Decomposition-based Algorithm Research Articles

Integrated optimization of charging infrastructure, fleet size and vehicle operation in shared autonomous electric vehicle system considering vehicle-to-grid

Shared autonomous electric vehicles (SAEVs) are predicted to become a significant solution to reduce global emissions and energy consumption resulting from urban transportation. The centralized operation of SAEVs not only allows large-scale travel demand response but also can provide essential ancillary services to the smart grid through the concept of vehicle-to-grid (V2G). With V2G technology, unused electric vehicles can work as a distributed energy storage facility for the electricity grid to smoothen the intermittent demand. Designing and operating a V2G-enabled SAEV system is challenging. This problem involves complicated planning and operational decisions, as well as time-varying electric tariffs. In this work, a flow-based Integer Linear Programming (ILP) model is formulated for determining the optimal configurations (charging infrastructure and fleet size) and daily operation strategies (serving passengers, relocation, charging/discharging). The developed mathematical model allows for maximizing the total profit, comprising investment cost, revenue from serving passengers, and V2G profit through charging/discharging schedules. A two-stage Benders decomposition-based algorithm is proposed to address the sophisticated ILP problem. Via testing instances in the Manhattan network based on real-world and synthetic data, we have demonstrated the feasibility of our approaches and studied the benefits of integrating V2G in the SAEV system.

Spatiotemporal Expansion of Algal Blooms in Coastal China Seas.

The coastal seas of China are increasingly threatened by algal blooms, yet their comprehensive spatiotemporal mapping and understanding of underlying drivers remain challenging due to high turbidity and heterogeneous water conditions. We developed a singular value decomposition-based algorithm to map these blooms using two decades of MODIS-Aqua satellite data, spanning from 2003 to 2022. Our findings indicate significant algal activity along the Chinese coastline, impacting an average annual area of approximately 1.8 × 105 km2. The blooms exhibit peak intensity in August, while the maximum affected area occurs in September, featuring multifrequency outbreaks in spring, and pronounced large-scale events in summer and autumn. Notably, our analysis demonstrates a robust 67% increase in bloom occurrences over the study period. This expansion is primarily attributed to increased nutrient inflow from terrestrial sources linked to human activity and precipitation, compounded by rising global sea surface temperatures. These spatiotemporal insights are critical for devising effective management strategies and policies to mitigate the impacts of algal blooms.

Joint optimization of UPF placement and traffic routing for 5G core network user plane

This paper investigates the dynamic deployment of the 5G core network user plane functions (UPFs) in the edge network under time-varying traffic conditions. The objective is to minimize the total cost, including energy consumption, user plane latency, and UPF deployment costs by jointly optimizing UPF placement and traffic routing over the entire planning horizon. We formulate the optimization problem as a mixed-integer linear programming (MILP) problem, which is proven to be NP-hard. To obtain the optimal solution for the problem, we propose a Benders decomposition-based algorithm. However, the high computational complexity of this algorithm limits its practical applicability for large-scale networks. Therefore, we propose a low-complexity algorithm based on nested Benders decomposition that can solve the problem suboptimally. The simulation results demonstrate the convergence and computational efficiency of the proposed algorithm and show that it outperforms two existing algorithms. Moreover, we demonstrate that cost-saving can be achieved by using more power-efficient servers or deploying more servers. Additionally, we show that adjusting the cost parameters can achieve a good tradeoff between energy consumption and user plane latency.

An exact algorithm for maximum electric vehicle flow coverage problem with heterogeneous chargers, nonlinear charging time and route deviations

Typical electric vehicles (EVs) should be recharged multiple times to reach a long distance due to the limited travel ranges. The EV flow covering problem determines the locations of charging stations to maximize the “covered” OD flows, respecting a given budget for the new charging stations. This paper proposes an exact algorithm for solving the problem by considering the heterogeneous EV chargers, nonlinear charging time, and route deviations from the shortest distance paths. We develop an exact Benders decomposition-based algorithm, in which the Benders subproblem utilizes a nested cut-generation via a customized labeling algorithm. Two methods for solving the Benders subproblem are developed, which are combined to accelerate the Benders cut generation. In addition, we present a heuristic algorithm based on the proposed exact algorithm for the larger-sized problems. The computational results show that the proposed algorithm could solve real-life problems. Especially, the heuristic algorithm could solve problems up to 339 nodes and 500 km of the EV’s travel range. The extensive computational study shows that addressing the multiple charger types, the charging time, and the deviation routes can be crucial to provide realistic charging infrastructure for EVs.

