Multi-objective Mixed-integer Nonlinear Programming Problem Research Articles

Stochastic multi-benefit planning of mobile energy storage in reconfigurable active distribution systems

This paper proposes a multi-benefit planning framework for mobile energy storage systems (MESSs) in reconfigurable active distribution systems (DSs). The goal of this framework is to improve the DS operation and reliability through achieving four objectives: (1) minimizing the DS costs, (2) minimizing the DS energy losses, (3) improving the DS voltage profiles, and (4) minimizing the expected energy not supplied (EENS) in the system. The developed framework determines optimal decisions associated with the network reconfiguration as well as the MESS sizes and locations, taking into account the variations in DS loads, energy prices, and renewable energy sources. The planning problem in this study is formulated as a stochastic multi-objective mixed-integer nonlinear programming problem, which is solved using a genetic algorithm (GA)-based hybrid optimization method. The proposed framework is tested using a case study of an active DS that includes various types of energy sources and load demands. Comparing the results of the developed planning framework with the base-case system demonstrates the efficacy of the planning framework and the techno-economic benefits of MESSs, where the proposed framework with MESSs successfully achieved significant improvements in the DS operating cost, energy losses, voltage profiles, and EENS. The advantages of MESSs are also verified through a comparison with stationary energy storage systems.

Loading optimization algorithm for solving assembly assignment problem in the final disposal of spent nuclear fuel in Finland

In Finland, the final disposal of spent nuclear fuel assemblies includes inserting them into disposal canisters being disposed of in bedrock. This final disposal will be a century long process. The choice of which fuel assemblies are assigned to which canisters determines the decay heat powers of canisters. A loading optimization algorithm to make these choices is developed. The assembly assignment problem is formulated as a multiobjective mixed-integer nonlinear programming problem, but the loading optimization algorithm will solve the problem heuristically. The developed algorithm can be seen as a new version of the algorithm to solve the minimax canister formation problem, where canisters disposed of in the near future are considered more carefully than the rest of the canisters being more exposed to uncertainties related to schedule and predicted decay heat powers of future fuel assemblies. Furthermore, new constraints and objectives have been taken into account. The developed loading optimization algorithm facilitates the safe and cost-efficient assignments of fuel assemblies to canisters in Finland.

Multi-Objective Optimal Scheduling of CHP Microgrid Considering Conditional Value-at-Risk

A combined heating and power (CHP) microgrid has high flexibility and economy, but the output of renewable energy is uncertain. Meanwhile, excessive flexible load adjustment in the demand response process will increase user dissatisfaction. In order to solve the above problems, this paper quantifies uncertainty with the conditional value-at-risk (CVaR) of relative disturbance. Additionally, a multi-objective optimal scheduling model that takes into account both the operating economy and the demand-side power consumption satisfaction is established. In order to solve the multi-objective mixed-integer nonlinear programming problem well, we propose an improved sparrow search algorithm (ISSA), which solves the problem that the sparrow search algorithm (SSA) is prone to low accuracy, insufficient in population diversity and easy to be trapped in local optimum. Combined with the non-dominated solution ranking method, ISSA has the ability of multi-objective optimization. Finally, simulation on a typical CHP microgrid is performed. The optimization results under different confidence levels and risk preference coefficients are compared and analyzed. When the risk preference coefficient is 0.1, 2 and 5, the minimum rotating reserve capacity is 75.17 kW, 82.83 kW, and 105.70 kW in the electric part and 40.08 kW, 59.89 kW, and 61.94 kW in the thermal part. The effectiveness of the proposed CVaR of relative disturbance is verified.

Reliability Enhancement by Strategic Placement of Remotely-Controlled Automation Devices: A Case Study on Tabriz Distribution Network

Achieving high distribution-reliability levels and concurrently minimizing operating costs are as the main issues in distribution system optimization. Determination of the optimal number and location of remote control switches (RCS) in the distribution system network is an essential issue from the reliability and economic points of view. To address these issues, this paper develops a novel multiobjective model from the distribution system viewpoint, wherein the primary objective, optimal RCS placement is implemented aiming at minimizing the operating costs, while in the second objective, the reliability index improvement is taken into account. So, a novel approach from a robust heuristic algorithm, modified non dominated sorting genetic algorithm (MNSGA-II), is developed and presented to solve this multiobjective mixed-integer non-linear programming problem. Simulation results received by the genetic algorithm have been compared with the other popular optimization algorithms, seperately. Results show that the proposed algorithm provides extensively the best performance, in terms of quality of the answer received and computational efficiency. The feasibility of the proposed algorithm was examined by application to two distribution feeders of the Tabriz city distribution network containing the fourth feeder of the TractorSazai substation.

