Mixed-integer Programming Method Research Articles

Unit commitment of power system with large-scale wind power considering multi time scale flexibility contribution of demand response

The large-scale wind power brings challenges to the power system flexibility. The demand response (DR) can provide flexible resources fast and economical. In this paper, a novel unit commitment model of large-scale wind power system considering the contribution of DR to multi time scale flexibility is presented. According to the multi time scale characteristics of DR resources, the multi time scale scheduling model of DR is established; Considering the flexible resource contribution of DR and the time-varying of wind power forecasting error, the multi time scale flexible resource supply and demand model is developed; Then the unit commitment model of large-scale wind power system considering the multi time scale flexibility contribution of DR resources is proposed. The mixed integer programming method is used as the solver. The proposed model can reflect the balance between flexibility supply and demand for multi time scale, and improve the economy of system operation on the premise of ensuring the system flexibility and security. Case studies are presented to demonstrate the effectiveness of the proposed model.

Examination of Daily Task Constraint in Technician Routing and Scheduling Problem

This paper deals with a multi-term technician routing and programming problem with a different concept. The problem is that technicians with various skills form teams, and these teams perform the tasks that take in distinct locations. Technicians have daily duty capacities while performing tasks. The cases where overtime costs are allowed by combining different technician numbers are analyzed. Paper provides a single-purpose mixed integer programming method for modeling the problem because the model implemented aims to optimize the travel cost while simultaneously minimizing the amount of overwork. The main issue also specifies the division of technicians with different skills into teams, assignment of tasks with different skill requirements to teams, and routes for each team at the same time. The number of customers visited on a route within the daily customer limit. In addition, the model included exceeding the daily customer limit in the model and bound it to a constraint. The various combinations of the daily normal and over-work number of customers were evaluated and examined their effects on the objective function. Finally, the paper presents computational experiments and analyses to evaluate the efficiency of the proposed mathematical formulation and solution approach. The results show that daily task constraints are effective in employee selection and amount of use.

Decision support models for annual catenary maintenance task identification and assignment

A well-maintained catenary system is crucial to efficient and safe railway operations. Schedule catenary maintenance tasks with consideration of reliability and cost is vital for annual maintenance planning. Since past research on catenary maintenance planning mainly adopt the preventive maintenance (PM) policy with fixed maintenance intervals, this study considers practical concerns of railway operators and applies predictive maintenance (PdM) policy in the annual catenary maintenance planning. A decision support model is proposed by using both mixed integer programming and heuristic methods to identify and assign catenary maintenance tasks with the objective of minimizing maintenance cost and labor cost. The numerical results show that the cost can be improved by 25% compared to the current PM-only practice. The proposed model assists planners to determine and schedule maintenance tasks effectively and ensures the required reliability.

Tabu-Based Large Neighbourhood Search for Time/Sequence-Dependent Scheduling Problems with Time Windows

An important class of scheduling problems is characterised by time-dependency and/or sequence-dependency with time windows. We introduce and analyze four algorithmic ideas for this class: a novel hybridization of adaptive large neighbourhood search (ALNS) and tabu search (TS), randomized generic neighbourhood operators, a partial sequence dominance heuristic, and a fast insertion strategy. An evaluation of the resulting hybrid algorithm on two domains, a realworld multi-orbit agile Earth observation satellite scheduling problem, and an order acceptance and scheduling problem, shows that it robustly outperforms a mixed integer programming method, a two-stage hybridization of ALNS and TS, and recent state-of-the-art metaheuristic methods.

Optimization operation strategy of electric boilers by mixed integer programming method in nickel production process

Nickel smelting process requires steam in the process of drying and calcining. Utilities Department is responsible for supplying steam either use electric boiler or fossil fuel. With fluctuations in fuel prices, limited electricity supply, boiler reliability, and government emission limits, it is a challenge for department utilities to produce steam. Planning and selection of boiler operations to produce steam to meet the needs of the smelting process are necessary in order to minimize operating costs and maintain boiler reliability in distributing steam. This condition makes mixed integer programming become the best method to solve the model. Mathematical models are used to determine boiler operations in the wet season and dry season by using mixed integer programming methods. In the wet season, boilers that use electricity can operate because electricity from hydropower is sufficient, although not fully the boiler can meet the steam needed. Whereas in the dry season boilers that use electricity cannot operate due to limited electricity supply generated from hydropower.