A hypervolume-based cuckoo search algorithm with enhanced diversity and adaptive scaling factor

Existing multi-objective cuckoo search (MOCS) algorithms are based on either Pareto dominance or decomposition. However, when dealing with complex multi-objective problems (MOPs), the Pareto dominance-based algorithms face a decrease in selection pressure, and the decomposition-based algorithms easily gain poor distributions. The objective of this paper is to repurpose an indicator-based MOCS by combining improved diversity enhancement (IDE) and adaptive scaling factor (ASF) for MOPs. In the proposed algorithm, hypervolume is used as the indicator to guarantee better convergence and enough spread of the population. IDE chooses the large hypervolume to rebuild the parent population to compensate for the lack of population diversity. Additionally, ASF makes full use of individuals information to enhance the search ability of Lévy component in cuckoo search. Comprehensive experiments on 31 benchmark functions including two classical suites ZDT, WFG, and one challenged suite proposed in CEC2019, as well as 8 real-world problems were conducted to test the proposed algorithm. Compared with several state-of-the-art multi-objective evolutionary algorithms, the effectiveness and efficiency of our proposed method were demonstrated by the results.

Optimal Siting and Sizing of Hydrogen Production Modules in Distribution Networks with Photovoltaic Uncertainties

Hydrogen production modules (HPMs) play a crucial role in harnessing abundant photovoltaic power by producing and supplying hydrogen to factories, resulting in significant operational cost reductions and efficient utilization of the photovoltaic panel output. However, the output of photovoltaic power is stochastic, which will affect the revenue of investing in an HPM. This paper presents a comprehensive analysis of HPMs, starting with the modeling of their operational process and investigating their influence on distribution system operations. Building upon these discussions, a deterministic optimization model is established to address the corresponding challenges. Furthermore, a two-stage stochastic planning model is proposed to determine optimal locations and sizes of HPMs in distribution systems, accounting for uncertainties. The objective of the two-stage stochastic planning model is to minimize the distribution system’s operational costs plus the investment costs of the HPM subject to power flow constraints. To tackle the stochastic nature of photovoltaic power, a data-driven algorithm is introduced to cluster historical data into representative scenarios, effectively reducing the planning model’s scale. To ensure an efficient solution, a Benders’ decomposition-based algorithm is proposed, which is an iterative method with a fast convergence speed. The proposed model and algorithms are validated using a widely utilized IEEE 33-bus system through numerical experiments, demonstrating the optimality of the HPM plan generated by the algorithm. The proposed model and algorithms offer an effective approach for decision-makers in managing uncertainties and optimizing HPM deployment, paving the way for sustainable and efficient energy solutions in distribution systems. Sensitivity analysis verifies the optimality of the HPM’s siting and sizing obtained by the proposed algorithm, which also reveals immense economic and environmental benefits.

Data-driven stochastic robust optimization of sustainable utility system

Sustainable utility systems reduce reliance on fossil fuels by using renewable energy sources. Multi-scale uncertainties associated with renewable energy and utility systems pose challenges to the modeling and optimization of sustainable utility systems. This study proposes a sustainable retrofit framework for utility systems based on a data-driven stochastic robust optimization approach. Kernel density estimation and fuzzy clustering were employed to capture the uncertainty features in a holistic framework. A life cycle assessment approach was used to calculate the global warming potential (GWP) of the sustainable utility system, and a multi-objective environmental and economic optimization model was developed. A nested decomposition-based algorithm was proposed to solve a large-scale mixed-integer nonlinear programming problem. Finally, a case study of an industrial utility system was conducted to demonstrate the effectiveness of the proposed method. The optimization results show that the proposed method reduces GWP by 9 % after introducing renewable energy and achieves a balance between economic and environmental performance.

