Mixed Integer Linear Programming Research Articles

Operation strategy and optimization configuration of hybrid energy storage system for enhancing cycle life

Hybrid energy storage system (HESS) can take advantage of complementarity between different types of storage devices, while complementary strategies applied to configuration or operation have a significant impact on the battery cycle life. Therefore, in order to enhance the battery cycle life, this paper proposes an operation strategy and configuration technique for HESS and verifies it by a scenario of HESS tracking scheduling plan. Firstly, a linear rainflow counting method, which can be embedded in the optimization process, is proposed to quantitatively evaluate the cycle life of energy storage based on the half cycle identification model. Secondly, an operation strategy with the integration of the constraint of state-of-charge (SOC) recovery capability considering the dynamic degradation of energy storage cycle life during operation is proposed to ensure a certain charging and discharging margin for storages, thereby enhancing the cycle life of HESS. Thirdly, an optimization configuration model considering the operation strategy of HESS is established based on the minimum annualized investment cost. And the linearization techniques are used to transform the original problem into a mixed-integer linear programming problem, and the mathematical programming technique is adopted to solve the problem. Finally, the effectiveness of the proposed method is validated through case studies. The results of the case studies show that the use of the HESS operation strategy proposed in this paper can manage the VRB's SOC more efficiently, and the control effect of VRB's SOC is improved by 71.5 %. Meanwhile, by controlling the VRB's SOC, the cycle life of the energy storage in the HESS can be effectively improved, which reduces the annualized cost of the HESS by 53 %.

Collaborative optimization of intersection signals and speed guidance for buses run on overlapping route segments under connected environment

AbstractIn order to reduce bus bunching in overlapping route segments and improve the efficiency of bus operation, a dynamic scheduling model is proposed to adjust bus operation states by adopting a cooperative strategy involving multi‐line bus timetable optimization, arterial signal control, and speed guidance. Based on mixed integer linear programming, an arterial signal coordination model with autonomous public transport vehicles (APTVs) dedicated lanes is developed, which enables APTVs to pass through intersections without stopping under conditions that almost have no effect on regular vehicles (RVs). Based on this, a speed guidance strategy of APTVs under connected environment is proposed. After guiding APTVs into the overlapping route segments at a reasonable interval, the optimization goal of maintaining the independent running headway of each bus line to the maximum extent is realized. The simulation verification based on three actual overlapping lines in Hangzhou shows that only the combination of signal coordination considering the characteristics of APTVs and speed guidance can realize the full benefits of bus operation based on dedicated APTVs lane.

Integrating random regret minimization-based discrete choice models with mixed integer linear programming for revenue optimization

Integrating random regret minimization-based discrete choice models with mixed integer linear programming for revenue optimization

Hierarchical model for design and operation optimization of district cooling networks

District cooling systems offer a promising alternative to conventional cooling, thanks to overall larger efficiencies and reduced carbon footprint. On the other hand they are characterized by large capital and operational costs that impede their diffusion. Optimizing the design and operation of these systems is therefore fundamental to fully exploit their potential. This paper proposes a novel optimization framework for the simultaneous optimization of design and operation of these systems. The model integrates a genetic algorithm at a master level with Mixed Integer Linear Programming models at a lower level. This approach enables the optimization of various aspects, including network topology, plant locations, supply temperatures and the selection of thermal storage technology. The study showed that in the specific case of Singapore, where the cost for space occupancy is significant, latent heat thermal storages are preferred. In addition, the results highlighted the cost benefits of thermal storage, as district cooling networks lacking it can be from 6.2% to 20.8% more expensive, depending on the scenario. Furthermore, the study demonstrated that the utilization of waste heat through absorption chillers enhances the economic feasibility of district cooling, lowering the payback time by up to 5 years. Lastly, it was observed that 3 °C increase of the indoor set point temperature could reduce the payback time by 3 years and increase the final net present value by 43%, as larger network supply temperatures allow chillers to operate with better performances. The developed model allows to estimate various crucial outcomes with few input parameters, representing a useful tool for both research and planning.

