Mixed Integer Linear Programming Approach Research Articles

Optimally integrated waste heat recovery through combined emerging thermal technologies: Modelling, optimization and assessment for onboard multi-energy systems

This paper investigates waste heat (WH) valorisation on maritime vessels from a systemic perspective. It aims to demonstrate how a set of innovative waste heat recovery (WHR) technologies can synergistically work together to valorise waste heat in multiple ways. It proposes and develops a dedicated techno-economic analysis framework and model, surpassing previous literature that focused on individual technologies or specific combinations. Employing a Mixed Integer Linear Programming (MILP) approach, this study evaluates the dynamic and flexible operation of the WHR system throughout the round-trip journey of a vessel. Identifying the most profitable WHR system layout, determining the capacity of technologies, optimising the interconnections between technologies, and establishing strategic WH dispatching are all among the key objectives of the study.An average-scale vessel with a 36 MW diesel engine, is selected for this study which involves a 17-day journey with multiple stops in Northern Europe. The vessel adequately represents the complexity of onboard energy systems in terms of types and variability of demands, as well as WH availability. The proposed WHR system, which is tailored for the selected vessel, integrates three active technologies: an isobaric expansion engine (IEE) to contribute to mechanical power demand, a sorption system for providing cooling, and an advanced Organic Rankine Cycle (ORC) for trigeneration of power, heating, and cooling. All technologies are supported by the passive WHR technology of Thermal Energy Storage (TES). The results show that deployment of the optimised WHR system onboard the selected vessel enhances energy efficiency by 5 to 7.5 percentage points and reduces fuel consumption by 13%. The study also explores economic key performance indicators (KPIs), such as the Internal Rate of Return (IRR) which is found at about 15%, clearly evidencing a compelling solution to ship owners. Additionally, the discussion includes a detailed analysis of the contribution of individual technologies in covering onboard demands, as well as their synergistic interactions.This work clarifies the role, value, and benefit of WHR technologies onboard, advancing the understanding from individual WH recovery interventions to a system-level approach. This is especially valuable in practice, considering its adaptability across various vessel types within the global fleet.

A stochastic programming approach to the antibiotics time machine problem

Antibiotics Time Machine is an important problem to understand antibiotic resistance and how it can be reversed. Mathematically, it can be modeled as follows: Consider a set of genotypes, each of which contain a set of mutated and unmutated genes. Suppose that a set of growth rate measurements of each genotype under a set of antibiotics is given. The transition probabilities of a ‘realization’ of a Markov chain associated with each arc under each antibiotic are computable via a predefined function given the growth rate realizations. The aim is to maximize the expected probability of reaching to the genotype with all unmutated genes given the initial genotype in a predetermined number of transitions, considering the following two sources of uncertainties: (i) the randomness in growth rates, (ii) the randomness in transition probabilities, which are functions of growth rates. We develop stochastic mixed-integer linear programming and dynamic programming approaches to solve static and dynamic versions of the Antibiotics Time Machine Problem under the aforementioned uncertainties. We adapt a Sample Average Approximation approach that exploits the special structure of the problem and provide accurate solutions that perform very well in an out-of-sample analysis.

A hybrid metaheuristic to optimize electric first-mile feeder services with charging synchronization constraints and customer rejections

This paper addresses the on-demand meeting-point-based feeder electric bus routing and charging scheduling problem under charging synchronization constraints. The problem considered exhibits the structure of the location routing problem, which is more difficult to solve than many electric vehicle routing problems with capacitated charging stations. We propose to model the problem using a mixed-integer linear programming approach based on a layered graph structure. An efficient hybrid metaheuristic solution algorithm is proposed. A mixture of random and greedy partial charging scheduling strategies is used to find feasible charging schedules under the synchronization constraints. The algorithm is tested on instances with up to 100 customers and 49 bus stops/meeting points. The results show that the proposed algorithm provides near-optimal solutions within less one minute on average compared with the best solutions found by a mixed-integer linear programming solver set with a 4-hour computation time limit. A case study on a larger sized case with 1000 customers and 111 meeting points shows the proposed method is applicable to real-world situations.

