CPLEX Solver Research Articles

Decentralized energy management system of distributed energy resources as virtual power plant: Economic risk analysis via downside risk constraints technique

A virtual power plant (VPP), as a decentralized energy management system (EMS), can be a handy application to aggregate and schedule distributed energy resources (DER). The DERs can be dispatchable and non-dispatchable energy resources wishing to participate in the day-ahead (DA) electricity market. Therefore, they can provide the grid with higher reliability and safety margins. However, there are uncertainties in the market that VPP should manage and the associated risks to obtain robust scheduling in such a probabilistic environment. In this paper, risk-oriented stochastic optimization is proposed to investigate the market's uncertainties and obtain the maximum profit while ensuring the safety margins of the network. Downside risk constraints (DRC) are integrated into the model to cover the risks. So, the risk-based scheduling of VPP is obtained. The proposed risk-based framework is formulated as the mixed-integer linear programming (MILP) model, solved by the CPLEX solver of GAMS software. The proposed model is applied to an 18-bus test system to investigate the proposed risk-oriented stochastic optimization of VPP. Finally, the costs, revenues, and total profit are illustrated, compared, and analyzed in the model's risk-neutral (RN) and risk-averse (RA) states so that an appropriate decision can be made. Moving toward the RA strategy lowers the amount of generated power of the DG and the purchased power from the upstream grid, consequently leading to a lower amount of sold power by the VPP within the studied power grid. The analysis shows that the RA strategy decides with low risk by decreasing the cost and revenue of the VPP simultaneously. In this regard, the results indicate that the average profit of the VPP decreased by 8.62%, from $15407 to $14079 when decision-maker tends to take risk-averse decisions with zero risk.

An Adaptive Large Neighborhood Search Heuristic for the Electric Vehicle Routing Problems with Time Windows and Recharging Strategies

This study addresses a new electric vehicle routing problem with time windows and recharging strategies (EVRPTW-RS), where two recharging policies (i.e., full or partial recharging) and three recharging technologies (i.e., normal, rapid, and ultra-rapid) are considered. For this problem, we first develop a mixed-integer linear programming model defined in a series of vertices including a depot, a series of recharging stations, and a set of customers. Due to the strong NP-hardness of EVRPTW-RS, a tailored adaptive large neighborhood search heuristic (ALNS) which contains a number of advanced efficient procedures tailored to handle the proposed problem is developed. Numerical experiments for benchmark instances generated based on the Greater Toronto Area and Ontario in Canada are conducted to evaluate the performance of the proposed model and ALNS. Computational results demonstrate that the ALNS is highly effective in solving EVRPTW-RS and outperforms commercial solver CPLEX. Moreover, the advantages of the proposed recharging strategies are illustrated and some recommendations are provided for stakeholders when using electric vehicles for delivery.

Multiobjective U-Shaped Disassembly Line Balancing Problem Considering Human Fatigue Index and an Efficient Solution

The progress of science and technology speeds up the replacement of products and produces a large number of end-of-life products. Traditional incineration causes a waste of resources and pollution to the environment. Disassembling and recycling end-of-life products are the recommended way to maximize the utilization of resources and reduce environmental pollution. Disassembly performance is affected by many factors, such as the disassembly posture of the human body, the fatigue of workers on a workstation, disassembly profit, and task precedence relationship. In this article, a mixed integer linear programming mathematical model for U-shaped layout disassembly line balancing problems is developed, in which the balance of workers’ fatigue indices is an optimization objective in addition to disassembly profits. An efficient solution to the problem that uses a collaborative resource allocation strategy of the multiobjective evolutionary algorithm is proposed. The linear programming solver CPLEX is used to verify the accuracy of the model and compared with the proposed algorithm. Experiments demonstrate that the algorithm is significantly superior to the CPLEX solver in handling large-scale cases. The proposed algorithm is also compared with two well-known algorithms, which further verifies its superiority.

