Mixed Integer Linear Programming Optimization Research Articles

Accurate THD Formulas for Multilevel Inverters with MILP Optimization

This study aims to derive simple formulas for calculating the accurate Total Harmonic Distortion (THD) of Multilevel Inverter (MLIs), that considers all low and high order harmonics, for single phase and three phase MLIs., since the THD is a main criterion when judging the performance of a MLI. In addition, a formula for the percentage route mean square value of high order harmonics %V HOrms is derived. These formulas could be applied for all types of MLIs that use different switching techniques for harmonics elimination or reduction, so long as the switching angles of the phase voltage are known and it is specially suitable to be applied with the Mixed Integer Linear Programming (MILP) optimization model, which is constructed for determining the switching angles of the MLI that minimize the absolute values of any undesired harmonics. This study aims also to show that this MILP model can produce solutions that have low values of the accurate THD, by giving the detailed solutions of two cases taken from the references.

Two-Stage Robust Generation Expansion Planning: A Mixed Integer Linear Programming Model

This paper presents a new uncertainty handling framework for optimal generation expansion planning (GEP) amalgamating the notions of single-stage and two-stage robust optimization (RO). The proposed multiyear robust GEP methodology, as a tractable mixed integer linear programming optimization problem, copes with the inherent planning uncertainties associated with forecasted electricity load demand, as well as estimated investment and operation costs through distribution-free bounded intervals producing polyhedral uncertainty sets. The optimal generation expansion plan obtained from the proposed RO approach is immunized against worst-case planning uncertainties considering the adopted degree of conservatism for each uncertainty set. Therefore, the proposed methodology is capable of controlling the robustness of the optimal investment schedule regarding the enforced planning uncertainties. Simulation results demonstrate the efficacy and efficiency of the proposed RO framework throughout GEP studies.

Modelling and optimization of CO2 abatement strategies

Burning coal is one of the most economical ways of generating electricity but is the most damaging in terms of carbon emissions. Conversely, renewable energy (RE), which produces no carbon emissions, has drawbacks such as intermittency, a lower electricity conversion rate and high cost. In this study, a mixed integer linear programming (MILP) optimisation model under carbon constraints is developed to address these issues. The model is able to determine the most economical low carbon power generation mix to satisfy the forecast electricity demand in Iskandar Malaysia (IM) for the year 2025 while being reliable and having less impact on the environment. The model includes fuel-switching, RE power generation and implementation of carbon capture and storage (CCS). The applicability of the model is tested and compared for scenarios of business as usual (BAU) and various CO2 emission reduction targets (CO2Em).

A Decisional Modeling for Network Franchise and Supply Chain Management

This article offers a modeling process that is aimed to evaluate and optimize logistics and financial flows in franchise networks. The proposed modeling consists in a combination of two modeling processes: the first reproduces the running logistic network through simulation and/or optimization; then data given by this model are used by a model that reproduces consequences on the mixed franchise network through a MILP (Mixed Integer Linear Programming) optimization based on the four Bradach management challenges: network growth, outlets uniformity, local responsiveness and system-wide adaptation.Applied to three networks types, the modeling process confirms that a combination of company-owned outlets and franchised outlets is the best way to manage the networks growth but also shows that the mix rate can be different between different type of networks.

Hybrid simulated annealing and mixed integer linear programming algorithm for optimal planning of radial distribution networks with distributed generation

This paper presents a hybrid simulated annealing (SA) and mixed integer linear programming (MILP) approach for static expansion planning of radial distribution networks with distributed generators (DGs). The expansion planning problem is first modeled as MILP optimization problem with the goal of minimizing the investment cost, cost of losses, cost of customer interruptions due to failures at the branches and at DGs and the cost of lost DG production due to failures at branches. In order to reduce the complexity of planning problems the decomposition of the original problem is proposed into a number of sequences of sub-problems (local networks) that are solved using the MILP model. The decomposition and solution process is iteratively guided and controlled by the proposed SA algorithm that employs the proper intensification and diversification mechanism to obtain the minimum total cost solution.