Resilient backup controller placement in distributed SDN under critical targeted attacks

Today, telecommunication networks are crucial infrastructures, as has, for example, been demonstrated by the COVID-19 crisis. Thus, protecting such infrastructures, including software-defined based networks (SDN), is of the utmost importance for network providers to assure society has constant access to reliable services. Targeted attacks on SDN can seriously affect their connectivity and thus service continuity. Such an attack, launched on network nodes, divides the network into disjoint components and, since the number of SDN controllers is limited, results in isolating a significant proportion of nodes from the (surviving) controllers, causing major disruptions in service availability. In this paper, we present an optimization approach which can be used by the SDN network operator to properly locate the controllers by taking into account predictable sets of critical targeted attacks on network topology. The proposed approach includes an algorithm for predicting, on the basis of appropriately defined attack effectiveness measures, the sets of most dangerous attacks. Such sets are then used as input data for controller placement optimization, which is performed by means of mixed-integer programming methods. In the optimization, the impact of the considered attacks is measured by a novel network availability measure. To minimize the consequences of attacks we consider additional backup controllers. Finally, we present results of a numerical study based on the introduced approach that illustrate the effectiveness of our approach.

A supervised method for scheduling multi-objective job shop systems in the presence of market uncertainties

In real industries, managers usually consider more than one objective in scheduling process. Minimizing completion time, operational costs and average of machine loads are amongst the main concerns of managers during production scheduling in practice. The purpose of this research is to develop a new scheduling method for job-shop systems in the presence of uncertain demands while optimizing completion time, operational costs and machine load average are taken into account simultaneously. In this research a new multi-objective nonlinear mixed integer programming method is developed for job-shop scheduling in the presence of product demand uncertainty. The objectives of the proposed method are minimizing cost, production time and average of machine loads index. To solve the model, a hybrid NSGA-II and Simulated Annealing algorithms is proposed where the core of the solving algorithm is set based on weighting method. In continue a Taguchi method is set for design of experiments and also estimate the best initial parameters for small, medium and large scale case studies. Then comprehensive computational experiments have been carried out to verify the effectiveness of the proposed solution approaches in terms of the quality of the solutions and the solving times. The outcomes are then compared with a classic Genetic Algorithm. The outcomes indicated that the proposed algorithm could successfully solve large-scale experiments less than 2 min (123 s) that is noticeable. While performance of the solving algorithm are taken into consideration, the proposed algorithm could improve the outcomes in a range between 9.07% and 64.96% depending on the input data. The results also showed that considering multi-objective simultaneously more reasonable results would be reached in practice. The results showed that the market demand uncertainty can significantly affect to the process of job shop scheduling and impose harms in manufacturing systems both in terms of completion time and machine load variation. Operational costs, however, did not reflect significantly to market demand changes. The algorithm is then applied for a manufacturing firm. The outcomes showed that the proposed algorithm is flexible enough to be used easily in real industries.

Optimization Algorithm of Gantry Route Problem for Odd-type Surface Mount Device

This paper proposes a methodology for gantry route optimization in order to maximize the productivity of a odd-type surface mount device (SMD). A odd-type SMD is a machine that uses a gantry to mount electronic components on the placement point of a printed circuit board (PCB). The gantry needs a nozzle to move its electronic components. There is a suitability between the nozzle and the electronic component, and the mounting speed varies depending on the suitability. When it is difficult for the nozzle to adsorb electronic components, nozzle exchange is performed, and nozzle exchange takes a certain amount of time. The gantry route optimization problem is divided into the mounting order on PCB and the allocation of nozzles and electronic components to the gantry. Nozzle and electronic component allocation minimized the time incurred by nozzle exchange and nozzle-to-electronic component compatibility by using an mixed integer programming method. Sequence of mounting points on PCB minimizes travel time by using the branch-and-price method. Experimental data was made by randomly picking the location of the mounting point on a PCB of 800mm in width and 800mm in length. The number of mounting points is divided into 25, 50, 75, and 100, and experiments are conducted according to the number of types of electronic components, number of nozzle types, and suitability between nozzles and electronic components, respectively. Because the experimental data are random, the calculation time is not constant, but it is confirmed that the gantry route is found within a reasonable time.

