CPLEX Solver Research Articles

Assessing the sustainability of time-dependent electric demand responsive transit service through deep reinforcement learning

Demand responsive transit (DRT) is expected to offer enormous possibilities for fulfilling the ever-growing diversified demand while promoting the urban sustainability. Nevertheless, it seems to remain critical but intractable to make the routing decision in response to the time-dependent travel speeds. Considering the risk of speed uncertainty, deep reinforcement learning (DRL) algorithm is presented to address the time-dependent electric DRT problem in this study. Long short-term memory (LSTM) is integrated into the attention mechanism at the decoding process. To evaluate the sustainability, the reward function can be subdivided into the number of served passengers, regret utility, and carbon emissions. To testify the effectiveness, we made a comparison between the CPLEX solver, NSGA-II, and the proposed algorithm in a realistic transportation network of Beijing. The computational results demonstrate that DRL algorithm with shorter computation time and better solutions is dramatically superior to the other approaches. Therefore, the DRL algorithm provides a more efficient framework for addressing the time-dependent electric DRT problem while improving the sustainability of the environment and society.

Optimal configuration of energy storage system capacity in traction power supply system considering photovoltaic consumption

In order to achieve energy savings and promote on-site integration of photovoltaic energy in electrified railways, a topology structure is proposed for the integration of photovoltaic (PV) and the energy storage system (ESS) into the traction power supply system (TPSS) based on a railway power conditioner (RPC). This paper analyzes the composition and operation principles of this structure. To assess the economic benefits brought by the integration of photovoltaic and energy storage systems, a bilevel optimization model is established, with the objectives of optimizing energy storage capacity configuration and photovoltaic energy integration. The KKT (Karush–Kuhn–Tucker) method is employed to transform the model into a single-layer mixed-integer linear programming model, which is then solved using the CPLEX solver in MATLAB. The research findings indicate that, with the configuration of the ESS, the optimal PV consumption rate achieved is 96.8749%. Compared to a 100% PV consumption rate, the ESS capacity configuration is reduced by 13.14%, and the overall operational cost of the TPSS is at its lowest. The study suggests that the proposed bilevel optimization algorithm can more effectively consider PV consumption, leading to enhanced economic performance of the TPSS operation.

A multi-objective optimization model for medical waste recycling network design under uncertainties

Transporting medical waste (MW) generated by medical institutions (MIs) is a process that poses potential threats to the environment and public safety. Therefore, it is vital to find a safe and efficient way to transport this type of waste to disposal centers (DCs). However, there are challenges in the transportation of MW due to random factors such as the generation of waste in an unpredictable manner and unforeseen travel times. In this paper, we propose a bi-level optimization model to minimize site selection costs, transportation costs, time-window penalties costs, and transportation risks under uncertainties. The concepts of “loading reliability”, “travel time reliability” and “transportation risk” are adopted in the proposed optimization model. The simulated annealing algorithm (SA) is employed to address the optimal location problem (Upper level), which involves minimizing the construction cost, transportation cost (DC-CP-DC), and transportation risk (estimated using Bayesian method). To tackle the capacity-constrained vehicle routing problem considering transportation risk and time window penalties (Lower level), we propose an improved genetic algorithm named harmony search algorithm (IHSGA). Subsequently, the results from the lower level are looped back to the upper level, fostering mutual influence between the two stages. We demonstrate the effectiveness and correctness of the proposed model and algorithm using S city in China as an illustrative example. Furthermore, a series of sensitivity analyses were conducted to examine the impact of various factors. The findings highlight the pivotal roles of both travel time reliability and loading reliability in designing the medical waste recycling network. In comparison to the general Genetic Algorithm (GA) and CPLEX solver, the modified IHSGA presented in this paper exhibits superior performance.