Least Economic Cost Regional Water Supply Planning – Optimising Infrastructure Investments and Demand Management for South East England’s 17.6 Million People

This paper presents a deterministic capacity expansion optimisation model designed for large regional or national water supply systems. The annual model selects, sizes and schedules new options to meet predicted demands at minimum cost over a multi-year time horizon. Options include: supply-side schemes, demand management (water conservation) measures and bulk transfers. The problem is formulated as a mixed integer linear programming (MILP) optimisation model. Capital, operating, carbon, social and environmental costs of proposed discrete schemes are considered. User-defined annual water saving profiles for demand management schemes are allowed. Multiple water demand scenarios are considered simultaneously to ensure the supply–demand balance is preserved across high demand conditions and that variable costs are accurately assessed. A wide range of supplementary constraints are formulated to consider the interdependencies between schemes (pre-requisite, mutual exclusivity, etc.). A two-step optimisation scheme is introduced to prevent the infeasibilities that inevitably appear in real applications. The model was developed for and used by the ‘Water Resources in the South East’ stakeholder group to select which of the 316 available supply schemes (including imports) and 511 demand management options (considering 272 interdependencies) are to be activated to serve the inhabitants of South East of England. Selected schemes are scheduled and sized over a 25 year planning horizon. The model shows demand management options can play a significant role in the region’s water supply and should be considered alongside new supplies and regional transfers. Considering demand management schemes reduced overall total discounted economic costs by 10 % and removed two large reservoirs from the least-cost plan. This case-study optimisation model was built using a generalised data management software platform and solved using a mixed integer linear programme.

Design for Energy-Efficient IP Over WDM Networks With Joint Lightpath Bypass and Router-Card Sleeping Strategies

To reduce the energy consumption of the Internet, much research effort has been dedicated to the design of energy-minimized IP over WDM networks. In this study, we design energy-minimized IP over WDM networks based on modular router cards and by jointly applying the lightpath bypass and router-card sleeping strategies. As a key advantage, the design does not require rerouting of IP flows or optical channels in either the IPor optical layer. Rather, to save energy, we only need to sleep or wake up the router cards according to user traffic demands when applying the sleeping strategy, which significantly simplifies the network control and management. To minimize the total energy consumption of the IPover WDM network in a time period (e.g., 1 day), we develop a mixed integer linear programming (MILP) optimization model. Moreover, to alleviate the computational complexity of the MILP model, we divide the minimization problem into two subproblems, namely, 1) establishing a virtual topology and 2) allocating router ports on router cards to the optical channels on different virtual links. For each of the subproblems, we develop a separate MILP optimization model. Further, for large-network design, we also propose two efficient heuristics to optimize energy consumption. Simulation studies indicate that the joint MILP model with the lightpath bypass and router-card sleeping strategies can maximally reduce energy consumption, up to 40% compared to the nonsleeping case. In addition, under the router-card sleeping strategy, the approach of allocating the router ports on different router cards to the optical channels plays an important role in the design of an energy-minimized IP over WDM network. A mixed mode that jointly performs interleaving and sequential router-port allocations can achieve the highest energy savings.

Robust Automated Mass Spectra Interpretation and Chemical Formula Calculation Using Mixed Integer Linear Programming

Untargeted metabolite profiling using liquid chromatography and mass spectrometry coupled via electrospray ionization is a powerful tool for the discovery of novel natural products, metabolic capabilities, and biomarkers. However, the elucidation of the identities of uncharacterized metabolites from spectral features remains challenging. A critical step in the metabolite identification workflow is the assignment of redundant spectral features (adducts, fragments, multimers) and calculation of the underlying chemical formula. Inspection of the data by experts using computational tools solving partial problems (e.g., chemical formula calculation for individual ions) can be performed to disambiguate alternative solutions and provide reliable results. However, manual curation is tedious and not readily scalable or standardized. Here we describe an automated procedure for the robust automated mass spectra interpretation and chemical formula calculation using mixed integer linear programming optimization (RAMSI). Chemical rules among related ions are expressed as linear constraints and both the spectra interpretation and chemical formula calculation are performed in a single optimization step. This approach is unbiased in that it does not require predefined sets of neutral losses and positive and negative polarity spectra can be combined in a single optimization. The procedure was evaluated with 30 experimental mass spectra and was found to effectively identify the protonated or deprotonated molecule ([M + H](+) or [M - H](-)) while being robust to the presence of background ions. RAMSI provides a much-needed standardized tool for interpreting ions for subsequent identification in untargeted metabolomics workflows.