Sensing-Efficient NOMA-Aided Integrated Sensing and Communication: A Joint Sensing Scheduling and Beamforming Optimization

Integrated sensing and communication (ISAC) system has been expected to play a vital role in future wireless networks and services. In this paper, we investigate a non-orthogonal multiple access (NOMA)-aided ISAC system in which the ISAC base station utilizes NOMA to serve multiple NOMA-users while performing radar sensing towards a group of sensing targets by leveraging the superimposed NOMA signals for NOMA-users. To investigate this problem, we formulate a joint optimization of the beamforming, the NOMA transmission duration and the sensing scheduling of sensing targets, with the objective of maximizing the sensing efficiency (i.e., the number of sensed targets within a time-interval) of ISAC system, while satisfying both the communication quality requirement of each NOMA-user and the sensing quality requirement of each selected targets. Despite that the formulated joint optimization problem is strictly non-convex, we propose a decomposition-based algorithm for solving the problem. Specifically, we exploit the successive convex approximation and penalty function method to equivalently transform the problem of optimizing the beamforming into a convex problem which can be addressed efficiently. Furthermore, with the optimal beamforming, we leverage the monotonic feature and adopt a bisection-search method to determine the NOMA transmission duration. Finally, we utilize an algorithm based on the cross-entropy learning to compute the optimal sensing scheduling. Numerical results verify the effectiveness of our proposed algorithms and show the performance advantage of our NOMA-aided ISAC system. Compared with some benchmark schemes, our NOMA-aided ISAC sensing scheduling scheme can achieve better performance in communication and sensing.

A matheuristic algorithm for block assignment problem in long-term production planning in the shipbuilding industry

This study introduced the block assignment problem in the long-term production planning of a very large real-world shipbuilder and formulated it as a mixed integer linear programming model. For the problem, blocks are assigned to assembly shops for processing; some blocks must be assigned as a group to a region, a collection of assembly shops, because of their mutual dependency. Each assembly shop has its target work level. The objective is to minimize the sum of workload deviations of the assembly shops during a specific planning period. Because the mathematical model could not be solved within a reasonable time, a two-stage matheuristic algorithm was proposed. The algorithm determines the region of blocks in the first stage and the assembly shop for each block in the second stage. Computational experiments were performed using a real-world instance provided by the shipbuilder, including instances of different sizes generated from real-world data. The experiment results demonstrated that the algorithm yielded remarkable reductions of 10.5% and 35.3% in assignment costs and factory workload violations compared with manual planning, respectively. The proposed decomposition-based algorithm also demonstrated superior effectiveness in solving the problem than the full mathematical model. The proposed algorithm is currently embedded in the planning system of the shipbuilder.

Energy-Efficient Hybrid NOMA-FDMA Assisted Distributed Two-Tier Edge-Cloudlet Multi-Access Computation Offloading

Driven by the increasing interests of multi-tier computing architecture, this paper considers a hybrid non-orthogonal multiple access (NOMA) and frequency division multiple access (FDMA) assisted two-tier edge-cloudlet multi-access computation offloading. In particular, part of the computation tasks of the edge-computing user (EU) can be offloaded to different edge servers (ESs) via NOMA, and part of the computing tasks received by the ESs can be further offloaded to the cloudlet server (CS) via FDMA. We formulate an optimization problem to minimize the total energy consumption of the two-tier offloading system by jointly optimizing the multi-access offloading decision, NOMA-transmission duration, FDMA-transmission duration and bandwidth allocations. Although the problem is non-convex, we identify the structural feature of the problem and propose a decomposition-based algorithm to attain the optimal two-tier offloading decisions and the associated allocations of the computing/communication resources. Specifically, by leveraging the hidden convexity after decomposition, we propose a distributed algorithm, which is based on the block coordinated descent (BCD) method and Lagrange duality, for solving the subproblem. In our distributed algorithm, the EU optimizes its Tier-I offloading towards different ESs, each ES individually optimizes its Tier-II offloading towards the CS, and moreover, the CS optimizes its bandwidth allocations to the ESs. Furthermore, based on the proposed algorithm for the singe-EU case, the multi-EU scenario is further analyzed. To improve the energy-efficiency and fairness for the multi-EU scheduling, we propose a gradient projection (GP) based multi-EU scheduling algorithm, which leverages our single-EU algorithm as a subroutine, to optimize all EUs’ energy-efficiency in computation offloading over a long-term period. Numerical results verify the performance of our proposed algorithms. For the single-EU scenario, our simulation results demonstrate that the decomposition-based algorithm can outperform some benchmark algorithms. In the case of multi-EU scenario, our proposed GP-based multi-EU scheduling can effectively improve all EUs’ energy-efficiency compared to the round-robin scheduling.