A chance-constrained optimization approach integrating project scheduling and material ordering to manage the uncertain material supply

To deal with the impact of uncertain material supply on the implementation of projects, we investigate a problem of concurrently finding a robust baseline schedule and a material ordering plan under different levels of uncertainty. Assuming the material warehouses are restricted, a chance-constrained model of the integrated resource-constrained project scheduling and material ordering problem with a confidence level (1−θ) is thus formulated. To tackle the difficult joint chance constraints, we firstly transform the chance-constrained model into a scenario-based integer programming model by the sample average approximation approach. Based on dominance relationship among scenarios, we then derive an exact branch-and-bound algorithm and a sampling-based genetic algorithm (SGA) to solve the model. For the branch-and-bound algorithm, a tailor-made branching scheme and four pruning rules are developed to accelerate the search process. For the SGA, two sampling methods and a local search procedure are presented to boost solution quality. Furthermore, extensive numerical experiments are carried out to test the performance of the proposed algorithms. Specifically, 4608 instances with four different confidence levels and six different sample sizes are generated. Then the Taguchi method is employed to calibrate the parameters of the SGA. Besides, the numerical results demonstrate that the proposed branch-and-bound algorithm can solve more instances with shorter CPU times than the CPLEX solver, and the solution quality of the proposed SGA is far better than that of two existing meta-heuristics and two variants of SGA. Finally, a sensitivity analysis for the key parameters of the model is conducted. By considering the uncertain material supply, limited warehouse capacity and various confidence levels, our research contributes to the effective decision on project scheduling and material ordering in real-world contexts.

The electric vehicle routing problem of a new mobile charging service

Abstract A novel mobile charging service that utilizes vehicle-to-vehicle (V2V) charging technology has recently been proposed as a supplement to fixed charging infrastructure (CI), enabling electric vehicles (EVs) to exchange electricity. This study formulates a vehicle routing problem (VRP) of vehicle-to-vehicle (V2V) charging, optimizing the routing of DVs to service RVs while taking into account their willingness to join the V2V charging platform. A mixed integer linear programming (MILP) model is established to optimize the VRP-V2V (i.e. the VRP of V2V charging), which is known to be NP-hard. To solve large-scale instances for real-world applications, we propose an adaptive large neighborhood search (ALNS) algorithm, which, when combined with the structure of the VRP-V2V problem, utilizes four local search procedures to enhance solution quality following destroy and repair operators. Results indicate that the proposed ALNS algorithm outperforms the optimization solver CPLEX in small-scale instances, and can solve large-scale instances that are infeasible using CPLEX solver. In a numerical analysis of Changsha's large-scale network, we demonstrate that the V2V platform can save an average of 33.1% on the charging cost of recharging vehicles, hence raising customer satisfaction with charging services and reducing range anxiety. The platform's profitability is also increased by using V2V charging in areas lacking fixed charging infrastructure.

A two-stage risk-based framework for dynamic configuration of a renewable-based distribution system considering demand response programs and hydrogen storage systems

Distribution feeder reconfiguration (DFR) in distribution systems can enhance operating conditions by reducing losses and improving voltage indices. This paper introduces a dual-stage risk-based framework that concurrently tackles day-ahead reconfiguration and microgrid scheduling within the distribution network. To control the negative aspects of uncertainties, the proposed framework integrates energy storage systems (ESS/HSS) and demand response programs (DRPs) at the network level, enhancing adaptability. The initial stage of the proposed model employs the AC power flow model, utilizing loss and voltage deviation functions as objective benchmarks for network reconfiguration. The scheduling is meticulously executed per interval, deriving optimized structures under diverse scenarios with the aid of a case reduction technique (CRT) to streamline solutions. The ultimate solution employs the grey wolf optimization (GWO) algorithm and CPLEX solver in the first and second stages respectively. Outcomes from applying this approach to the adjusted 118-bus network manifest improved operational conditions and voltage quality through reconfiguration. Impressively, the integration of ESS/HSS and DRPs yields a substantial 22.34% reduction in total operating costs, a conclusion substantiated by the numerical findings. Furthermore, by leveraging the CRT, a remarkable 56.17% reduction in problem-solution time is achieved.

An Optimized Advantage Actor-Critic Algorithm for Disassembly Line Balancing Problem Considering Disassembly Tool Degradation

The growing emphasis on ecological preservation and natural resource conservation has significantly advanced resource recycling, facilitating the realization of a sustainable green economy. Essential to resource recycling is the pivotal stage of disassembly, wherein the efficacy of disassembly tools plays a critical role. This work investigates the impact of disassembly tools on disassembly duration and formulates a mathematical model aimed at minimizing workstation cycle time. To solve this model, we employ an optimized advantage actor-critic algorithm within reinforcement learning. Furthermore, it utilizes the CPLEX solver to validate the model’s accuracy. The experimental results obtained from CPLEX not only confirm the algorithm’s viability but also enable a comparative analysis against both the original advantage actor-critic algorithm and the actor-critic algorithm. This comparative work verifies the superiority of the proposed algorithm.