A data-driven approach to support voltage profiles & loss reduction in wind generator integrated active distribution network considering solid-state transformers with twofold reactive power compensation

ABSTRACT The paper proposes an optimal planning strategy for an active distribution network (ADN) with wind energy-based distributed generation (WDG) by considering the twofold reactive power compensation (TRPC) feature of a three-stage type solid-state transformer (SST). A model for wind speed and load demand estimation for each hour of the day is formulated by using the partition around medoids (PAM) technique over an annual database of load demand and wind speed. A multi-objective mixed-integer non-linear programming (MINLP) approach for optimally locating and sizing the SST installations in the radial distribution network (RDN) is presented to address the dual objectives of voltage profile improvement (VPI) and energy loss reduction (ELR). Along with the SST parameters, the locations and number of wind turbine (WT) units to be integrated into the system are treated as optimization variables. Furthermore, the distribution power flow accounts for the distribution transformer’s (DT) operating losses as well as the approximate losses of the SST. The presented approach is tested on a 33-bus RDN and the results are reported for multiple case studies. The programming was developed in the MATLAB R2020a environment and the paretosearch algorithm (PSA) is used to address the MINLP problem. Other standard multi-objective optimization algorithms, including multi-objective multi-verse optimization (MOMVO), non-dominated sorting genetic algorithm (NSGA-II), and multi-objective salp swarm algorithm (MSSA) are used to compare the performance of the proposed method. The outcomes of the peak hour evaluation, with a 20% over-rating, show the active and reactive power demand on the MV side of the substation to have decreased by 56.3% and 30.1% respectively. The active line loss has been lowered by 76.95% and the reactive line loss has decreased by 76.14%. The absolute minimum voltage has increased by 7.314%. Furthermore, according to the annual technical evaluation, there was a 29.42% reduction in active energy served by the DTs and SSTs.

Economic-environmental evaluation and multi-objective optimization of supercritical CO2 based-central tower concentrated solar power system with thermal storage

We address the optimal design of central tower-concentrated solar power (CSP) system combined with supercritical CO2 Brayton cycle and thermal storage under economic and environmental objectives. The economic objective is measured by the levelized cost of electricity (LCOE), and the environmental objective by the power plant’s total environmental impact potential (TEIP) considering the system’s global warming, acidification, and eutrophication emission. A multi-objective mixed-integer nonlinear programming (MINLP) model is developed that takes into account the main characteristics of CSP plant, e.g. unit operations, working fluid thermodynamics, equipment sizing, thermal storage capacity. Life cycle assessment and economic evaluation of the manufacturing, construction, operation and decommission stages of the systems are also embedded in the model. The multi-objective MINLP problem is solved by a tailored algorithm, and the resulting Pareto solutions are analyzed to identify the tradeoffs between the economic and environmental performance. The proposed approach is illustrated through a case study of a 50 MWe CSP plant. Results show that the framework is able to obtain the system’s economically-environmentally optimal design in reasonable time. A minimum LCOE of 115.82 $/MWh can be achieved for the most cost-effective design, and a minimum TEIP of 320.54 × 103 mPE90 can also be achieved for the most environmentally friendly design. A ‘balanced’ solution is identified with an LCOE of 116.89 $/MWh and TEIP of 330.29 × 103 mPE90. Numerical studies also reveal that while the Brayton cycle only accounts for a small proportion of the total investment, spending more on enhancing the efficiency of its equipment is cost-effective to improve the overall economic and environmental performance of the system.

Integrated active/reactive power scheduling of interdependent microgrid and EV fleets based on stochastic multi‐objective normalised normal constraint

This study proposes an integrated framework for coordinated optimisation of the interdependent microgrid (MG) and electric vehicle (EV) fleet entities using the normalised normal constraint approach. By considering the active/reactive power management option of the bidirectional charger enabled EVs in the proposed model, the authors investigate the effectiveness of EV's integration in the presence of the techno-economical objective functions. This work concentrates on the trade-off analysis of two conflicting objectives, including the economic objective of the MG's operation cost minimisation and the technical objective of the MG's voltage deviation. Besides, they consider several uncertainty sources, e.g. wind, EV and solar panel (PV) power provision, as well as market price fluctuations in the proposed model affecting the aforementioned techno-economic trade-off solution. The proposed model is a stochastic multi-objective mixed-integer non-linear programming problem where the authors apply the designed integrated framework on a modified IEEE 18-bus test case in GAMS software. Through numerical results, they demonstrate MG optimal operation changes due to different MGO priorities and study the positive effects of EVs integrated energy management on the bi-objective operation.