Knowledge-Based Reinforcement Learning and Estimation of Distribution Algorithm for Flexible Job Shop Scheduling Problem

In this study, a flexible job shop scheduling problem with time-of-use electricity price constraint is considered. The problem includes machine processing speed, setup time, idle time, and the transportation time between machines. Both maximum completion time and total electricity price are optimized simultaneously. A hybrid multi-objective optimization algorithm of estimation of distribution algorithm and deep Q-network is proposed to solve this. The processing sequence, machine assignment, and processing speed assignment are all described using a three-dimensional solution representation. Two knowledge-based initialization strategies are designed for better performance. In the estimation of distribution algorithm component, three probability matrices corresponding to solution representation are provided. In the deep Q-network component, 34 state features are selected to describe the scheduling situation, while nine knowledge-based actions are defined to refine the scheduling solution, and the reward based on the two objectives is designed. As the knowledge for initialization and optimization strategies, five properties of the considered problem are proposed. The proposed mixed integer linear programming model of the problem is validated by exact solver CPLEX. The results of the numerical testing on wide-range scale instances show that the proposed hybrid algorithm is efficient and effective at solving the integrated flexible job shop scheduling problem.

Design of urban medical waste recycling network considering loading reliability under uncertain conditions

The ongoing global coronavirus pandemic (COVID-19) has significantly increased urban medical waste. Such waste often contains pathogenic microorganisms, harmful chemicals, and even radioactive and defective substances, hence imposing disease transmission and public health risks. Nevertheless, due to multiple factors, the amount of medical waste produced in medical institutions is stochastic. This paper proposed an optimization model for a waste recycling network consideration of loading reliability to minimize the collective cost of location, vehicle usage, and transportation. A modified ant colony algorithm combined with the K-means clustering method based on a genetic algorithm is then proposed (MACO-GKA) to solve the optimal location problem and the vehicle routing problem (LP-VRP). The numerical examples are then conducted in Xuzhou City, China to evaluate the performance of the proposed model. Taking the loading reliability level θ=0.9 as an example, the results show that the total cost will reach $100546.53 when collection points are not set, but decrease to $86,907.11 when they are set. In the latter case, the total cost was reduced by 13.57%. The detailed results indicate that the selection and establishment of medical waste collection points are essential factors in designing an urban medical waste recycling network. The proposed MACO-GKA algorithm also outperforms the CPLEX solver.

Optimized Power and Capacity Configuration Strategy of a Grid-Side Energy Storage System for Peak Regulation

The optimal configuration of the rated capacity, rated power and daily output power is an important prerequisite for energy storage systems to participate in peak regulation on the grid side. Economic benefits are the main reason driving investment in energy storage systems. In this paper, the relationship between the economic indicators of an energy storage system and its configuration is first analyzed, and the optimization objective function is formulated. Then, according to the objective limitations of the energy storage system configuration and operation, the constraints are formulated. A set of typical parameters is selected, and the CPLEX (IBM ILOG CPLEX Optimization Studio) solver is used in MATLAB to solve the optimal configuration results. Several sets of optimization results are obtained by taking different subjective coefficient β values, and the economic and social benefits of the optimization results are analyzed. When the economic benefits of the energy storage system are more important, the value of β needs to be smaller, such as a value of 1000. Conversely, when the peak-regulation effect is more important, the value of β should be larger. Finally, configuration results of the control groups are given, and the effect of optimizing the calculation for improving economic benefits is verified.

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.

Integrated Planning of Feeder Route Selection, Schedule Design, and Fleet Allocation with Multimodal Transport Path Selection Considered

In the shipping network optimization, the feeder liner companies not only need to decrease the operation cost by comprehensively optimizing the route, schedule, and fleet but also try to increase the operation income by attracting more shippers, with multimodal transport-path selection considered. Therefore, this paper proposes the integrated planning of feeder route selection, schedule design, and fleet allocation with shippers’ transport-path selection considered. We utilize the nested Logit model to analyze the shipper selection behavior for the multimodal transport path and then formulate a mixed-integer nonlinear programming model of integrated optimization for route, schedule, and fleet. To solve our nonlinear model, we propose a particle swarm optimization (PSO) framework embedded with CPLEX solver by combining the constraint relaxations and the linearization techniques with the heuristic rules. Based on the multimodal transport system in Northern China, computational experiments were conducted to verify the effectiveness of our model and algorithm. The sensitivity analyses of model parameters show that with the increase in ship rent, feeder liner companies should reduce the ship capacity or try to increase the number of port call. With the increase in fuel price, feeder liner companies should reduce the ship speed under the constraints of the arrival-time window and schedule interval. If shippers’ time utility coefficient is high, feeder liner companies should shorten the sailing time of ships by decreasing the number of port calls or shorten the at-port time of ships by increasing the service frequency. If the multimodal transport paths are cost-advantaged or if the waterway transport time has a small impact on multimodal transport time, feeder liner companies should weigh the increase in income and cost when using the measures of time saving. These management insights provide decision support for the operation practice of liner shipping network optimization.