Large-volume LEO satellite imaging data networked transmission scheduling problem: Model and algorithm

With the current miniaturization and cost reduction trend, many small imaging satellites are deployed in low Earth orbit (LEO). Efficient scheduling of transmission links is crucial for handling the large volume of imaging data in the time-varying inter-satellite broadband communication networks. This ensures optimal utilization of inter-satellite link resources and gives rise to a novel problem known as the Large-volume LEO satellite Imaging Data Networked Transmission Scheduling Problem (LLSIDNTSP). This problem requires the integrity of the imaging data received on the ground station. A Specific Time-Evolving Graph (STEG) model is introduced to formulate this problem, while a highly effective Sequential Two-Phased Heuristic Algorithm (STPHA) is proposed to solve it. STPHA determines an optimized Contact Plan (CP) with a Contact-Fast Construction Algorithm (CFCA) in the first phase. With this CP as input, it produces an optimal transmission schedule with Linear Programming in the second phase. The CFCA incorporates a novel heuristic called Mission Residual Volume Factor(MRVF), which guides the selection of a proper inter-satellite and satellite-to-ground link at each construction step. Extensive simulation results demonstrate the effectiveness of the proposed STPHA. In particular, it can achieve the optimal solution for small-sized scenarios with one-hundredth of the computing time used by the exact solver CPLEX. Also, it is consistently better than other heuristic algorithms adapted from the literature for large-sized scenarios. Additional experimental analysis is conducted to showcase the effectiveness of the innovative components of STPHA.

An integrated energy system “green-carbon” offset mechanism and optimization method with Stackelberg game

The low-carbon economic operation of integrated energy systems (IES) cannot be separated from the carbon trading and green certificate trading market. Therefore, a low-carbon market mechanism and optimization method for IES is proposed. First, we establish a “green-carbon” offset mechanism to realize the conversion from tradable green certificate (TGC) to carbon quotas to offset system's carbon emissions. Second, considering the impact of market incentives and users' consumption behavior on IES, an energy management method of IES is put forward based on Stackelberg game. IES operators as leaders decide energy prices and trading strategies of carbon, TGC and multi-energy. Energy users as followers participate in the integrated demand response based on energy price. The game is solved by an improved adaptive catastrophic genetic algorithm and CPLEX solver. Finally, we take an industrial park in China as an example to analyze. The results show that the proposed method can significantly reduce the system's carbon emissions while improving the benefits for both IES and consumers.

An ensemble of brain storm optimization and Q-learning methods for distributed flexible job shop scheduling problems with distribution operations

Distributed manufacturing scheduling problems have attracted much concern from both industrial and academic areas. Nevertheless, distributed scheduling problems with distribution operations are seldom studied. This work proposes a distributed flexible job shop scheduling problem with distribution operations. A set of jobs is handled at distributed flexible job shops, and then the finished jobs are transported to their corresponding customers following given due dates. First, a mixed integer programming model is established to minimize total tardiness. Second, an ensemble of brain storm optimization and Q-learning methods is developed to solve the formulated model. Six heuristics are hybridized to generate a high-quality initial population. A Q-learning method is devised by fully employing found search information to guide subsequent search processes instead of using fixed parameters as basic brain storm optimization. A variable neighborhood search method combining problem-specific knowledge is designed to further refine the found best individual. At last, the formulated model and method are compared with three state-of-the-art metaheuristics and a mathematical programming solver CPLEX via using a group of problem instances. The results and analysis demonstrate that the developed model and algorithm have more powerful competitiveness in addressing the studied problem.