Passenger demand oriented train scheduling and rolling stock circulation planning for an urban rail transit line

We study the integration of train scheduling and rolling stock circulation planning under time-varying passenger demand for an urban rail transit line, where the practical train operation constraints, e.g., the capacity of trains, the number of available rolling stocks, and the entering/exiting depot operations, are considered. Three solution approaches are proposed to solve the resulting multi-objective mixed-integer nonlinear programming (MINLP) problem to deliver both an irregular train schedule (i.e., departure and arrival times of all train services) and a rolling stock circulation plan (including entering/exiting depot operations of rolling stocks and connections between train services) simultaneously. We first present an iterative nonlinear programming (INP) approach, where the solutions of the original MINLP problem are obtained by solving a nonlinear programming problem and a mixed integer linear programming (MILP) problem iteratively. Moreover, an equivalent MILP formulation of the original MINLP model is developed and an approximated MILP approach is proposed to reduce the number of constraints introduced by passenger demand. A case study is conducted based on the practical data of the Beijing Yizhuang line, where the three proposed approaches are compared with a state-of-the-art approach and a practical method used by the traffic planners. This comparison shows the effectiveness and efficiency of the three proposed approaches.

Sustainable Design and Synthesis of Shale Gas Processing and Chemical Manufacturing Processes

In this work, we propose a superstructure of integrated shale gas processing and chemical manufacturing processes with 51,840 alternative possible process designs. The superstructure consists of eight sections, namely acid gas removal, dehydration, NGLs recovery, NGLs separation, hydrocarbons conversion, light olefins separation, C4 separation, and acid gas disposal. For the steam cracking reactions in the hydrocarbons conversion section, we optimize the product distributions of steam cracking of ethane, propane, n-butane, and i-butane. Extensive process simulations are performed for all the involved processes in the superstructure in order to collect high-fidelity process data and develop detailed process models for the technology/process alternatives in the superstructure. Next, we propose a multiobjective mixed-integer nonlinear programming (MINLP) superstructure optimization model with five groups of constraints, namely superstructure network configuration constraints, mass balance constraints, energy balance constraints, techno-economic evaluation constraints, environmental impact assessment constraints. Three objective functions are maximizing the net present value per GJ of raw shale gas, minimizing the global warming potential per GJ of raw shale gas, and minimizing the water footprint per GJ of raw shale gas, respectively. A tailored global optimization algorithm is applied to efficiently solve the resulting nonconvex MINLP problem. The application of the proposed framework is illustrated through a case study based on a Marcellus shale gas feed.

A capacity maximization scheme for intersection management with automated vehicles

With the advent of connected and automated vehicle technology, in this paper, we propose an innovative intersection operation scheme named as MCross: Maximum Capacity inteRsection Operation Scheme with Signals. This new scheme maximizes intersection capacity by utilizing all lanes of a road simultaneously. Lane assignment and green durations are dynamically optimized by solving a multi-objective mixed-integer non-linear programming problem. The demand conditions under which full capacity can be achieved in MCross are derived analytically. Numerical examples show that MCross can almost double the intersection capacity (increase by as high as 99.51% in comparison to that in conventional signal operation scheme).

A capacity maximization scheme for intersection management with automated vehicles

With the advent of connected and automated vehicle technology, in this paper, we propose an innovative intersection operation scheme named as MCross: Maximum Capacity inteRsection Operation Scheme with Signals. This new scheme maximizes intersection capacity by utilizing all lanes of a road simultaneously. Lane assignment and green durations are dynamically optimized by solving a multi-objective mixed-integer non-linear programming problem. The demand conditions under which full capacity can be achieved in MCross is derived analytically. Numerical examples show that MCross can almost double the intersection capacity (increase by as high as 99.51% in comparison to that in conventional signal operation scheme).

Integrated design and control of multigeneration systems for building complexes

Building complexes have demands of electricity, cooling capacity for air conditioning, and sanitary hot water. These demands can be met efficiently using multigeneration systems. The design of a multigeneration system involves three integrated layers of decisions that include technology selection, equipment sizing and operational (control) policy design. In this work we cast this integrated design problem as a multi-objective mixed-integer nonlinear programming problem. The optimization formulation considers internal combustion engines, fuel cells, microturbines, Stirling engines, solar water heaters, and absorption chillers as technology options. The formulation also considers the sizing of a storage tank for hot water. Optimal operating policies are considered using daily scenarios of ambient temperature, solar radiation, fuel costs, electricity prices, and energy demands over an entire year. We compute compromise solutions that trade-off total annual costs, greenhouse gas emissions, and water consumptions. The method is demonstrated using real data for a Building complex with 420 households located on the Pacific Coast of Mexico. Our approach finds technologies that provide an optimal compromise between cost, emissions, and water consumption. In particular, we have found designs that reduce water consumption by 75% and emissions by 74% compared to the cost minimization case while increasing total cost by only 10%.