Prefiltering-based reduced rank multiuser detection in uplink generalized spatial modulation massive MIMO system

Exploiting generalized spatial modulation in massive MIMO system, we develop an efficient uplink multiuser detection scheme. Different from the maximum likelihood detection algorithm, the spatial and temporal data in the proposed detection scheme are decoded in a sequential manner: At the front end of base station receiver, a bank of spatial filters is first employed to mitigate the multiuser interference using the benefits of large-scale antenna array. There then, a reduced rank generalized Eigen-value decomposition-based algorithm is proposed to identify the antennas activated at each user terminal. In the second stage, a least-squares-based multiuser detector is employed to decode the multiplexed temporal symbols. Both theoretical analysis and computer simulations are conducted to evaluate system performance in terms of correct identification probability and overall symbol error rate. Simulation results demonstrate that the proposed algorithm outperforms most of the existing algorithms yet the complexity is extensively reduced.

Distributionally robust optimization for collaborative emergency response network design

The post-disaster emergency response capacity of a single country is limited, and a collaborative approach that pools emergency resources can improve disaster resilience. In this paper, we study a multi-country collaborative emergency response network design problem with uncertain demand and transportation time. Considering the benefits of inter-regional cooperation in sharing emergency facilities and resources, we construct a collaborative emergency response network (CERN) design framework. The cost of CERN is allocated among the partner countries according to their expect standalone response cost and the level of economic development. In practice, the distribution information of random parameters is not perfectly known, so we propose a distributionally robust optimization (DRO) model to design the CERN. A scenario-wise ambiguity set is constructed to characterize the uncertain parameters based on disaster-level-related events. To solve the proposed DRO model, we propose a decomposition-based algorithm with a valid inequality. In the numerical study, we first verify the advantage of the CERN design approach. The proposed scenario-wise DRO method is subsequently compared with alternative modeling approaches to assess its out-of-sample performance. The findings confirm the efficacy of the constructed ambiguity set in capturing the uncertainty stemming from varying magnitudes of catastrophic events. The computational study demonstrates that the proposed algorithm exhibits superior computational efficiency compared to the commercial solver CPLEX for large-scale problems. Additionally, we conduct sensitivity analyses on various parameter configurations and provide managerial insights for the CERN design problem.

A Decomposition Algorithm for Dynamic Car Sequencing Problems with Buffers

In this paper, we research the dynamic car sequencing problem with car body buffer (DCSPwB) in automotive mixed-flow assembly. The objective is to reorder the sequence of cars in the paint shop using the post-painted body buffers to minimize the violation of constraint rules and the time cost of sequencing in the general assembly shop. We establish a mathematical model of DCSPwB and propose a decomposition-based algorithm based on the dynamic genetic algorithm (DGA) and greedy algorithm for delayed car release (PGDA). Experiments are conducted based on production orders from actual companies, and the results are compared with the solution results of the underlying genetic algorithm (GA) and greedy algorithm (GDA) to verify the effectiveness of the algorithm. In addition, the effect of buffer capacity on DCSPwB is investigated.