Orderly charging strategy for electric vehicles based on multi-level adjustability

The development of electric vehicles (EVs) is one of the essential ways to reduce environmental pollution. With the rapid growth in EVs, an orderly charging strategy based on multi-level adjustable charging power is proposed to address the problem of increasing peak-to-valley difference due to disorderly charging in different scenarios. Based on the information of multi-level adjustable charging power, information about staying in the residential area, and charging demands of EVs, this research designs a centralized charging mode with complete information under the centralized scenario and a decentralized charging mode with incomplete information under the decentralized scenario. This research takes the minimization of peak-to-valley difference in the residential area as the objective function and considers that the charging pile can have the function of multi-level adjustable charging power to support these two scenarios. Two charging modes of the charging pile are designed, and orderly charging model of EVs in the residential area is constructed. EVs can select charging time and charging power by using Bluetooth or code scanning in the charging pile. This research aims to design two orderly charging modes to effectively implement peak shaving and valley filling while ensuring the charging demand of EVs. This research uses the CPLEX solver in MATLAB to solve the objective. The simulation results show that EVs can reasonably select the multi-level adjustable charging power under different scenarios and provide a reference for engineering related to orderly charging. Strategy 4, proposed in this research, has the lowest peak-to-valley difference of the four strategies. The peak-to-valley difference is only 87 kW under the centralized scenario, and the peak-to-valley difference is 282 kW under the decentralized scenario.

Low-Carbon Economy Optimization of Integrated Energy System Considering Electric Vehicles Charging Mode and Multi-Energy Coupling

To realize the multi-energy coupling integrated energy system to meet the multi-class load demand and achieve the goal of low-carbon economic operation, a bi-level optimal configuration method for low-carbon economic operation of multi-energy coupling integrated energy system under different charging modes of electric vehicles is proposed. Firstly, an integrated energy system including cooling-heating-power-gas coupling is established. Then, within the level of intraday scheduling, factors such as ladder carbon trading mechanisms and different charging modes of electric vehicles are considered to achieve the lowest daily scheduling cost. In the configuration planning level, based on the daily operation cost, the equipment capacity is configured with the lowest equipment investment and annual operation costs. The bi-level model is solved by CPLEX solver and the optimal configuration scheme and scheduling results are obtained by mutual iteration. Finally, the impact of different charging methods of electric vehicles on the system economy and low-carbon performance is demonstrated through simulation examples. The results show that the charging method of electric vehicles and the carbon trading mechanism in this paper can significantly reduce carbon emissions and improve the system's operating cost. The proposed configuration approach can well achieve low-carbon economic operation of the multi-energy coupling integrated energy system.

A novel socio-economic-environmental model to maximize prosumer satisfaction in smart residential complexes

As the adoption of distributed and renewable energy resources helps consumers evolve into prosumers who generate and trade their own energy, optimizing distributed renewable energy resources, electric vehicles, and energy storage in smart residential complexes is crucial to enhance satisfaction and capitalize on their potential for environmental and economic benefits. Nonetheless, limited progress has been made to quantify the impact of prosumer and energy manager preferences and the integrated socio-economic-environmental dynamics on energy scheduling and stakeholder satisfaction within smart communities. This study aims to overcome this challenge by proposing a socio-economic-environmental optimization model based on a preference-oriented management approach, which quantifies the impact of energy scheduling on stakeholder satisfaction in smart communities. The model inputs include infrastructure configurations, energy consumption patterns, and weather data. The simulation method includes the application of deep learning and System Advisor Model software in predicting weather conditions and photovoltaic and wind turbine systems energy generation. The simulation results are then imported as parameters in GAMS software to optimize the stakeholder satisfaction using CPLEX solver. Quantitative results show that with the simultaneous use of electric vehicles and energy exchange between energy communities, the highest level of satisfaction of the stakeholders in the smart grid including energy communities has been achieved at hour 24 and at the rate of 0.99 per-unit. The model reveals notable enhancements in stakeholder satisfaction, particularly through the integration of electric vehicles and energy trading in smart grids. It underscores the critical impact of aligning renewable energy strategies with prosumer socio-economic-environmental preferences, offering valuable insights for energy managers, policymakers, and community planners in fostering efficient, community-oriented smart grid systems.