Dynamic Delay-Sensitive Observation-Data-Processing Task Offloading for Satellite Edge Computing: A Fully-Decentralized Approach

Satellite edge computing (SEC) plays an increasing role in earth observation, due to its global coverage and low-latency computing service. In SEC, it is pivotal to offload diverse observation-data-processing tasks to the appropriate satellites. Nevertheless, due to the sparse intersatellite link (ISL) connections, it is hard to gather complete information from all satellites. Moreover, the dynamic arriving tasks will also influence the obtained offloading assignment. Therefore, one daunting challenge in SEC is achieving optimal offloading assignments with consideration of the dynamic delay-sensitive tasks. In this paper, we formulate task offloading in SEC with delay-sensitive tasks as a mixed-integer linear programming problem, aiming to minimize the weighted sum of deadline violations and energy consumption. Due to the limited ISLs, we propose a fully-decentralized method, called the PI-based task offloading (PITO) algorithm. The PITO operates on each satellite in parallel and only relies on local communication via ISLs. Tasks can be directly offloaded on board without depending on any central server. To further handle the dynamic arriving tasks, we propose a re-offloading mechanism based on the match-up strategy, which reduces the tasks involved and avoids unnecessary insertion attempts by pruning. Finally, extensive experiments demonstrate that PITO outperforms state-of-the-art algorithms when solving task offloading in SEC, and the proposed re-offloading mechanism is significantly more efficient than existing methods.

Flexible dynamic boundary microgrid operation considering network and load unbalances

Flexible microgrids with dynamic boundaries have recently been introduced in the literature. With the ability to reconfigure the topology of the microgrids dynamically through remotely controlled switches, flexible microgrids with dynamic boundaries can further improve the resiliency and energy efficiency of microgrids with distributed energy resources (DERs). This paper focuses on the optimal operation considering one of the predominant characteristics of microgrids and distribution systems – unbalanced networks and loads. In existing literature, balanced modeling of microgrids is more common due to its attractive simplicity. The three-phase power unbalance has not been considered as a constraint on the generation units in a microgrid. Negative sequence constraints have also been neglected. In this article, we propose a set of constraints that is specifically related to the capabilities of inverter interfaced resources to supply unbalanced current/power when the microgrid is islanded from the main distribution grid. We incorporate the new set of constraints into two optimization formulations leveraging two convex relaxations of the three-phase power flow equations: mixed-integer linear programming (MILP) and mixed-integer semidefinite programming (MISDP) that optimize the dispatch of controllable switches and DERs in the microgrid. The algorithms are then extended to networked microgrids with grid-forming sources. We test the algorithms on a realistic community microgrid model in Puerto Rico as well as standardized IEEE distribution test feeders. The testing results demonstrate the performance of the proposed algorithms. The MILP is fast and scalable, and the MISDP enforces the negative sequence voltage constraints.

Container drayage problem integrated with truck appointment system and separation mode

Growing demand for seaborne trade has exacerbated the challenges faced by drayage operators in inland container transportation. In some cases, drayage operators must make truck scheduling decisions and book periods for trucks to visit terminals daily. This paper considers the appointment system and separation mode in container drayage problem, which consists of delivery and pickup transportation tasks for empty and full containers. A mixed-integer linear programming model is developed to minimize the total truck operating time while solving the truck scheduling problem, the empty container allocation problem, and the appointment problem. Another key feature of the model is considering the temporal constraints between tasks from a more realistic perspective. Due to the complexity of the problem, it is not practical to obtain exact solutions for large instances. Therefore, we complete the implementation of a new genetic algorithm (GA) that introduces a topological sort tailored to this problem. Several experiments and analyses are used to demonstrate the correctness of the proposed model as well as the efficiency of the algorithm. The findings indicate that, when compared to traditional mode, separation mode can reduce total truck operating time by an average of 29.4%. The total truck operating time difference between the two modes shows an overall positive trend if the task size increases. In addition, a rational setting of the appointment system will have a beneficial effect on truck scheduling. The decision on the selection of periods and the increment of each quota is crucial in optimizing the setting of the appointment system to reduce the total truck operating time for the mutual benefit of both terminals and drayage operators.