A Decomposition-Based Approach for Multitask Scheduling With Execution Uncertainty in Industrial Internet of Things

Industrial Internet of Things (IIoT) is changing the way in which factories operatewith the help of various industrial applications. However, the execution uncertainty of computing tasks has always been ignored in IIoT applications. In this paper, we define a novel conditional task graph to describe the execution uncertainty and present a generation algorithm to obtain all task scenario graphs and corresponding occurrence probabilities. Then, a new IIoT-oriented multi-task scheduling model under executionuncertainty is built. This model is simplified by reformulating the nonlinear constraints and subsequently decomposed into several small-scale models using Lagrange multipliers, from which a decomposition-based algorithm is derived to solve the decomposedsmall-scalemodels and progressively acquire a well-optimized solution of the initial model. Furthermore, a patching algorithm is constructed to improve the obtained solution. Finally, many test cases are generated, and fourselected algorithms are taken for comparison to evaluate the performance of our algorithms. The results demonstrate that our algorithms remarkably outperform the others. Besides, the solutions of the proposed algorithms can completely satisfy the execution deadline constraints of differenttask scenarios.

A many-objective evolutionary algorithm with estimating the convexity-concavity of Pareto fronts and clustering

Many real-world applications involve several conflicting objectives that can be solved using multiobjective evolutionary algorithms (MOEAs). Nevertheless, when considering the convexity-concavity of Pareto fronts (PFs), which is not common in the existing MOEAs, it may improve the performance of MOEAs. Spurred by this advantage, we propose a many-objective evolutionary algorithm with estimating the Convexity-Concavity of PFs and Clustering, named MaOEA-3C. Specifically, the convexity-concavity of PF is estimated according to a well-converged and well-distributed elitist archive that is updated periodically using non-dominated sorting and a niche-based method. Then, the solution fitness is computed according to the estimation result, enhancing the selection pressure and promoting the convergence when the Pareto dominance fails to select solutions. Additionally, the solutions in the elitist archive guide evolving directions for the current population by clustering, acting like reference vectors in decomposition-based algorithms, thus maintaining the diversity of solutions. The performance of MaOEA-3C is compared with seven state-of-the-art algorithms, and the results demonstrate the effectiveness and competitiveness of MaOEA-3C on many-objective optimization problems.

Production-sharing of critical resources with dynamic demand under pandemic situation: The COVID-19 pandemic

The COVID-19 virus’s high transmissibility has resulted in the virus’s rapid spread throughout the world, which has brought several repercussions, ranging from a lack of sanitary and medical products to the collapse of medical systems. Hence, governments attempt to re-plan the production of medical products and reallocate limited health resources to combat the pandemic. This paper addresses a multi-period production-inventory-sharing problem (PISP) to overcome such a circumstance, considering two consumable and reusable products. We introduce a new formulation to decide on production, inventory, delivery, and sharing quantities. The sharing will depend on net supply balance, allowable demand overload, unmet demand, and the reuse cycle of reusable products. Undeniably, the dynamic demand for products during pandemic situations must be reflected effectively in addressing the multi-period PISP. A bespoke compartmental susceptible-exposed-infectious-hospitalized-recovered-susceptible (SEIHRS) epidemiological model with a control policy is proposed, which also accounts for the influence of people’s behavioral response as a result of the knowledge of adequate precautions. An accelerated Benders decomposition-based algorithm with tailored valid inequalities is offered to solve the model. Finally, we consider a realistic case study – the COVID-19 pandemic in France – to examine the computational proficiency of the decomposition method. The computational results reveal that the proposed decomposition method coupled with effective valid inequalities can solve large-sized test problems in a reasonable computational time and 9.88 times faster than the commercial Gurobi solver. Moreover, the sharing mechanism reduces the total cost of the system and the unmet demand on the average up to 32.98% and 20.96%, respectively.

