dynamic job scheduling in cloud-edge collaborative manufacturing systems

The cloud-edge collaborative manufacturing system (CCMS) connects distributed factories to a cloud centre through cloud-edge collaborative communication, introducing both opportunities and challenges to conventional dynamic job scheduling. Enhancing each factory's scheduling performance by sharing general scheduling knowledge among heterogeneous factories under the consideration of data privacy protection remains challenging. To this end, this paper proposes to solve the dynamic job scheduling in the context of CCMS with a novel federated deep reinforcement learning (FDRL) approach. Within each factory, the scheduling objective involves minimising the makespan and energy consumption, accounting for machine warm-up procedures and real-time dynamics. To handle heterogeneous policy structures, we aggregate their hidden parameters through FDRL, with states, actions, and rewards designed to facilitate the aggregation. The two-phase algorithm, comprising iterative local training and global aggregation, trains the scheduling policies. Constraint items are introduced to the loss functions to smooth local training, and the global aggregation considers production scales and obtained objectives. The proposed approach enhances the solution quality and generalisation of each factory's scheduling policy without exposing original production data. Numerical experiments conducted on sixty scheduling instances validate the superiority of the proposed approach compared to twelve dynamic scheduling methods. Compared to independently trained DRL-based approaches, the proposed FDRL-based approach achieves up to an 8.9% reduction in makespan and a 22.3% decrease in energy consumption through knowledge sharing.

A Multi-Objective Learning Whale Optimization Algorithm for Open Vehicle Routing Problem with Two-Dimensional Loading Constraints

With the rapid development of the sharing economy, the distribution in third-party logistics (3PL) can be modeled as a variant of the open vehicle routing problem (OVRP). However, very few papers have studied 3PL with loading constraints. In this work, a two-dimensional loading open vehicle routing problem with time windows (2L-OVRPTW) is described, and a multi-objective learning whale optimization algorithm (MLWOA) is proposed to solve it. As the 2L-OVRPTW is integrated by the routing subproblem and the loading subproblem, the MLWOA is designed as a two-phase algorithm to deal with these subproblems. In the routing phase, the exploration mechanisms and learning strategy in the MLWOA are used to search the population globally. Then, a local search method based on four neighborhood operations is designed for the exploitation of the non-dominant solutions. In the loading phase, in order to avoid discarding non-dominant solutions due to loading failure, a skyline-based loading strategy with a scoring method is designed to reasonably adjust the loading scheme. From the simulation analysis of different instances, it can be seen that the MLWOA algorithm has an absolute advantage in comparison with the standard WOA and other heuristic algorithms, regardless of the running results at the scale of 25, 50, or 100 datasets.

Demand Allocation and Lot-Sizing Solution of Single Product Deterministic Demand

In this study, a two-phase algorithm has been developed to address the single-product supplier selection and order allocation problem (SP-SSOAP). In the first phase, a novel demand allocation algorithm is developed using a recursive demand equation. Subsequently, an adaptive genetic algorithm is employed in the second phase, with additional constraints for capacity and minimum order quantity, to determine the best lot-sizing plan for each supplier. Experimental results demonstrate that, on average, the proposed heuristic achieves an objective value within 1% of the optimal solution for small-sized instances and outperforms the previous heristic solution by an average of 12% in terms of objective value for larger problems. Additionally, the numerical results emphasize that the proposed method performs better when input parameters such as price, ordering cost, and holding cost exhibit lower fluctuations. This suggests that managers should focus on improving supplier relationships and coordination strategies to reduce variability in price, order cost, and holding cost.