Multi-Scheme Optimal Operation of Pumped Storage Wind–Solar–Thermal Generation System Based on Tolerable Energy Abandonment

In multi-energy complementary power generation systems, the complete consumption of wind and photovoltaic resources often requires more costs, and tolerable energy abandonment can bring about the more reasonable optimization of operation schemes. This paper presents a scheduling model for a combined power generation system that incorporates pumped storage, wind, solar, and fire energy sources. Through a comparison of schemes, the energy regulation function of the pumped storage power station was verified and analyzed. The CPLEX solver and MOPSO algorithm were employed to solve the daily output of a pumped storage power station in the Gansu region under various scenarios. The incorporation of pumped storage power plants has the potential to provide many benefits, including a reduction in operating expenses by about CNY 1.1163 million, a decrease in carbon emissions by 491.24 t, an enhancement in the stability of thermal power by 2.39%, and an improvement in the combined system capability to absorb additional energy. The correlation between the indicators of the combined system and the penetration rate of renewable energy is non-linearly influenced by changes in the power capacity configuration. Ultimately, the multi-objective optimization computation yields the ideal operational scheme for each power source, taking into account a tolerable energy abandonment mode.

Optimal scheduling of the CSP–PV–wind hybrid power generation system considering demand response

In order to solve the problem of there being a high proportion of wind and photovoltaic (PV) abandonment in the new energy system, an optimal dispatching method of concentrated solar power (CSP)–PV–wind hybrid power generation considering demand response is proposed. First, on the basis of the combination of wind and PV power stations and CSP stations, electric heating (EH) devices are used to convert unconsumed wind and PV power into thermal energy stored in the thermal storage system of the CSP station. Second, based on the difference in response time and response volume of customers, a stepped incentive-based demand response (IBDR) approach is introduced. Thus, a CSP–PV–wind power optimal dispatch model taking into account IBDR is established to achieve coordinated source-load dispatch. Finally, the CPLEX solver is invoked to optimize day-ahead scheduling with the goal of the lowest system comprehensive cost. Example analysis is used to confirm the proposed method’s usefulness in enhancing the system’s wind and PV power consumption capacity and reducing the system’s comprehensive cost.

A math-heuristic approach for scheduling the production and delivery of a mobile additive manufacturing hub

This paper investigates an innovative printing-while-delivering paradigm within a mobile additive manufacturing (MAM) hub. Different from the conventional production-first-delivery-second (PFDS) mode, the MAM hub, comprising a 3D printer and a truck, can seamlessly integrate the production and delivery processes. Throughout the delivery process of the MAM hub, the embedded 3D printer within the truck concurrently prints products for customers in batches. This capability significantly diminishes customer dissatisfaction caused by time delays between order placement and product receipt, which requires coordinating the delivery routing of truck and the production scheduling of 3D printer. To tackle this problem, a mixed integer programming model is firstly established to minimize the required time of the MAM hub returning to depot after completing all deliveries. Then, a math-heuristic approach combining the genetic algorithm and branch-and-bound is devised to solve the mathematical model efficiently. The delivery sequence of truck is represented as a chromosome in the genetic algorithm; while, for each delivery sequence, the optimal production scheduling of 3D printer is obtained by branch-and-bound based on the theoretical analysis about the relationship between production and delivery sequences. In the numerical experiments, the proposed math-heuristic algorithm produces results identical to CPLEX solver outcomes in small-scale cases. For larger instances, it outperforms traditional genetic algorithms by 3.39% to 19.54%. The proposed batch printing mode consistently surpasses the non-batch mode by 10% to 25%. Moreover, compared to PFDS, the printing-while-delivering paradigm reduces trip time by over 40%. Finally, we analyze the effects of customer quantity, distribution radius, and printing time on the objective, providing management insights about optimal production and delivery strategy. The research finding not only aids in scheduling the MAM hub but also holds the potential to address other applications characterized by simultaneous production and delivery requirements.