Modeling and Optimization of Container Drayage Problem with Empty Container Constraints across Multiple Inland Depots

Container drayage involves the transportation of containers by trucks. Although the distance is relatively short compared to maritime and rail transport, container drayage accounts for 25% to 40% of the total container transportation costs and significantly contributes to increased fuel consumption and carbon emissions. Thus, the modeling of the container drayage problem (CDP) has received a lot of attention in the last two decades. However, the three fundamental modeling factors, including the combination of trucking operation modes and empty container relocation strategies, as well as empty container constraints and multiple inland depots, have not been simultaneously investigated. Hence, this study addressed a comprehensive CDP that simultaneously incorporates the three modeling factors. The problem was formulated as a novel mixed integer linear programming (MILP) model based on the DAOV graph. Given the complexity of this problem, it was not realistic to find an exact solution for large instances. Therefore, an improved genetic algorithm (GA) was designed by integrating the “sequential insertion” method and “solution re-optimization” operation. The performance of Gurobi and GA was validated and evaluated through randomly generated instances. The results indicate that (1) the proposed algorithm can provide near-optimal solutions for large-scale instances within a reasonable running time, (2) the greatest cost savings from combining trucking operation modes and empty container relocation strategies range from 10.45% to 31.86%, and (3) the three modeling factors significantly influence the fuel consumption and carbon emissions, which can provide managerial insights for sustainable container drayage practices.

Integrated procedure to design optimal hybrid renewable power plant for railways’ traction power substation

The paper suggests a 3-steps methodology, integrated in a unique-procedure, to optimally design a hybrid RPP (Renewable Power Plant) to be installed in the available areas of railway’s power plants. The procedure takes into account power profiles and time schedule of trains, traction line’s features, sizing and siting of TPSSs (Traction Power Substations) and features of renewable sources as PV (Photovoltaic) and wind turbines for optimizing the siting of the RPP, considering the investment convenience. The optimal sizing of a hybrid power plant is based on mixed-integer linear programming (MILP) taking into account the energy absorbed by TPSSs, the physical and geometric constraints and the operating and maintenance costs of RPP. The integrated procedure has been tested on a real case study regarding a new 3 kV DC railway located in the South of Italy. The main results show that a hybrid RPP with 4980 PV panels and 3 wind turbines installed in a TPSS area, adopting a capital cost of 645,000 €/MW for PV panels and 3000 €/kW for wind farms, ensures an annual revenue of 227,439 €, with a total investment of 897,400 €. Results show that the available areas in TPSS should be the target of relevant investments to support a new sustainable and green power traction supply system.

Demand Response Power-Gas Interconnection Energy System and Power Metering Based on SOGA

Under the double background of global energy crisis and environmental pollution, China vigorously develops renewable energy while accelerating the construction of energy Internet. Taking demand response into account, this paper proposes the optimal design of power-gas interconnection energy system and power metering, and establishes the optimization research model of IEGES (integrated electricity-gas energy system) with demand response. Firstly, the structure model of the electric-gas interconnection energy system with CHP (Cogeneration, combined heat and power) as the core is constructed, and the energy conversion relationship and different energy flow directions of the coupling equipment are expounded from three aspects. The natural gas source point, pipeline equation, power side branch equation, voltage and current equation are modeled and sorted out, and the square term in the equation is linearized by second-order cone programming method, and the mixed integer nonlinear programming problem is transformed into mixed integer linear programming problem. A single objective genetic algorithm with “elite strategy” was selected to solve the equipment capacity optimization problem of IEGES system with system economy as the optimization objective. After a long time of parameter combination attempts, the current population size is 30, the number of iterations is 600, the crossover rate is 0.8, and the heritability is 0.3. The above parameters can obtain better convergence results on the basis of considering the operation time. Finally, a stochastic optimization method of energy Internet considering integrated demand response and uncertainty of wind power is proposed, which aims to meet the energy demand of end users while minimizing the operating cost of the system. The comprehensive demand response strategy including internal and external demand response is considered in the model. Internal demand response is realized by adjusting the internal operation mode of EH, while external demand response is implemented by the end user’s active response, and the load is time-shifted or interrupted under the guidance of external signals.