Simple population-based algorithms for solving optimization problems

Heuristic algorithms are simple yet powerful tools that are capable of yielding acceptable results in a reasonable execution time. Hence, they are being extensively used for solving optimization problems by researchers nowadays. Due to the quantum of computing power and hardware available today, a large number of dimensions and objectives are considered and analyzed effectively. This paper proposes new population-based metaheuristic algorithms that are capable of combining different strategies. The new strategies help in fast converging as well as trying to avoid local optima. The proposed algorithms could be used as single-phase as well as two-phase algorithms with different combinations and tuning parameters. “Best”, “Mean” and “Standard Deviation” are computed for thirty trials in each case. The results are compared with many efficient optimization algorithms available in the literature. Sixty-one popular un-constrained benchmark problems with dimensions varying from two to thousand and fifteen constrained real-world engineering problems are used for the analyses. The results show that the new algorithms perform better for several test cases. The suitability of the new algorithms for solving multi-objective optimization problems is also studied using five numbers of two-objective ZDT problems. Pure Diversity, Spacing, Spread and Hypervolume are the metrics used for the evaluation.

Performance Analysis of a Two-Phase Algorithm with Tuning Option for Solving Optimization Problems

Performance Analysis of a Two-Phase Algorithm with Tuning Option for Solving Optimization Problems

A novel degradation model and reliability evaluation methodology based on two-phase feature extraction: An application to marine lubricating oil pump

The Wiener-process-based Degradation Approach with Two-phase Algorithm (W-DATA) is introduced as a multi-dimensional framework explicitly designed for modeling mechanical system reliability. This approach leverages an enhanced Empirical Mode Decomposition, known as P-EMD, for degradation feature extraction, and utilizes Approximate Entropy (ApEn) for quantifying feature complexities. W-DATA seamlessly integrates these components into a time-resolved degradation model. To enhance its robustness, the proposed reliability model synergizes with a Box-Cox transformed Wiener model, allowing for improved adaptability to non-Gaussian data landscapes. The paper outlines a strategy for establishing a reliable threshold for this data-driven degradation model based on non-Gaussian data, a critical aspect for reliability modeling using the Wiener process. This strategy addresses the challenge of Wiener process verification through normality and independent testing of data increments. The integrative methodology is recommended for application in machinery reliability analytics and has undergone rigorous validation through a 770 h real-world test on a marine lubricating oil pump reducer. The results affirm its efficacy and feasibility in accurately estimating mechanical system reliability.

Supervised Fusion Music Composition Through Long Short-Term Memory and Stochastic Modelling

Music composition has witnessed significant advancements with the infusion of artificial intelligence, particularly using Long Short-Term Memory (LSTM) networks. However, most existing algorithms offer minimal control to composers in influencing the genre fusion process, thereby potentially undermining their creative preferences. This study introduces a novel, two-phase algorithm for personalized fusion music generation that reflects the composer's individual preferences. In the first phase, melodies are generated for individual genres using Recurrent Neural Networks (RNNs) employing techniques like Sequential, Dense, and one-hot encoding. These generated melodies serve as input for the second phase, where an LSTM network fuses them into a coherent composition. Notably, the algorithm incorporates weights set by the composer for each genre, allowing for a personalized composition. A stochastic approach is employed in both phases to introduce creative variance while balancing structural coherence. We demonstrate this balance through various metrics offering a more tailored fused music generation experience enriched by stochastic modeling.

HEPM: High-efficiency pattern mining

Pattern mining (PM) is an important field of data mining and has gained considerable momentum recently, mainly owing to the massive growth of big data. PM often sets attentive objectives such as mining frequent or high utility patterns to obtain attractive patterns. High utility patterns address the defect of frequent patterns that cannot reveal the maximum profit. However, it neglects another vital factor, cost or investment. This paper proposes a new high-efficiency PM problem that considers both utility and investment. The problem aims to find patterns with the maximum profit-to-investment ratio. Our paper is devoted to studying high-efficiency itemsets in transaction databases. We first formulate the criteria for a high-efficiency PM problem. Subsequently, we propose a two-phase algorithm called HEPM and an improved one-phase algorithm called HEPMiner to discover high-efficiency patterns in a transaction database. We design a corresponding pruning strategy within HEPM to reduce the search space. In HEPMiner, we utilize a novel efficiency-list and an estimated efficiency co-occurrence structure in the pruning strategies to further improve the mining performance. Moreover, we derive the upper bounds of efficiency for both algorithms. The experimental results demonstrate the effectiveness and efficiency of our two algorithms.