MPILS: An Automatic Tuner for MILP Solvers

The parameter configuration problem consists of finding a parameter configuration that gives a particular algorithm the best performance. This paper introduces a new multi-phase tuner based on the iterated local search meta-heuristic. This tuner addresses the parameter configuration problem for deterministic MILP solvers that are used to solve challenging industrial optimization problems. Further, the proposed tuner offers a new search strategy based on three ideas. First, instead of tuning in the entire configuration space induced by the parameter set, the multi-phase tuner focuses on a small parameter pool that is dynamically enriched with new promising parameters. Second, it leverages the gathered knowledge during the search using statistical learning to forbid less promising parameter combinations. Third, it tunes on a single instance provided by earlier clustering of MILP instances. A computational study on the widely-used commercial solver CPLEX with instances from the MIPLIB library and a real large-scale optimization problem highlights the promising potential of the tuner.

A GVNS algorithm applied to the single allocation hub location problem with heterogeneous economies of scale

This paper addresses the single allocation hub location problem with heterogeneous economies of scale. This problem consists of selecting the nodes to establish the hubs in order to minimize the total cost of installing the hubs and routing demand flows, assuming that there is an economy of scale that depends on the amount of flow routed in each arc. We proposed a formulation to model the problem and an algorithm based on the General Variable Neighborhood Search (GVNS) meta-heuristic to handle the problem. Computational experiments were performed using instances from the literature with up to 500 nodes. The results show that the GVNS algorithm is effective for solving the instances in terms of runtime and solution quality. The results also show that the proposed formulation outperforms the literature formulation when activating the Benders decomposition method available in the CPLEX solver.

Optimum exploitation of an integrated energy system considering renewable sources and power-heat system and energy storage

The increasing population and energy consumption have led to a greater emphasis on managing and storing different energy sources. Researchers are now focusing on integrating renewable energy into energy systems and improving efficiency through accurate modeling and calculations. This article presents the optimal operation of an integrated energy system that incorporates wind energy as a renewable source. The study focuses on enhancing the modeling accuracy of equipment such as combined heat and power units and storage devices to align the obtained results with real-world scenarios. To effectively manage electrical and thermal loads, a load management program is implemented. Furthermore, the uncertainty of wind speed is addressed using the interval-valued grey decision Theory method. Two sensitivity analyses are conducted to further investigate the system's performance. Firstly, the impact of incorporating storage resources and load management programs on the overall operating cost is examined. The results demonstrate a significant 22.87% improvement in the objective function when both storage devices and load management programs are employed simultaneously. Secondly, a sensitivity analysis is performed to evaluate the objective function's response to changes in the uncertainty budget parameters and wind speed deviation. The findings highlight the greater impact of wind speed deviation on the objective function compared to changes in the uncertainty budget. The problem is formulated as a mixed integer linear programming problem, and the GAMS software and CPLEX solver are utilized to obtain the relevant results. The findings emphasize the potential of integrating wind energy into an integrated energy system and underscore the importance of accurate modeling, load management, and the consideration of storage resources. These insights contribute to the optimization of energy system operations and the advancement of sustainable energy practices.

Daytime and Overnight Joint Charging Scheduling for Battery Electric Buses Considering Time-Varying Charging Power

This work investigates the joint daytime and overnight charging scheduling problem associated with battery electric buses (BEBs) at a single charging station. The objective is to minimize the total charging costs of all BEBs. Two important factors, i.e., peak–valley price and time-varying charging power, are considered to depict real-world charging situations. We establish a mixed-integer programming model for the considered problem, and then conduct a case study together with sensitivity analysis. Numerical results show that compared with the existing first come, first serve rule-based charging solution, the charging schedule obtained by solving the established model via the CPLEX solver can save 7–8% of BEB charging costs. Hence, our model could be applied to improve the BEB charging schedule in practice.