Minimizing the Expected Renewable Resource Costs in a Project with Stochastic Resource Availability

In this paper, we study the well-known resource availability cost problem with stochastic resource availability. The objective is to determine the initial levels of all renewable resources and establish a schedule corresponding to each scenario such that the expected resource availability cost is minimized. We assume that resource shortfalls can be compensated externally but at a noticeable higher cost. We formulate the problem as a two-stage stochastic programming model (TSSPM). We also develop an exact decomposition-based algorithm (DBA) for the particular case of the problem with at most two resources, which also functions as a heuristic for the original problem. Since the number of scenarios influences the performance of the developed solution approaches, we utilize a fast scenario reduction method to reduce the number of scenarios. Computational results indicate that the DBA outperforms the TSSPM formulation in solution quality and CPU runtime.

A generalized Benders decomposition-based algorithm for heat conduction optimization and inverse design

Heat conduction optimization benefits many important applications and attracts researchers’ interest unceasingly. Here we present an alternative heat conduction optimization algorithm on the basis of generalized Benders decomposition technique. In this algorithm, the heat conduction optimization problem is first decomposed to a subproblem and a master problem. The subproblem calculates the temperature field with the given thermal conductivity distribution, updates the upper boundary of objective, and constructs an optimality cut at the current point. The master problem updates the lower boundary of objective from solving the programming problem formed by all optimality cuts generated. The subproblem and master problem are solved alternately, the two boundaries approach mutually, and the optimal solution can be reached. The proposed algorithm is validated by applying it on the classic “volume-to-point” problem. Results show that the average and maximum temperature in the domain can be effectively reduced. It is further extended to the topology optimization to obtain discrete material distribution, and numerical studies are also conducted for validation. Finally, the inverse design of thermal cloak is studied by using the proposed algorithm, and square and circular thermal cloaks are numerically designed and verified. All cases studied demonstrate the efficacy and flexibility of the proposed algorithm.

A nested Benders decomposition-based algorithm to solve the three-stage stochastic optimisation problem modeling population-based breast cancer screening

Population-based cancer screening programmes invite high-risk population groups to screenings in order to increase the probability of an early diagnosis. In this paper, we study the organisation of preventive breast cancer screening, accounting for both scheduling of patients and planning of resources. Mammography screening comprises a two-stage healthcare process, encompassing a patient scan in a mammography unit and a scan examination by a central coordination center. Objectives are to minimise patient flow times and maximise resource efficiency and number of patients treated. Performance of population-based screening programmes is hampered due to large rates of patient no-shows, which is partially remedied by giving patients the option to cancel or reschedule their appointment. We model the scheduling problem as a three-stage stochastic optimisation problem and propose a diving heuristic relying on Sample Average Approximation and nested Benders decomposition to find high-quality integer solutions. Computational experimentation is performed on real-life instances to benchmark the proposed method to alternative methodologies. Results demonstrate that the proposed heuristic yields a stable performance for instances of different sizes. However, integrating the three decision stages increases significantly the complexity, such that larger-sized instances are preferably solved via two separate solution stages to improve resource efficiency. In addition, insights are provided in the value of stochastic optimisation and strategies to cancel or reschedule appointments mitigating the impact of no-show uncertainty.

A resilient inventory management of pharmaceutical supply chains under demand disruption

Inspired by the global supply chain disruptions caused by the COVID-19 pandemic, we study optimal procurement and inventory decisions for a pharmaceutical supply chain over a finite planning horizon. To model disruption, we assume that the demand for medical drugs is uncertain and shows spatiotemporal variability. To address demand uncertainty, we propose a two-stage optimization framework, where in the first stage, the total cost of pre-positioning drugs at distribution centers and its associated risk is minimized, while the second stage minimizes the cost of recourse decisions (e.g., reallocation, inventory management). To allow for different risk preferences, we propose to capture the risk of demand uncertainty through the expectation and worst-case measures, leading to two different models, namely (risk-neutral) stochastic programming and (risk-averse) robust optimization. We consider a finite number of scenarios to represent the demand uncertainty, and to solve the resulting models efficiently, we propose L-shaped decomposition-based algorithms. Through extensive numerical experiments, we illustrate the impact of various parameters, such as travel time, product’s shelf life, and waste due to transportation and storage, on the supply chain resiliency and cost, under optimal risk-neutral and risk-averse policies. These insights can assist decision makers in making informed choices.