Mining High Utility Itemsets Using Prefix Trees and Utility Vectors

High utility itemsets can reveal combinations of items that have a high profit, expense, or importance. Mining high utility itemsets in a database with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> items generally results in a huge search space, composed of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2^{n}$</tex-math></inline-formula> itemsets, and heavy utility calculations for the explored itemsets. Previous algorithms using prefix tree structures perform two phases, namely candidate generation and testing. To avoid generating candidate itemsets, one-phase algorithms use list or hyper-link structures and have been proven to be superior to two-phase algorithms. However, it should be noted that a prefix tree is still an efficient structure for itemset mining problems, and especially algorithms using prefix trees such as FP-Growth have shown excellent performance for mining frequent itemsets. This paper proposes Hamm, a High-performance AlgorithM for Mining high utility itemsets. Hamm employs a novel TV (prefix Tree and utility Vector) structure and mines high utility itemsets in one phase without candidate generation. We also develop an efficient optimization which is incorporated into Hamm as a component. Using prefix trees and utility vectors, Hamm outperforms state-of-the-art algorithms on various databases in experiments. Experimental results also show that the proposed optimization remarkably reduces the search space and speeds up Hamm.

Transceiver Beamforming for Over-the-Air Computation in Massive MIMO Systems

This paper investigates the transmitter and receiver beamforming (TB and RB) for over-the-air computation (AirComp) in massive multiple-inputs and multiple-outputs (MIMO) systems. First, we propose a two-phase hybrid beamforming algorithm to design TB and hybrid RB. In the first phase, we adopt a projected gradient descent with momentum (PGDM) algorithm to search for the optimal fully-digital TB matrices. Compared with the benchmarks on the mean square error (MSE) performances, PGDM can achieve up to 5 dB gain in signal-to-noise ratio (SNR) with less algorithm execution time when fully-digital RB is assumed. In the second phase, we plug the TB matrices obtained in PGDM as well as the optimal baseband RB (BBRB) matrix into the MSE objective, and adopt gradient descent to search for the optimal radio-frequency RB (RFRB) matrix. Compared with the state-of-the-arts, the proposed two-phase algorithm reduces up to 30% of the algorithm execution time and 18% of the MSE. Second, we propose a statistical TB algorithm to reduce the communication overheads, in which TB completely depends on statistical channel state information (CSI) and thus does not rely on the feedback from the base station (BS). We prove that orthonormal matrices are asymptotically optimal for statistical TB when uncorrelated <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rayleigh</i> channels are assumed and the number of receiving antennas approaches to infinity. For correlated channels, experimental results show that the proposed statistical TB can achieve about 5 dB gain in SNR compared with orthonormal matrices in terms of the MSE performance. Third, a large scale system analysis is made in this paper. As the number of the receiving antennas approaches to infinity, asymptotically optimal choices for TB and RB are provided, and upper bounds of MSE are derived in terms of the number of clients and receiving antennas. For hybrid RB, an upper bound of the squared distance between the optimal hybrid RB and the optimal fully-digital RB is also derived.

A Fully Online Clustering Approach for Enhanced Performance of Health Information System

Health Data clustering is a significant research direction aiming to extract knowledge from a continuous health data flow to support online health decisions. However, processing health data clusters is still a challenging task. Existing clustering approaches are subject to various limitations in terms of considering the neighbor clusters and conducting multiple operations during the maintenance process. In this paper, we model, design and implement a novel framework called IClustMaint for efficiently clustering and maintaining health data clusters incrementally. A two-phase algorithm is embedded in the framework. We first employ the Principal Component Analysis (PCA) method to efficiently reduce the high costs of the initial clustering phase. Next, in the maintenance phase, we propose the incremental Cluster maintenance (ICM) approach for managing the generated cluster during a period of time. Technically, when the data clusters are evolving over time and need to be maintained frequently, the ICM approach improves the performance of cluster maintenance by only tracking the edge points. The experimental results on a real medical dataset verify the efficiency of the proposed approaches.