Proposed assembly line balancing using mixed integer programming to minimize idle time of union fuselage

This study is aimed to help the company doing an assembly line balancing to minimize station time as not to exceed takt time and minimize idle time between workstation, using Mixed Integer Programming (MIP) method with Multi-manned Assembly Line Balancing (MmALBP) approach using two mathematical model, which 1st model aimed to minimize the cycle time of all workstation, then those cycle time being a parameter in 2nd Mathematical model to specified the optimal number of workers also balancing workload between operators. Result from this research were able to minimize station time from 218.56 hour to 166.3 hour so it didn’t exceed the takt time and also could reduce total idle time until 45% from 905.2 hour in actual condition become 499.49 hour with decreased number of operator from 52 to 22 person, and increase the efficiency of assembly line from 54% in previous to 67% in the proposed line.

Efficient stowage plan with loading and unloading operations for shipping liners using foldable containers and shift cost-sharing

ABSTRACT In this paper, we investigate the foldable container slot planning problem with loading and unloading operations that include shifting containers in a shipping line. We use the global optimal perspective in which a terminal operator generates an optimal stowage plan created on the basis of demand at subsequent ports. State-of-the-art foldable containers have been recently used in commercial maritime transport systems because they confer space-saving advantages when folded. We investigate container use through mixed-integer programming and shift cost-sharing methods as means to prevent conflicts between ports over inessential shifts and to provide guidelines for distributing shift costs among all ports in a logical and fair way. Through the proposed model, we found that most inessential shifts, considered inevitable from the local optimal perspective, can be eliminated, and the inevitable shift costs can be fairly distributed. This article is a revised and expanded version of a paper entitled ‘Shift Minimization with Loading and Unloading Operations using Foldable Containers’ presented at the first Conference of the Yangtze-River Research and Innovation Belt(Y-RIB), Zhoushan, China; 2–5 December 2018.

Waste material recycling and exchanging decisions for industrial symbiosis network optimization

The industrial symbiosis initiative, which aims to reuse waste resources, is considered as a potential solution for sustainable manufacturing. Compared with much literature for the industrial symbiosis optimization about waste energy and wastewater, this paper proposes an industrial symbiosis optimization model based on the waste material recycling and exchanging network. By-products from the production process are considered the main components of waste material flows. A Mixed-integer programming method is employed to formulate the optimization model. In response to the three pillars of sustainability, three sub-objectives, namely the economy, environment, and society, are built for the proposed optimization model. The Epsilon-constraint technology is established to tackle the multi-objective model efficiently. Decisions on waste material recycling and exchanging flow are formulated in the proposed model, as well as options on reprocessing sites and reprocessing technology levels. The results show that the proposed Mixed-Inter Programming optimization method and Epsilon-constraint technology are sufficient to obtain the solutions of industrial symbiosis optimization. Technology level decisions integrated into the optimization model can balance the objectives of economy, environment, and society and provide a more extensive decision option space for managers. Raw material price and by-product recycling cost are two main elements of the waste material exchanging of industrial symbiosis optimization based on the parameter robustness analysis. Multi-objective optimization of waste material reprocessing and exchange network allows managers to make decisions based on different objective priorities.

A novel stochastic optimization model to design concentrated photovoltaic/thermal systems: A case to meet hotel energy demands compared to conventional photovoltaic system

This study offered a novel optimization model to design hybrid solar photovoltaic systems. In addition, the model was able to compare results from conventional photovoltaic panel systems to combined cooling, heating and power systems coupled with concentrated photovoltaic/thermal technology. In the trigeneration system, the concentrated photovoltaic/thermal collector, operating with an absorption chiller and hot water tank stratified, was modeled to supply the energy loads of hotels located in the city of Rio de Janeiro. Monte Carlo simulation considering uncertainty scenarios was applied to model the electric, cooling, and hot water demands, minute by minute, over a year. The optimal size of each system maximized the equivalent uniform annual cost through nonlinear programming, using the Basic Open-source Nonlinear Mixed Integer programming method. The decision variables for the combined cooling, heating and power system were the number of concentrated photovoltaic/thermal collectors and the hot water storage capacity. For the conventional photovoltaic system, the decision variable was the number of photovoltaic panels to be installed. In total, 16 hotels were optimized, showing that the total electrical demands met by the photovoltaic systems vary between 30% and 65%, decreasing as the hotel demands grow. Conversely, the trigeneration system would supply around 26–48% of electrical demands, 40–50% of cooling requirements, in addition to providing 20–45% of hot water for heating.