Optimal Dispatch Strategy for Virtual Power Plants with Adjustable Capacity Assessment of High-Energy-Consuming Industrial Loads Participating in Ancillary Service Markets

Amid the context of a sustainable development strategy, there is a growing interest in renewable energy as an alternative to traditional energy sources. However, as the penetration rate of clean energy gradually increases, its inherent features, such as randomness and uncertainty, have led to a surging demand for flexibility and regulation in power systems, highlighting the need to enhance the flexibility of power systems in multiple dimensions. This paper proposes a method for evaluating the adjustable power capacity of a virtual power plant (VPP), which considers the high-energy-consuming industrial load in the day-ahead to real-time stages and establishes an optimization scheduling model for auxiliary service markets based on this method. Firstly, within the day-ahead phase, the VPP is categorized and modeled based on its level of load flexibility regulation. The assessable capacity is then evaluated to establish the adjustable power range of the VPP, and the capacity of the VPP is subsequently reported. Secondly, the adjustable loads inside the VPP are ranked using the performance indicator evaluation method to obtain the adjustment order of internal resources. Finally, on the real-time scale, an optimization scheduling model to minimize the net operating cost of the VPP is established based on real-time peak-shaving and frequency regulation instructions from the auxiliary service market and solved using the CPLEX solver. The case study results show that the proposed method effectively reduces the net operating cost of the VPP and improves the stability of its participation in the auxiliary service market, which verifies the effectiveness of the proposed method.

A tri-layer stochastic framework to manage electricity market within a smart community in the presence of energy storage systems

In recent years, with the restructuring of the electricity market, the main goal of all market participants is to maximize their profits. Among these, the stability of the system as well as the consumers' comfort index (CI) are two important points that should be considered in the scheduling. Hence, this paper presents a tri-layer model for managing a competitive electricity market in the presence of microgrids and demand response (DR) aggregators, in which microgrids determine their strategy for market participation by considering the CI of consumers. In the first layer of the proposed model, the DR aggregator buys part of the consumers load through shiftable and curtailable demand response programs (DRPs), and offers it for sale in the market. The second layer, microgrids do their scheduling with the aim of minimizing operating costs and maximizing the CI, and submit their offers/bids into the market. Finally, in the third layer, the market-clearing price (MCP) is determined by the market manager with the aim of maximizing social welfare. This model is formulated in mixed-integer linear programming (MILP) format and is solved through CPLEX solver in GAMS environment. The simulation results show that the two-objective modelling of the operation problem, despite a 12.18 % increase in total operating costs, increases the average CI by 5.57 %. The results also demonstrate that DR aggregator through the implementation of DRPs leads to a reduction in MCP during the peak period and thus a 5.01 % reduction in total operating costs.

A robust optimization approach for the production-routing problem with lateral transshipment and outsourcing

Despite the fact that there is a large body of literature on the Production Routing Problem (PRP), we were struck by the dearth of research on outsource planning and lateral transshipment. This paper presents a mixed-integer linear programming model for incorporating outsourcing, lateral transshipment, back ordering, lost sales, and time windows into production routing problems. Then a robust optimization model will be introduced to overcome the detrimental effects of demand uncertainty. Considering the scale and complexity of the suggested problem, addressing it in a reasonable time was a challenge. Therefore, three matheuristic algorithms, including Genetic Algorithm (GA), Simulated Annealing (SA), and Modified Simulated Annealing (MSA), are developed for solving large-scale problems. Eventually, computational experiments on disparate instances are performed, and the results show the effectiveness and efficiency of the proposed algorithms. In other words, our recommended algorithms outperform the CPLEX solver in terms of the quality and time of obtaining the solutions.

Solving the Multi-Choice Two Dimensional Shelf Strip Packing Problem with Time Windows

In the tool coating field, scheduling of production lines requires solving an optimisation problem which we call the multi-choice two-dimensional shelf strip packing problem with time windows. A set of rectangular items needs to be packed in two stages: items are placed on shelves, which in turn are placed on one of several available strips. Crucially, the item's width depends on the chosen strip and each item is associated with a time window such that items can only be placed on the same shelf if their time windows overlap. In collaboration with an industrial partner, this real-world optimisation problem is tackled in this paper by both exact and heuristic methods. The exact method is an arc-flow-based integer linear programming formulation, solved with the commercial solver CPLEX. Experimental evaluation shows that this approach can solve instances to proven optimality with up to 20 different item sizes. Larger, more realistic instances are solved heuristically by an adaptive large neighbourhood search, using first fit and best fit decreasing approaches as repair heuristics. In this way, we obtain high-quality solutions with a remaining optimality gap below 3.3% for instances with up to 2000 different item sizes. The work reported is due to be incorporated into an end-to-end decision support system with the industrial partner.