Efficient configuration of heterogeneous multistatic sonar networks: A mixed-integer linear programming approach

The work undertaken in this paper pertains to the optimal spatial configuration of a heterogeneous Wireless Sensor Network (WSN) for the Area Coverage (AC) problem. Specifically, this research falls under the heading of Anti-Submarine Warfare (ASW) with an emphasis on active sonar systems and, more pointedly still, on a specific type of sensor: sonobuoys (portmanteau word formed by “sonar” and “buoy”). These buoys are further divided into three main categories: transmitter-only (Tx), receiver-only (Rx) and transmitter–receiver (TxRx). In this paper, we will therefore try to determine the geographical location of the different buoys comprising a Multistatic Sonar Network (MSN), special case of WSN, so as to maximize the overall surface area covered. To do this, we discretize an Area of Interest (AoI) into regular cells using bathymetric and altimetric data, and place a deployment position and a fictitious target at the center of each cell so that we can evaluate the network’s performance. More precisely, we are taking into account a limited number of sensors (buoys) with possible pairwise incompatibilities, variable performances, probabilistic detection models, an adverse masking effect (direct blast) as well as coastlines features. Finally, in order to solve this problem, we have developed several efficient Mixed-Integer Linear Programs (MILPs), all of which have been thoroughly tried-and-tested on a benchmark set of 100 instances derived from real elevation data. This has led us to identify an ideal model, i.e. one that is significantly better than all the others in the statistical sense.

English

English

Operational strategies and integrated design for producing green hydrogen from wind electricity

Realizing the potential of renewable hydrogen production requires flexible operation of electrolysis systems to integrate with intermittent power sources. This work develops an optimization model to assess flexible operational strategies for alkaline and proton exchange membrane (PEM) electrolysers powered by wind energy. The model quantitatively analyses trade-offs between electrolyser shutdown strategies, overloading capacities, and battery integration to identify optimal regimes balancing efficiency, flexibility, and economics. The results reveal a mixed-integer linear programming approach can optimize system configurations and control strategies to minimize the levelized cost of hydrogen production. Optimal near-minimum load operation is achieved by independently optimizing the load of each electrolyser block, while avoiding shutdowns above a critical load level. Strategic electrolyser overloading can provide economic benefits by reducing installed capital costs, if technical feasibility and accelerated degradation are addressed. Battery energy storage integration significantly improves economics by enhancing asset utilization, provided excess renewable energy is available. The model provides novel insights on integrating alkaline and PEM electrolysis with intermittent wind power to advance renewable hydrogen production. Quantifying trade-offs between operational flexibility and economics will help guide flexible design and control strategies for cost-optimal renewable electrolysis systems.

A BI-OBJECTIVE COST MINIMIZATION MODEL FOR THE INSULAR TOUR ROUTE PLANNING PROBLEM

This article presents a study on the development of a bi-objective cost problem optimization model in planning tourist routes in the island zone. This problem is a new variant of the tour route plan problem. Bi-objective view of two cost components, namely maritime transportation costs and ground transportation costs. Two models were formulated using a mixed integer linear programming approach. The first model was designed to minimize one of the two cost components separately. The second model was bi-objective cost minimization based on the priority weights of the two costs. It was designed to determine minimum transportation costs based on priority weights. Model testing was carried out through numerical experiments on several cases that often occur in industries in Maluku, Indonesia, especially tourism and goods shipping. Each case has variations in the number of islands and nodes. As a result, the model can demonstrate its adaptability to changes in objectives and parameters. For cases that do not have a single solution, an increase in the network structure on the number of islands and nodes will increase the variety of efficient alternative solutions. The set of efficient solutions also shows an inverse relationship between MTC and GTC. The results also show that MTC minimization cannot be used as a reference for TC minimization in cases with many nodes and islands. Efforts to minimize MTC in the island zone impact reducing total costs but do not mean minimizing total costs. In addition, based on the exponential trend line of computing time, the number of nodes has a more significant influence on computing time compared to the number of islands.

Research on capacity optimization of new energy hybrid energy storage system of high-speed railway

With the fast expansion of electrified railways, the need for energy is growing. Thus, improving railway coupling and interconnection, new energy, and energy storage is critical to support low-carbon and green railway development. Therefore, this paper proposes an optimal configuration method for the access capacity of wind power generation system (WPGS), photovoltaic power system (PVPS), and hybrid energy storage system (HESS) in the traction power supply system (TPSS) of high-speed railways. Firstly, the HESS’s mathematical model is developed, then the high-speed railway TPSS’s economic optimization operating model is built, and a HESS energy management approach is presented, taking the energy management strategy parameters and model capacity configuration parameters as the optimization variables. The mixed integer linear programming approach is used to resolve the actual example with the least daily operational cost of the high-speed rail system as the optimization goal, and the optimal capacity of WPGS, PVPS, and HESS is obtained. Finally, through comparison and analysis, it is verified that the economic benefit is the highest when the distributed complementary energy system covering WPGS, PVPS, and HESS is connected to the traction substation, and 10.47% of the daily expenditure is saved.