A proximal-point outer approximation algorithm

Many engineering and scientific applications, e.g. resource allocation, control of hybrid systems, scheduling, etc., require the solution of mixed-integer non-linear problems (MINLPs). Problems of such class combine the high computational burden arising from considering discrete variables with the complexity of non-linear functions. As a consequence, the development of algorithms able to efficiently solve medium-large MINLPs is still an interesting field of research. In the last decades, several approaches to tackle MINLPs have been developed. Some of such approaches, usually defined as exact methods, aim at finding a globally optimal solution for a given MINLP at expense of a long execution time, while others, generally defined as heuristics, aim at discovering suboptimal feasible solutions in the shortest time possible. Among the various proposed paradigms, outer approximation (OA) and feasibility pump (FP), respectively as exact method and as heuristic, deserve a special mention for the number of relevant publications and successful implementations related to them. In this paper we present a new exact method for convex mixed-integer non-linear programming called proximal outer approximation (POA). POA blends the fundamental ideas behind FP into the general OA scheme that attepts to yield faster and more robust convergence with respect to OA while retaining the good performances in terms of fast generation of feasible solutions of FP.

Moth flame optimizer-based solution approach for unit commitment and generation scheduling problem of electric power system

Abstract This paper proposes a new approach based on the moth flame optimizer algorithm. Moth flame optimizer simulates the natural fervent navigation technique adopted by moths looking for a source of light. The proposed method is further improved by priority list-based ordering; the unit commitment problem (UCP) is a non-linear, non-convex, and combinatorial complex optimization problem. It contains both continuous and discrete variables. This further increases its complexity. Moth flame optimizer is very good at obtaining a commitment pattern: allocation of power on the committed units obtained by mixed-integer quadratic programming method. Heuristic search strategies are used to adopt for the repair of minimum up and downtime, and spinning reserve constraints. MFO effectiveness is tested on the standard UCP reference IEEE model buses 14 and 30, and 10 and 20 units. The efficiency of the projected algorithms is compared to classical PSO, PSOLR, HPSO, PSOSQP, hybrid MPSO, IBPSO, LCA-PSO, NPSO, PSO-GWO, and various other evolutionary algorithms. The comparison result shows that MFO can lead to all methods reported earlier in literature.

A mixed integer programming method for multi-project resource leveling

A mixed integer programming method for multi-project resource leveling

Consumer phase identification in low-voltage distribution network considering vacant users

Accurate consumer phase connectivity in low-voltage distribution network (LVDN) plays a key role in maintaining high reliability of electricity supply and good power quality. However, vacant consumers, a lack of connectivity between feeders and consumers, and measurement error increase the difficulty to identify consumer phase connectivity for the existing data analytics methods. To overcome these hurdles, this paper proposes a novel consumer phase identification (CPI) algorithm based on consumer classification, quadratic programming, and probability distribution. Firstly, a consumer classification method based on voltage characteristics among users is proposed to deal with the vacant user problem. Then, a quadratic programming model based on Nodal Current Law is established to identify consumer phase when the network connectivity information between feeders and consumers is lack. Moreover, in order to improve robustness of the proposed phase identification algorithm on measurement error, a Monte Carlo probability distribution model is developed. The proposed algorithm is applied on a real-world LVDN in Guangdong. The comparison analysis between the proposed method and the Mix Integer Programming (MIP) method, and the impact of the variation rate threshold of correlation coefficient on the identification accuracy are also investigated. The results indicate that the proposed method effectively increases CPI accuracy compared with the MIP method when there are vacant users and measurement error of meters in LVDN.