A Chance-Constrained Unit Commitment With an $n-K$ Security Criterion and Significant Wind Generation

This paper presents a new approach for the joint energy and reserves scheduling and unit commitment with n-K reliability constraints for the day-ahead market. The proposed method includes a novel n-K criterion where demand must be met with a specified probability under any simultaneous loss of K generating units. A chance-constrained method is proposed with an α-quantile measure to determine the confidence level to meet the demand under K simultaneous contingencies. The chance-constrained optimization problem is recast as a mixed integer linear programming optimization problem. Wind and demand uncertainty are included into the model. The methodology proposed is illustrated with several case studies where the effect of increasing wind power penetration is analyzed showing the performance of our model.

Design and optimization of industrial power systems for natural gas processing

This paper presents a novel design methodology for power systems. A superstructure-based modelling technique has been applied to identify the cost-effective match between available power generation equipment and energy consumers. Multi-period design is conducted to ensure accurate equipment performance estimation. The proposed MILP (mixed integer linear programming) optimization model is able to reflect the machinery performance variations affected by the environmental conditions, and to estimate the deteriorated machinery performance due to part-load operation. To maintain the linear nature of the overall mathematical model, machinery performance is linearized with reasonable accuracy. Moreover, the multi-period methodology is able to conduct synthesis of power systems for processes with non-constant energy demands. Case studies are illustrated to demonstrate the importance of considering the effect of ambient conditions and part-load operation on machinery performance. With the ability to satisfy varying energy demands, and more accurate description of the machinery performance, the optimal design yielded from the improved model would exhibit better flexibility and reliability.

Reach-Related Energy Consumption in IP-Over-WDM 100G Translucent Networks

The quest of extended optical reach has been one of the major drivers for the transmission systems research field. Since extending the optical reach does not come for free and that reducing the power consumption has become a mandatory task for network designers, we investigate IP-over-WDM network power consumption as a function of 100 Gb/s Transponders' (TXP) transmission reach. In order to achieve this target, we propose a novel analytical model that captures the increase of TXP power consumption versus its optical reach. Network design is performed via a Mixed Integer Linear Programming (MILP) optimization engine. We have used two Multi-Layer design strategies, the Bypass (Bp) and the Direct-Bypass (DBp), that we have both applied to the “All-On” and the “On-Off” planning approaches: the former considers that transmission devices are always on and provides an upper bound to the network power consumption whereas the latter maximizes power savings by switching network devices On-Off according to daily traffic variations. Finally, simulations on a European-like backbone network show that there exists an optical reach that leads to a minimum network power consumption, the so-called optimal reach. By performing network design at the optimal reach we can achieve up to 36% and 37% of energy savings with respect to an extended reach-based design in the All-On and in the On-Off planning respectively.

Aggregation operators for fuzzy ontologies

Fuzzy ontologies extend classical ontologies to allow the representation of imprecise and vague knowledge. Although a relatively important amount of work has been carried out in the field during the last years and they have been successfully used in several applications, several notions from fuzzy logic have not been considered yet in fuzzy ontologies. Among them are aggregation operators, mathematical functions used to fuse different pieces of information, which is a very common need. Some examples of aggregation operators are weighted sums, Ordered Weighting Averaging operators and fuzzy integrals.In this work, we integrate fuzzy ontologies and aggregation operators. As a theoretical formalism, we provide the syntax and semantics of a fuzzy Description Logic with fuzzy aggregation operators. We provide a reasoning algorithm for the family of operators that are representable using a Mixed Integer Linear Programming optimization problem. We also show how to encode some examples of aggregation operators using the language Fuzzy OWL 2.

Hardwood Biomass to Gasoline, Diesel, and Jet Fuel: 2. Supply Chain Optimization Framework for a Network of Thermochemical Refineries

Biomass-based energy processes pose logistical challenges because of the dispersed nature of biomass resources. A nationwide supply chain optimization framework is applied to a biomass-to-liquid (BTL) system that uses hardwood biomass resources in the United States to produce gasoline, diesel, and jet fuel. Using optimized BTL refineries of differing capacities (i.e., 0.8, 1, 2.5, and 10 thousand barrels per day) and fuel product ratios (i.e., commensurate with the United States demand, maximization of diesel, and maximization of jet fuel), the supply chain case studies that correspond to the three product ratios are addressed via a large-scale mixed-integer linear programming (MILP) optimization model. The mathematical formulation includes the locations of hardwood biomass in the United States, the delivery locations of fuel products, the transportation costs of every input and output of the refinery, the material balances of each BTL refinery, water resources, and electricity requirement of the supply c...