Modeling a closed-loop inventory routing problem for returnable transport items under horizontal logistics collaborations and dynamic demand structure

ABSTRACT This paper addresses a closed-loop inventory routing problem with multiple suppliers, products, and periods under horizontal collaboration assumptions. Our problem encompasses various decision aspects, including routing, inventory management, product delivery, returnable transport item collection and cleaning. We analyze various logistics collaboration scenarios. The effects of demand dynamicity are also assessed. The problem has been mathematically defined as a Mixed Integer Linear Programming model. A rolling horizon approach and a hybrid heuristic algorithm are proposed for instances that exceed the computational requirements of solving the exact MILP model. The applicability and potential benefits of the MILP model and the proposed solution methodologies are demonstrated through a base case and additional numerical analyses on larger-sized instances and networks. The results show that supplier collaboration significantly reduces routing costs, while customer collaboration reduces inventory costs. Numerical comparisons reveal that the proposed algorithms outperform the MILP model for large-scale problem instances.

A discrete moth-flame optimization algorithm for multiple automated guided vehicles scheduling problem in a matrix manufacturing workshop

The growing need for customized and varied production has highlighted the significance of smart and automated factories in the manufacturing sector. In this particular context, the scheduling of multiple Automated Guided Vehicles (AGVs) plays a pivotal role in enhancing the efficiency of operations within an intelligent manufacturing shop. This study centers on the material handling process within a matrix manufacturing shop with the objective of identifying the most cost-effective transportation routes for materials. To accomplish the specified objective, this research aims to identify an optimal solution for reducing transportation costs. In particular, this study formulates a mixed-integer linear programming model and introduces a novel discrete variant of the moth-flame optimization (MFO) algorithm, named DMFO, to address the scheduling problem. The DMFO algorithm incorporates several significant enhancements. Firstly, a population initialization method is proposed, which combines a nearest-neighbor-based adaptive heuristic and a random sorting technique to ensure the formation of a well-structured population. Secondly, the flame generation mechanism and spiral flight search processes within the MFO have been redefined to achieve a more optimal balance between exploration and exploitation. A neighborhood search mechanism is subsequently devised, employing the concept of neighborhood relevance to accelerate the convergence process. Additionally, a heuristic approach is introduced to reduce the computational cost. Moreover, a population regeneration mechanism is proposed to avoid the algorithm falling into a local optimum. To validate the effectiveness of the DMFO, a comparative analysis is conducted using a dataset of 110 real-world factory instances. In this analysis, eight well-established optimization algorithms are employed. The simulation results consistently demonstrate that the relative percentage deviation (RPD) value of the DMFO tends to approach 0% more closely compared to other algorithms, thereby substantiating the effectiveness of the proposed algorithm.

An Energy-Efficient Logistic Drone Routing Method Considering Dynamic Drone Speed and Payload

Unmanned aerial vehicles (UAVs), or drones, are recognized for their potential to improve efficiency in last-mile delivery. Unlike the vehicle routing problem, drone route design is challenging due to several operational signatures, such as speed optimization, multi-trip operation, and energy consumption estimation. Drone energy consumption is a nonlinear function of both speed and payload. Moreover, the high speed of drones can significantly curtail the drone range, thereby limiting the efficiency of drone delivery systems. This paper addresses the trade-off between speed and flight range in a multi-trip drone routing problem with variable flight speeds (DRP–VFS). We propose a new model to specifically consider energy constraints using a nonlinear energy consumption model and treat drone speeds as decision variables. The DRP–VFS is initially formulated using mixed-integer linear programming (MILP) to minimize energy consumption. To solve large-scale instances, we propose a three-phase adaptive large neighborhood search (ALNS) algorithm and compare its performance with a commercial MIP solver. The experimental results demonstrate that the proposed method is capable of effectively identifying suboptimal solutions in practical scenarios. Furthermore, results indicate that operating drones at variable speeds leads to about 21% energy savings compared to fixed speeds, with advantages in cost savings and range extension.

Metaheuristics for solving a flexible flow‐shop scheduling problem with s‐batching machines

AbstractA scheduling problem for a two‐stage flexible flow shop with s‐batching machines motivated by processes in additive manufacturing is considered. A batch is a group of jobs that are processed together on a single machine. Each job belongs to an incompatible family. Only jobs of the same family can be batched together. A maximum batch size is given. A setup time occurs between different batches. The jobs of a batch are processed in a serial manner, that is, the processing time of a batch is the sum of the processing times of the jobs forming the batch. Batch availability is assumed. A job has a weight, a due date, and a release date. The total weighted tardiness is considered as performance measure. We establish a mixed integer linear programming formulation for this scheduling problem. For large‐sized problem instances, an iterative decomposition approach (IDA) is proposed that uses a grouping genetic algorithm or an iterated local search (ILS) scheme to solve the single‐stage subproblems. Moreover, an alternative ILS scheme based on a disjunctive graph representation of the problem at hand is designed. Results of computational experiments based on randomly generated problem instances demonstrate that the IDA hybridized with ILS outperforms the two other schemes.