Stochastic optimal sizing of distributed energy resources for a cost-effective and resilient Microgrid

Recent developments and advances in distributed energy resources (DERs) make them more affordable, accessible, and prevalent in microgrids. Research on designing and operating a microgrid with various DERs has received increasing attention during the past few years. This paper proposes a two-stage stochastic mixed-integer programming method for jointly determining optimal sizes of various DERs, considering both economic benefits and resilience performance. The proposed method explicitly models the interaction between DER sizing at the planning stage and hourly or sub-hourly microgrid dispatch at the operating stage in both grid-connected and island modes, considering stochastic grid disturbances, load, and renewable generation. A formulation method is then proposed to convert the stochastic sizing problem to an equivalent mix-integer linear programming problem, which can be efficiently solved even with a large number of system operating conditions. Using the proposed stochastic sizing method, a resource planning analysis for a military base in the U.S. is presented. It is found that the proposed method can effectively determine the optimal DER sizes to meet a required resilience goal at the maximum net-benefit. Impacts of several key factors including tariff rates, discount rate, and survivability level on optimal DER sizes are analyzed through case studies.

Two echelon vehicle routing problem with drones in last mile delivery

In recent years, drone routing and scheduling has become a highly active area of research. This research introduces a new routing model that considers a synchronized truck-drone operation by allowing multiple drones to fly from a truck, serve one or multiple customers, and return to the same truck for a battery swap and package retrieval. The model addresses two levels (echelons) of delivery: primary truck routing from the main depot to serve assigned customers and secondary drone routing from the truck, which behaves like a moveable intermediate depot to serve other sets of customers. The model takes into account both trucks' and drones’ capacities with the objective of finding optimal routes of both trucks and drones that minimizes the total arrival time of both trucks and drones at the depot after completing the deliveries. The problem can be solved by formulated mixed integer programming (MIP) for the small-size problem, and two efficient heuristic algorithms are designed to solve the large-size problems: Drone Truck Route Construction (DTRC) and Large Neighborhood Search (LNS). Numeric results from the experiment compare the performance of both heuristics against the MIP method in small/medium-size instances from the literature. A sensitivity analysis is conducted to show the delivery time improvement of the proposed model over the previous truck-drone routing models.

Time/sequence-dependent scheduling: the design and evaluation of a general purpose tabu-based adaptive large neighbourhood search algorithm

In intelligent manufacturing, it is important to schedule orders from customers efficiently. Make-to-order companies may have to reject or postpone orders when the production capacity does not meet the demand. Many such real-world scheduling problems are characterised by processing times being dependent on the start time (time dependency) or on the preceding orders (sequence dependency), and typically have an earliest and latest possible start time. We introduce and analyze four algorithmic ideas for this class of time/sequence-dependent over-subscribed scheduling problems with time windows: a novel hybridization of adaptive large neighbourhood search (ALNS) and tabu search (TS), a new randomization strategy for neighbourhood operators, a partial sequence dominance heuristic, and a fast insertion strategy. Through factor analysis, we demonstrate the performance of these new algorithmic features on problem domains with varying properties. Evaluation of the resulting general purpose algorithm on three domains—an order acceptance and scheduling problem, a real-world multi-orbit agile Earth observation satellite scheduling problem, and a time-dependent orienteering problem with time windows—shows that our hybrid algorithm robustly outperforms general algorithms including a mixed integer programming method, a constraint programming method, recent state-of-the-art problem-dependent meta-heuristic methods, and a two-stage hybridization of ALNS and TS.

Energy Market Management for Distribution Network with a Multi-Microgrid System: A Dynamic Game Approach

This paper proposes an energy market management framework to address the day-ahead optimization of a distribution network (DN) with a multi-microgrid (MMG). In this framework, an economic optimization based on a dynamic game is designed to ensure the reliability and stability of the DN operation while setting the internal transaction price to minimize the operation cost of the distribution network operator (DNO). The DNO, as a leader, sets the power flow constraints and microgrid operators (MGOs), as followers, respond to the internal transaction price and in turn affect the DNO’s price decision. The price incentive mechanism of the DNO is to encourage MGs to participate in energy market management, to promote joint operation of MGs and to reduce the operation cost of MGOs. The differential evolution algorithm and mixed integer programming method are applied to find the equilibrium solution to the dynamic game. Numerical simulations of a modified IEEE 33-bus system show the effectiveness of the proposed energy market management framework.