Modeling and analysis of a new production methodology for achieving mass customization

In this paper, we address a Stochastic-Demand Assembly Job Shop Scheduling Problem (SD-AJSSP) in the presence of the commonality of sub-assemblies across products. We propose a new production methodology, named Assemble-to-Order with Commonality of Sub-Assemblies (ATO-CS) to not only solve the SD-AJSSP, but also, achieve a successful implementation of a mass customisation system by collectively aiming to (1) keep the production costs low by leveraging upon commonality of sub-assemblies in products’ BOM and producing sub-assemblies on a mass scale during one of the two stages of production, (2) minimise the loss due to excess inventory build-up in anticipation of stochastic demand of products by postponing the production of certain apex sub-assemblies in products’ BOM until the actual demand is realised, and (3) reduce the time of the products’ delivery to customers. The ATO-CS method determines optimum production levels as well as schedules assembly operations/jobs over the machines at each stage of production, where the second stage is an assembly job shop and is shown to outperform commonly-used production methodologies. We also develop an algorithm for its implementation and show its efficacy over the use of the state-of-the-art commercial solver CPLEX® in obtaining a lower solution cost and smaller optimality gap.

Optimal Allocation of Energy Storage Capacity in Microgrids Considering the Uncertainty of Renewable Energy Generation

The high dimensionality and uncertainty of renewable energy generation restrict the ability of the microgrid to consume renewable energy. Therefore, it is necessary to fully consider the renewable energy generation of each day and time period in a long dispatching period during the deployment of energy storage in the microgrid. To this end, a typical multi-day scenario set is used as the simulation operation scenario, and an optimal allocation method of microgrid energy storage capacity considering the uncertainty of renewable energy generation is designed. Firstly, the historical scenarios are clustered into K types of daily state types using the K-means algorithm, and the corresponding probability distribution is obtained. Secondly, the Latin hypercube sampling method is used to obtain the state type of each day in a multi-day scenario set. Then, the daily scenario generation method based on conditional generative adversarial networks is used to generate a multi-day scenario set, combining the day state type as a condition, and then the typical scenario set is obtained using scenario reduction. Furthermore, a double-layer optimization allocation model for the energy storage capacity of microgrids is constructed, in which the upper layer optimizes the energy storage allocation capacity and the lower layer optimizes the operation plans of microgrids in each typical scenario. Finally, the proposed model is solved using the PSO algorithm nested with the CPLEX solver. In the microgrid example, the proposed method reduces the expected annual total cost by 19.66% compared with the stochastic optimal allocation method that assumes the scenic power obeys a specific distribution, proving that it can better cope with the uncertainty of renewable energy generation. At the same time, the expected annual total cost is reduced by 6.99% compared with the optimal allocation method that generates typical daily scenarios based on generative adversarial networks, which proves that it can better cope with the high dimensionality of renewable energy generation.

Two stages of halal food distribution model for perishable food products

Two stages of halal food distribution model for perishable food products are a mixed integer linear program (MILP) model proposed to solve the distribution problem of halal food, especially for perishable food products. The model can simultaneously minimize overstock, shortage, transportation, and deterioration costs. The model is developed into two stages. The first stage is the location-allocation model to determine the halal cluster and the number of suppliers in each cluster. The second stage is the vehicle routing model to determine the routing at each cluster. Numerical experiments are done using CPLEX Solver and the proposed model is applied to solve a real case of halal meat distribution in Yogyakarta. The results show that the proposed model can be used as a decision tool for supply chain and distribution managers to determine the strategy for distributing halal food products with the least total logistics cost for daily application.

A Hybrid Stochastic/Robust Planning Model for Integrated Energy System Considering Multiple Uncertainties

Abstract Complex energy flows exist in integrated energy systems (IESs), and the optimal assignment of different energy sources has become a primary challenge in the initial stage of its construction. In addition, multiple uncertainties, such as wind power fluctuations and multiple energy load fluctuations, are not well-respected in IES planning. In order to solve the above problems, the generation expansion planning model in IES is proposed. In the model the uncertainties of renewable energy resources (RESs) are described by scenarios, while the power price and fuel price are described by intervals, and a stochastic/robust (S/R) optimization is established to minimize the sum of annual investment cost, operation cost and reliability cost. Based on duality theory, the proposed multi-level S/R optimization model is transformed into a mixed integer linear programming (MILP) model, which can be solved using the CPLEX solver. The proposed model is tested on the IEEE 33-node distribution system with an 11-node cold-heat system. The validity and effectiveness of the proposed model are illustrated by case studies.