A Two-Echelon Multi-Trip Capacitated Vehicle Routing Problem with Time Windows for Fresh E-Commerce Logistics under Front Warehouse Mode

Given the swift expansion of fresh e-commerce, the front warehouse mode can respond quickly and ensure the quality of fresh products. However, the complexity of the supply chain structure under front warehouse mode poses a challenge in reducing logistics costs and improving distribution efficiency while meeting consumers’ immediate delivery demands. Therefore, this paper studies the vehicle routing problem of two-echelon fresh e-commerce under front warehouse mode. Considering trans-shipment time constraints between the two echelons and the characteristics of terminal distribution, this paper initially models the vehicle routing problem for front warehouses as a two-echelon multi-trip capacitated vehicle routing problem with time windows. A mixed-integer linear programming model is subsequently established. To solve the model, a hybrid genetic algorithm integrated with neighborhood search is developed. Matrix coding is employed to merge vehicle selection and route assignment decisions. Simultaneously, neighborhood search is applied to enhance the search capability of algorithms, thereby improving the quality of solutions. Furthermore, the effectiveness and efficiency of the model and algorithm are verified through experiments of varying scales. Finally, comparative strategies and sensitivity analysis highlight the advantages of multi-trip strategies and provide insights into the optimal vehicle capacity limit.

Integrated scheduling of production and material delivery for the intelligent manufacturing system

This paper addresses the issue of integrated scheduling of production and material delivery in an intelligent manufacturing system. The system includes multiple flexible flowlines and a fleet of automated guided vehicles (AGVs), whose capacity is shared among the flowlines. Multiple orders from different customers are processed on the flowlines, with AGVs delivering materials in different batch sizes based on varying product quantities of orders and limited load capacity. The problem is formulated as a mixed-integer linear programming model to minimise total order delays and the number of used AGVs. To handle the complexity caused by the uneven temporal coupling relationship between production and material delivery, a bi-level neighbourhood search solution algorithm is proposed. This algorithm uses variable neighbourhood search for production scheduling and adaptive large neighbourhood search for material delivery scheduling. Extensive numerical experiments using real-case-based instances are conducted to demonstrate the satisfactory performance of our proposed algorithm. Furthermore, we emphasise the advantages of integrated scheduling compared to traditional sequential scheduling across various problem settings.

Analyzing effective external interventions for optimizing energy hubs with electric and TS: A numerical study from a network topology perspective

Currently, there has been a notable surge in sabotage targeting critical infrastructures, particularly energy hub systems. External interventions on these infrastructures have significantly affected various loads, including electrical and thermal loads. Considering the significance of cybersecurity in energy hubs, there are high expectations for investigating the role of topology in their measures. The aim of this study is to investigate the impact of cyber sabotage on energy management within the demand sector, with a specific emphasis on the topology of an energy hub system. According to the structure of the desired energy hub that has been mathematically modeled, the CPLEX solver is used as a powerful optimization tool with the mixed integer linear programming (MILP) model, which serves as a framework for optimizing the operation cost of the energy hub. The findings reveal the occurrence of false data injection (FDI) into the real network loads. This inconsistency has led to disruption of energy management in the system. Utilizing considered scenarios, the first of them as the base scenario, representing the system under normal network conditions. The second scenario is modeled an attack vector aimed at the electric load, specifically utilizing FDI tactics with an understanding of the network topology. In the third scenario, attention turns to modeling a thermal load attack vector, utilizing FDI tactics with an understanding of its topology. In the final scenario, the emphasis is placed on designing an FDI-based attack vector that targets electric loads within the network, without prior knowledge of the energy hub's topology. Although in all scenarios where the attack is executed, the measuring devices during peak load indicate values lower than the actual ones, the intensity of the attack on the system is considerable in attacks conducted with knowledge of the energy hub topology. Taking into account the importance of the peak load intervals, the maximum changes in electric load during peak hours in the second scenario are compared to those in the first scenario, attributing them to interventions, representing approximately a 17.4 % difference. Similarly, assuming knowledge of the network topology during peak consumption, the impact of the attack on the thermal loads results in changes of 17.17 %. Additionally, in the fourth scenario compared to the first, the maximum changes in electric load during peak hours are approximately 2 %. In the meantime, the optimal cost has remained consistent across all scenarios, rendering the attacks undetectable to the operator and ultimately demonstrating the effectiveness of the proposed method.