A mixed-integer linear programming approach for collateral management

Collateral management involves the efficient monitoring and allocation of assets to mitigate credit risk in financial transactions and is crucial for institutions such as commercial banks, investments banks, and central counterparties. It helps to ensure financial stability and compliance with regulatory requirements. This study is centered on a fundamental objective of collateral management, namely to collateralize as much as possible a set of transactions given a limited asset portfolio. In practice, an allocation is dynamic, necessitating periodic adjustments due to fluctuations over time in the asset pool, the transactions set, and asset value. Consequently, the objective is not merely the identification of an optimal allocation from zero but the optimization of an obsolete allocation in response to these fluctuations. The size and complexity of real-world problems often preclude direct resolution through conventional MILP solvers. In addition, each collateral adjustment movement incurs associated costs. In this research, a two-step method based on linear and mixed-integer linear programming formulations with ℓ1 penalties is devised, with the principal aim of minimizing under-allocation while simultaneously controlling the number of adjustment movements required. The method is tested on 20 real-world collateral givers and invariably reaches a good trade-off between solution quality, computational time, and the number of movements.

A multi-objective two-stage stochastic programming approach for wind farms and demand side provider decisions using the weighted metric method

The rapid expansion of wind-based renewable energy sources highlights the critical need to enhance reserve capacity within power systems. This research aims to develop an effective model for harnessing the combined potential of flexible demand-side resources, acting as demand-side providers (DSPs), to address the inherent unpredictability of wind power. The DSP framework comprises three demand response aggregators: the capacity market program (CAP), energy storage systems (ESSs), and plug-in electric vehicle parking lots (PEVs PLs). To achieve this, a multi-objective two-stage stochastic programming model is introduced. It not only minimizes operational costs for system operators but also maximizes returns for demand-side resource owners supervised by DSPs in the energy and reserve market environment. The problem is tackled using a mixed-integer linear programming (MILP) approach employing a weighted metric methodology. Within this framework, the Weibull probability distribution function (WPDF) is utilized to model wind power uncertainty, while the truncated Gaussian distribution function (GDF) encapsulates the uncertainty regarding electric vehicle owner behavior. The results demonstrate that employing this method for simultaneous programming of energy and reserve not only reduces system operator costs but also enhances profits for resource owners.

A mixed integer linear programming approach for the design of chemical process families

The need for rapid and widespread deployment of new technologies to address climate change goals (e.g., deep, economy-wide decarbonization) presents new opportunities for advancing modular design strategies. Conventional engineering approaches focus on unique designs for each installation, while missing opportunities for manufacturing standardization. Extending insights from the automotive industry, we optimize a platform of common unit module designs while simultaneously designing an entire family of process variants that make use of that platform. This reduces engineering effort, deployment timelines, and manufacturing costs. We propose a nonlinear generalized disjunctive programming formulation and convert this to an efficient mixed-integer linear programming (MILP) formulation through discretization of the design space. We formulate our optimization in Pyomo with costing from IDAES, and we demonstrate the computational performance and solution quality on a water treatment desalination system from the PARETO framework and a carbon capture system built in Aspen Plus® as part of CCSI2.

A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations Problems

AbstractWater distribution systems (WDSs) are critical infrastructure used to convey water from sources to consumers. The mathematical framework governing the distribution of flows and heads in extended period simulations of WDSs lends itself to application in a wide range of optimization problems. Applying the classical mixed integer linear programming (MILP) approach to model WDSs hydraulics within an optimization framework can contribute to higher solution accuracy with lower computational effort. However, adapting WDSs models to conform to a MILP formulation has proven challenging because of the intrinsic non‐linearity of system hydraulics and the complexity associated with modeling hydraulic devices that influence the state of the WDS. This paper introduces MILPNet, an adjustable framework for WDSs that can be used to build and solve an extensive array of MILP optimization problems. MILPNet includes constraints that represent the mass balance and energy conservation equations, hydraulic devices, control rules, and status checks. To conform to MILP structure, MILPNet employs piece‐wise linear approximation and integer programming. MILPNet was implemented and tested using Gurobi Python API. Modeling accuracy was shown to be comparable to EPANET, a public domain software for hydraulic modeling, and sensitivity analyses were conducted to examine the impacts of the modeling assumptions on the performance of MILPNet. Additionally, application of the framework was demonstrated using pump scheduling optimization examples in single and rolling horizon scenarios. Our results show that MILPNet can facilitate the construction and solution of optimization problems for a range of applications in WDSs operations.