Ruin Theory for User Association and Energy Optimization in Multi-Access Edge Computing

In this correspondence, a novel framework is proposed for analyzing data offloading in a multi-access edge computing system. Specifically, a two-phase algorithm, is proposed, including two key phases: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1) user association phase</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2) task offloading phase</i> . In the first phase, a ruin theory-based approach is developed to obtain the users association considering the users' transmission reliability and resource utilization efficiency. Meanwhile, in the second phase, an optimization-based algorithm is used to optimize the data offloading process. In particular, ruin theory is used to manage the user association phase, and a ruin probability-based preference profile is considered to control the priority of proposing users. Here, ruin probability is derived by the surplus buffer space of each edge node at each time slot. Giving the association results, an optimization problem is formulated to optimize the amount of offloaded data aiming at minimizing the energy consumption of users. Simulation results show that the developed solutions guarantee system reliability, association efficiency under a tolerable value of surplus buffer size, and minimize the total energy consumption of all users.

Solving a Two-Level Location Problem with Nonlinear Costs and Limited Capacity: Application of Two-Phase Recursive Algorithm Based on Scatter Search

Abstract This study examines the issue of distribution network design in the supply chain system. There are many production factories and distribution warehouses in this issue. The most efficient strategy for distributing the product from the factory to the warehouse and from the warehouse to the customer is determined by solving this model. This model combines location problems with and without capacity limits to study a particular location problem. In this system, the cost of production and maintenance of the product in the factory and warehouse is a function of its output. This increases capacity without additional costs, and ultimately does not lose customers. This algorithm is a population-based, innovative method that systematically combines answers to obtain the most accurate answer considering quality and diversity. A two-phase recursive algorithm based on a scattered object has been developed to solve this model. Numerical results show the efficiency and effectiveness of this two-phase algorithm for problems of different sizes.

An algorithm for training a class of polynomial models

In this paper we propose a new training algorithm for a class of polynomial models. The algorithm is derived using a learning bound for predictors that are convex combinations of functions from simpler classes. In our case, the hypotheses are polynomials over the input features, and they are interpreted as convex combinations of homogeneous polynomials. In addition, the coefficients are restricted to be positive and to sum to 1. This constraint will simplify the interpretation of the model. The training is done by minimizing a surrogate of the learning bound, using an iterative two-phase algorithm. Basically, in the first phase the algorithm decides which monomials of higher degree should be added, and in the second phase the coefficients are recomputed by solving a convex program. We performed several experiments on binary classification datasets from different domains. Experiments show that the algorithm compares favorably in terms of accuracy and speed with other classification methods, including some new interpretable methods like Neural Additive Models and CORELS. In addition, the resulting predictor can sometimes be understood and validated by a domain expert. The code is publicly available.

A new truck-drone routing problem for parcel delivery by considering energy consumption and altitude.

The high population density in metropolitan areas, high-rise buildings, and changes in people's lifestyles have completely changed the way postal packages are delivered. People no longer go to the ground floor to receive a postal package. In the meantime, the delivery of postal packages through the balconies and windows of the units on the upper floors of the buildings will gradually become inevitable. Hence, a new Vehicle Routing Problem with Drone mathematical model has been developed with the objective of minimizing total delivery time and with the ability to deliver postal packages in the path of drones at different heights. In addition, the drone's energy consumption is computed by taking into account wind speed, the weight of the postal parcel, the weight of the drone's body, and other factors in the drone's path. A two-phase algorithm based on the nearest neighborhood and local search is presented to solve the developed mathematical model in different instances. Several small-sized test problems are designed and solved, and the performance of the heuristic approach is evaluated compared to the outputs of the CPLEX solver. Finally, the proposed model is implemented on a real-world scale to demonstrate the efficacy and applicability of the proposed model as well as the heuristic approach. The results show that the model successfully finds the optimal planning of the delivery routes, especially when we deal with delivery points at different heights.