A learning-based granular variable neighborhood search for a multi-period election logistics problem with time-dependent profits

Planning the election campaign for leaders of a political party is a complex problem. The party representatives, running mates, and campaign managers have to design an efficient routing and scheduling plan to visit multiple locations while respecting time and budget constraints. Given the limited time of election campaigns in most countries, every minute should be used effectively, and there is very little room for error. In this paper, we formalize this problem as the multiple Roaming Salesman Problem (mRSP), a new variant of the recently introduced Roaming Salesman Problem (RSP), where a predefined number of political representatives visit a set of cities during a planning horizon to maximize collected rewards, subject to budget and time constraints. Cities can be visited more than once and associated rewards are time-dependent (increasing over time) according to the day of the visit and the recency of previous visits. We develop a compact Mixed Integer Linear Programming (MILP) formulation complemented with effective valid inequalities. Since commercial solvers can obtain optimal solutions only for small-sized instances, we develop a Learning-based Granular Variable Neighborhood Search and demonstrate its capability of providing high-quality solutions in short CPU times on real-world instances. The adaptive nature of our algorithm refers to its ability to dynamically adjust the neighborhood structure based on the progress of the search. Our algorithm generates the best-known results for many instances.

Strategic trading equilibria in local community considering co-existence of pool-based and peer-to-peer energy markets with free-rider problem in network usage cost

The peer-to-peer (P2P) energy trading market is considered a promising method for allocating prosumers’ locally produced power in smart buildings. However, the existing literature overlooks the coexistence of P2P and pool-based energy markets. Therefore, this paper establishes a bi-level energy market model that incorporates both P2P and pool-based markets. The prosumers’ individual profit maximization model considering their network usage costs in the P2P energy trading network at the upper level is first developed. A hybrid market-clearing framework determining the optimal trading amounts with the prosumers’ strategic offers at the lower level is then exploited. The distribution network power flow model in the market clearing framework is then convexified. The lower-level problem is replaced with its strong duality conditions. This bi-level problem can be reformulated as an equilibrium problem with equilibrium constraints (EPEC). This EPEC is then solved after being transformed into an equivalent mixed integer linear programming (MILP) model. Finally, a fifteen-bus system is employed to illustrate the characteristics of the hybrid market equilibrium depicted by this EPEC model. The influences of the prosumers’ strategic offers on the distribution locational marginal prices (DLMPs) and network usage costs are highlighted. Since the prosumers can choose to transmit their energy in the pool-based or P2P markets, the emission and pollution costs caused by power transmission can be minimized. A cleaner energy production is thus guaranteed. The free-rider problem is verified by comparing the network usage charges in the strategic and perfect competition scenarios.

An improved ALNS for hybrid pickup and drones delivery system in disaster by penalizing deprivation time

Humanitarian logistics aims to reduce the time relief goods and services take to reach affected areas; deprivation time is one of the most significant factors in such conditions. Thus, utilizing a suitable transport fleet, including modern vehicles like drones, is essential. This paper introduces a new hybrid vehicle routing problem with pickup and delivery services, minimizing deprivation costs with multiple trucks and drones in a disaster. The model is presented as a mixed-integer linear programming problem focusing on minimizing deprivation cost in post-disaster situations through proper routing and inventory decisions made by heterogeneous vehicles. The deprivation time is divided into three main categories based on the arrival time of relief goods to affected areas and will be served by multiple relief goods. Due to the complexity of the problem, an improved adaptive large neighborhood search (ALNS) metaheuristic has been developed. This algorithm employs a heuristic algorithm to generate high-quality initial solutions and improve solutions with 17 destroy and repair operators. The algorithm was tested on a large-scale dataset based on real-world data from a crisis such as the Tehran earthquake, and the results demonstrate its superiority in providing better-quality solutions and lower solution time.