4D BIM integrated optimization of construction steel bar procurement plan for limited storage capacity

Purpose Due to its longer length compared to other construction materials and distinctive stacking patterns, obtaining construction steel bars in congested construction sites with limited storage capacity becomes challenging. Lack of storage space in crowded places prompts the need for building steel bar storage choice optimization. Therefore, this study aims to optimize the construction steel bar procurement plan by providing when and how much rebar to order and how to stack different sizes of rebar considering limited storage capacity. Design/methodology/approach A novel approach has been presented in this paper by integrating 4D building information modelling (BIM) and mixed-integer linear programming (MILP). This technique uses BIM to retrieve material quantities, including rebar, during the design phase. Following that, activities are scheduled depending on the duration determined by crew productivity data and material quantity. Then, based on the prior price, the price of each unit of rebar is projected for the duration of construction using the exponential smoothing method. After that, the MILP approach is used to generate an optimal steel bar procurement plan for limited storage space following the scheduled rebar-related operations. Findings The developed strategy minimizes overall procurement costs and ensures the storage of rebar as per standard guidelines. An optimal rebar procurement and storage plan to construct a six-storied RC frame has been presented in this paper as a demonstrative example to show the effectiveness of the proposed method. Originality/value This work partially satisfies a long-sought research need for establishing a comprehensive construction steel bar procurement system, making it a very useful source of information for practitioners and researchers. The proposed method can be used to minimize a key performance limitation that the conventional rebar procurement practice for crowded building sites may experience.

Integrating Minimum Spanning Tree and MILP in Urban Planning: A Novel Algorithmic Perspective

This paper presents a novel eight-step iterative algorithm for optimizing the layout of a neighborhood, focusing on the efficient allocation of houses to strategically placed facilities, herein referred to as ’points of interest’. The methodology integrates a mixed integer linear programming (MILP) approach with a heuristic algorithm to address a variant of the facility location problem combined with network design considerations. The algorithm begins by defining a set of geographic coordinates to represent houses within a predefined area. It then identifies key points of interest, forming the basis for subsequent connectivity and allocation analyses. The methodology’s core involves applying the Greedy algorithm to assign houses to the nearest points of interest, subject to capacity constraints. The method is followed by computing a Minimum Spanning Tree (MST) among these points to ensure efficient overall connectivity. The proposed algorithm’s iterative design is a key attribute. The most promising result of this approach is its ability to minimize the distance between houses and points of interest while optimizing the network’s total length. This dual optimization ensures a balanced distribution of houses and an efficient layout, making it particularly suitable for urban planning and infrastructure development. The paper’s findings demonstrate the algorithm’s effectiveness in creating a practical and efficient neighborhood layout, highlighting its potential application in large-scale urban planning and development projects.

Energy Management Scheme for Optimizing Multiple Smart Homes Equipped with Electric Vehicles

The rapid advancement in technology and rise in energy consumption have motivated research addressing Demand-Side Management (DSM). In this research, a novel design for Home Energy Management (HEM) is proposed that seamlessly integrates Battery Energy Storage Systems (BESSs), Photovoltaic (PV) installations, and Electric Vehicles (EVs). Leveraging a Mixed-Integer Linear Programming (MILP) approach, the proposed system aims to minimize electricity costs. The optimization model takes into account Real-Time Pricing (RTP) tariffs, facilitating the efficient scheduling of household appliances and optimizing patterns for BESS charging and discharging, as well as EV charging and discharging. Both individual and multiple Smart Home (SH) case studies showcase noteworthy reductions in electricity costs. In the case of multiple SHs, a remarkable cost reduction of 46.38% was achieved compared to a traditional SH scenario lacking integration of a PV, BESS, and EV.