Sustainable Integration of Trigeneration Systems with Heat Exchanger Networks

A novel superstructure-based approach for synthesizing sustainable trigeneration systems (i.e., heating, cooling, and power generation cycles) integrated with heat exchanger networks is presented in this paper. The trigeneration system accounts for steam and organic Rankine cycles and an absorption refrigeration cycle. The steam Rankine cycle can be driven by multiple primary energy sources (i.e., solar, biofuels, and fossil fuels) for sustainable generation of power and process heating. The waste energy from the steam Rankine cycle and/or the excess of process heat can be used to drive both the organic Rankine cycle and the absorption refrigeration cycle to produce power and process cooling below the ambient temperature, respectively. The synthesis problem is formulated as a multiobjective mixed-integer nonlinear programming problem for the simultaneous consideration of the economic, environmental, and social dimensions of sustainability. Two example problems are presented to show the applicability of th...

Optimal Intersection Operation with Median U-Turn

The median U-turn intersection is a potential method for relieving traffic congestion at intersections. Median U-turn intersections can be classified into six types, according to the prohibited traffic movements. Although much is known about the technology of the median U-turn, efforts have focused on its geometric design, safety analysis, and evaluation. In this paper, a lane-based optimization model is proposed for the integrated design of median U-turn intersection types, lane markings, distances between the median crossovers and the main intersection, and signal timings. The capacity maximization problem is considered, and a set of constraints is determined that ensures the feasibility and safety of the optimization results. The optimization is formulated as a multi-objective mixed-integer nonlinear programming problem. It is solved by transformation to a series of mixed-integer linear programming models. The latter can be solved by the standard branch-and-bound technique. Extensive numerical analysis and a case study have shown the effectiveness of the proposed method. In addition, the method can assist transportation professionals in the proper selection of U-turn types and in the design of intersections with median U-turns.

Sustainable design and synthesis of hydrocarbon biorefinery via gasification pathway: Integrated life cycle assessment and technoeconomic analysis with multiobjective superstructure optimization

This paper proposes a multiobjective, mixed-integer nonlinear programming (MINLP) model for the superstructure optimization of hydrocarbon biorefineries via gasification pathway under economic and environmental criteria. The proposed hydrocarbon biorefinery superstructure includes a number of major processing stages, such as drying of the cellulosic biomass feedstocks, air separation unit, gasification, syngas conditioning, Fischer–Tropsch synthesis, hydroprocessing, power generation, and the diesel and gasoline production. The superstructure considers alternatives of technologies and equipment, such as gasification technologies, cooling options, hydrogen production sources, and Fischer–Tropsch synthesis catalysts. The economic objective is measured by the net present value (NPV), and the environmental concern is measured using global warming potential (GWP) that follows the life cycle assessment procedures, which evaluates the gate-to-gate environmental impacts of hydrocarbon biofuels. The multiobjective MINLP model simultaneously determines the technology selection, operation conditions, flow rate of each stream, energy consumption of each unit, economic performance, environmental impacts, and equipment sizes. The multiobjective MINLP problem is solved with the ɛ-constraint method. The resulting Pareto-optimal curve reveals the trade-off between the economic and environmental performances. The optimal solution reveals that the high-temperature gasification, direct cooling, internal hydrogen production and cobalt catalysis have the best environmental and economic performances. At the breakeven point, where the optimal NPV is 0, the unit production cost of hydrocarbon biorefinery is $4.43 per gasoline-equivalent gallon (GEG) with unit GWP of 20.92kg CO2 eqv./GEG. In the case of maximum NPV of $810 MM, the corresponding unit production cost is $3.17/GEG.

Modeling Resilience Enhancement Strategies for International Express Logistics

International express is a most time-sensitive industry, and members of this industry must be able to respond to disruptions quickly to ensure service quality and to avoid a loss of their competitiveness with other logistics service providers. Instead of a method that arbitrarily makes rushed decisions during the postdisruption phase, this paper describes a method for quantifying and optimizing resilience strategies based on concepts of integrated resource assignment, regardless of where the available resources are located in the logistics network studied or how much capacity can be rented from others. The study started with the use of a typical transportation network modeling approach and then incorporated nonlinear time-dependent cargo value functions into a multiobjective mixed-integer nonlinear programming problem. A set of optimal actions from resilience strategies, such as the selection of alternative routes, switching of shipping modes, rental of other carriers' capacities, reallocation of local trucks, and prioritization of the order of shipments because of limited capacities, was considered. Decisions should be based on overall trade-off considerations and, at the same time, joint maximization of the product of the total time-dependent cargo value and the corresponding throughput and minimization of the costs incurred with resilience enhancement strategies.