A multi-neighborhood tabu search for solving multi-budget maximum coverage problem

Many practical decision-making problems involve selecting k distinct subsets of objects from a set of candidate objects such that the chosen objects optimize a given goal while satisfying some constraints. The multi-budget maximum coverage problem (MMCP) is a general model that facilitates formulating such decision-making problems. Given a budget of k, a set of elements with profits, and a set of items with costs where each item is composed of a subset of the elements, the MMCP aims to select k disjoint subsets of items that maximize the total profits of the elements covered by these subsets, while their costs do not exceed their respective budgets. In this work, we present a multi-neighborhood tabu search (MTS) for this NP-hard problem. MTS comprises three essential components that employ four efficient neighborhoods to collaboratively perform the neighborhood exploration to obtain high-quality local optima, select neighborhood solutions with added perturbations, and generate offspring solutions based on population information exchange. To evaluate the effectiveness of MTS, we performed computations on 30 benchmark instances of the extended BMCP. We compared the results with the approximation algorithm, genetic algorithm, particle swarm optimization algorithm, and CPLEX solver. We also provide experiments to highlight the beneficial effect of the essential components in the MTS algorithm. The experimental results demonstrate that MTS not only performs efficiently but also yields solutions of superior quality.

Optimizing Connectivity and Coverage for Millimeter-Wave-Based Networks

In this article, the problem of achieving the minimum backbone connectivity cost while simultaneously maximizing user coverage for 5G millimeter-wave (mmWave)-based networks is considered. Let G=(N,E) be an input graph instance with a set of nodes N (base stations) and a set of edges E. It is assumed that G represents a wireless backbone network. Let M represent a set of users to be covered by G. Note that mmWave technology has been considered in the literature as an important candidate solution for 5G networks due to its low latency. However, there remain some problems to be addressed before using this technology. A serious one is that millimeter waves cannot cover large transmission distances. In this article, the proposed methodology consists of formulating mixed-integer programming models to deal with the problem from a management point of view. Our models allow the determination of which of the nodes of G should be active and connected while simultaneously maximizing the total number of covered users. The models are solved with the CPLEX solver using its branch and cut and automatic Benders decomposition algorithms. For this purpose, symmetric complete and sparse graphs are considered. Using the symmetry concept, it is considered that the distances between base stations and users and between base stations themselves are symmetrical. Finally, an efficient local search meta-heuristic is proposed that allows for finding near-optimal solutions. Our numerical experiments indicate that the problem is hard to solve optimally. Thus, instances with up to 40 nodes and 500 users have been solved to optimality so far. In particular, it is observed that one of the models presents slightly better performance in terms of CPU time. Finally, the heuristic approach allows us to obtain tight solutions with less computational effort when dealing with even larger instances of the problem.

Bi-level optimization configuration method for microgrids considering carbon trading and demand response

Under the background of the shortage of traditional energy and the increasingly serious environmental problems, this paper proposes a bi-level optimization configuration method for microgrids based on stepped carbon trading and price-based demand response. The stepped carbon trading mechanism is introduced into the planning model to clarify the impact of construction processes on land carbon emissions. Simultaneously, price-based demand response during system operation is introduced, guiding users to change the electricity consumption strategies to promote the consumption of renewable energy. Then, a bi-level optimal configuration framework is constructed. The upper level is optimized to allocate the capacity of the microgrid, with the lowest annual equivalent comprehensive cost as the objective function. The lower level is optimized for microgrid operation, with the minimum sum of the microgrid operation cost and carbon emission cost as the objective function. In view of the advantages of enhanced whale optimization algorithm (E-WOA) in solving multi-dimensional feature selection problems, E-WOA and CPLEX solver are combined to solve the bi-level optimization model for the first time. Simulation results show that after introducing a stepped carbon trading mechanism, the system carbon emissions decreased by 23.09%. Considering price-based demand response under the premise of introducing a stepped carbon trading mechanism, the total cost decreased by 3.57% and the carbon emissions decreased by 19.83%.

Optimized operational approach for multi-type reactive power compensation to enhance the grid integration strength of new energy clusters

The insufficient system strength in the high-proportion new energy access area has gradually emerged as a crucial factor contributing to the transient overvoltage issue. Therefore, it is imperative to propose a reactive power optimization operation mode that takes into consideration both the power grid strength and system operating voltage of the new energy cluster system. Firstly, the relationship between the evaluation index of power grid strength and the performance of system voltage response is elucidated, while analyzing the influence mechanism of various reactive power compensation devices on the power grid strength of new energy cluster systems. Then, a reactive power operation optimization model is proposed to maximize the strength of the system grid and minimize the voltage deviation. To solve this problem, a hybrid approach combining genetic algorithm and CPLEX solver is employed. Finally, the effectiveness of the proposed method is validated through a typical simulation example.