A design and analysis of computer experiments based mixed integer linear programming approach for optimizing a system of electric vehicle charging stations

This paper formulates a mixed integer linear programming (MILP) model to optimize a system of electric vehicle (EV) charging stations. Our methodology introduces a two-stage framework that integrates the first-stage system design problem with a second-stage control problem of the EV charging stations and develops a design and analysis of computer experiments (DACE) based system design optimization solution method. Our DACE approach generates a metamodel to predict revenue from the control problem using multivariate adaptive regression splines (MARS), fit over a binned Latin hypercube (LH) experimental design. Comparing the DACE based approach to using a commercial solver on the MILP, it yields near optimal solutions, provides interpretable profit functions, and significantly reduces computational time for practical application.

Lead-time-based freight routing in multi-modal networks considering the Physical Internet

This paper addresses the problem of optimizing the transport of goods in the Physical Internet (PI) framework in a multi-modal setting using a multi-objective mixed-integer linear programming (MILP) approach. The model is specifically designed to meet the requirements related to modular shipments and PI-hubs, and in particular, determines the allocation of modular shipments to each transport mode in an intermodal setting. In doing so, parallel direct connection via road, the delivery times and the transportation costs are minimized. The model is applied to a numerical case study, to test its effectiveness to enhance freight transport efficiency within the PI framework, by exploiting, in particular, all the capacities of the available vehicles. In addition, a sensitivity analysis is conducted on some model parameters, to test its reaction to changes in the supply system and in the objective priorities. Results show that all the shipments are effectively transported between the origin and the destination terminals, they are divided into modules when necessary, and the selected transport modes, allocation strategy, and delivery times vary accordingly to the objective priorities.

Comparative Analysis and Optimal Operation of an On-Grid and Off-Grid Solar Photovoltaic-Based Electric Vehicle Charging Station

One of the key strategies for decarbonization and green transportation is using electric vehicles (EVs). However, challenges like limited charging infrastructure, EV battery characteristics, and grid integration complexities persist. This study proposes a mixed-integer linear programming (MILP) approach to optimize a grid-connected solar PV-based commercial EV charging station (SPEVCS) with a battery energy storage system (BESS) for profit maximization. The MILP model efficiently manages SPEVCS operations, considering solar power fluctuations, EV charging patterns, and BESS usage. By coordinating charging schedules, grid stability is reinforced, and excess solar power can be lucratively managed. Comparing grid-connected and off-grid SPEVCS scenarios highlights grid integration benefits. Solar power mismatches with optimal charging periods pose a challenge, addressed here by BESS utilization and import/export of deficit/surplus power from/to the grid. The proposed framework incorporates solar power forecasts and probabilistic EV arrival predictions, enhancing decision accuracy. This approach fosters viable commercial EV charging, promotes green transportation, and reinforces grid resilience.

A Mixed-Integer Linear Programming Approach to Deploying Base Stations and Repeaters

A Mixed-Integer Linear Programming Approach to Deploying Base Stations and Repeaters

Optimization of the power output scheduling of a renewables-based hybrid power station using MILP approach: The case of Tilos island

Hybrid energy systems comprising renewables (mainly wind and solar) and storage systems are increasingly welcome to serve small communities or areas, such as small islands. In particular, the present study deals with the hybrid power station of Tilos, a little island located in the Greek Dodecanese, which includes a 800 kW wind turbine, a 160kWp PV field, and a 2.88 MWh NaNiCl2 battery; the system is also connected to the Kos-Kalymnos electrical network via a submarine cable. Currently, it is used to export its whole energy production under the management of the Greek company Eunice Energy Group. The agreement with the grid regulator is conceived to involve a remuneration for the energy output in three power levels (0 kW, 200 kW, 400 kW), with hourly dispatch provided the day before. Economic penalties will be applied in the near future for failure to respect power levels, whether in the form of excess or deficiency. This must be done in accordance with the available power to avoid surpluses or deficits, as well as excessive curtailment of renewable energy. In this work, a way to optimize energy fluxes of the island is proposed to better exploit the potential revenue, without excessively resorting to curtailments. The optimizations are performed in a Python environment through the “Gurobi” optimization solver, which is based on Mixed Integer Linear Programming (MILP). Scheduling emerges as a result of a rolling horizon approach. The new scheduling method reveals that there is potential for an increase in exported energy by 87.1% and potentially doubles the earnings over the current operation. Furthermore, novel scenarios are proposed to explore how different agreements with the grid operator would shift the optimal solution. Compared to an ideal optimized control under the current restrictions, a scenario that introduces the possibility of shutting down the wind turbine may increase the annual earnings by 10%, while a scenario that introduces a higher power band has the potential to increase annual earnings by 29.1%.