Refinery scheduling of crude oil unloading with tank inventory management

The aim of this study is to develop a methodology for short-term crude oil unloading, tank inventory management, and crude distillation unit (CDU) charging schedule using mixed integer linear programming (MILP) optimization model as an extension to a previous work reported by Lee et al. (1996). The authors attempt to improve the previous model by adding an interval–interval variation constraint to avoid CDU charging rate fluctuation, a shutdown penalty within the scheduling cycle and a set up penalty for tank-tank transfer and introducing demand violation permit for a more flexible model against obtaining infeasible solution. Three different cases from the original paper were used to test the validity of the improved model. Comparison between Cases 1 and 2 shows the advantage of using smaller time interval as the operating cost of Case 2 is lower. Two scenarios were created from Case 3 to show the benefits of the improved model in deciding the best schedule to use. The improved model was implemented using the CPLEX solver in GAMS.

An Efficient Formulation of the Real-Time Feasibility Region for Design Optimization

In the design of time-critical applications, schedulability analysis is used to define the feasibility region of tasks with deadlines, so that optimization techniques can find the best design solution within the timing constraints. The formulation of the feasibility region based on the response time calculation requires many integer variables and is too complex for solvers. Approximation techniques have been used to define a convex subset of the feasibility region, used in conjunction with a branch and bound approach to compute suboptimal solutions for optimal task period selection, priority assignment, or placement of tasks onto CPUs. In this paper, we provide an improved and simpler real-time schedulability test that allows an exact and efficient definition of the feasibility region in Mixed Integer Linear Programming (MILP) optimization. Our method requires a significantly smaller number of binary variables and is viable for the treatment of industrial-size problem, as shown by the experiments.

Modeling-based Design of Strategic Supply Chain Networks for Aircraft Manufacturing

The aerospace supply chain network has evolved and become more complex over the years. New methods are needed to design and analyze the system, and to establish the interactions between aircraft (product) design and supply chain (process) design. This paper aims to introduce a strategic multi-product, multi-period design model for the manufacturing of an aircraft wing-box with a planning horizon of the full program duration. The supply chain systems consist of a number of external suppliers, candidate manufacturing sites, and a number of customers at fixed locations. The design model is a mixed-integer linear programming optimization routine that minimizes the total time-discounted network cost. The model generates a system configuration that specifies the location and capacity of the manufacturing sites, the material flow, and the transportation routes within the network. The model is implemented using open-source tools, and has a comprehensive and flexible data structure to support the decision-making process during the early aircraft design stages.

If you build it, he will come: Anticipative power transmission planning

Like in the film Field of Dreams, the sentence “if you build it, he will come” also applies in power systems. In this sense, if a transmission planner suggests building some lines in anticipation of generation capacity investments, then it can induce generation companies to invest in a more socially efficient manner. In this paper, we solve for the optimal way of doing this anticipative power transmission planning. Inspired in the proactive transmission planning model proposed by Sauma and Oren (2006) we formulate a mixed integer linear programming optimization model that integrates transmission planning, generation investment, and market operation decisions and propose a methodology to solve for the optimal transmission expansion. Contrary to the proactive methodology proposed by Sauma and Oren (2006), our model solves the optimal transmission expansion problem anticipating both generation investment and market clearing. We use the marginalist theory with production cost functions inversely related to the installed capacity in a perfectly competitive electricity market and we find all possible generation expansion pure Nash equilibria. We illustrate our results using 3-node and 4-node examples.

Optimal Operation of Residential Energy Hubs in Smart Grids

This paper presents mathematical optimization models of residential energy hubs which can be readily incorporated into automated decision making technologies in smart grids, and can be solved efficiently in a real-time frame to optimally control all major residential energy loads, storage and production components while properly considering the customer preferences and comfort level. Novel mathematical models for major household demand, i.e., fridge, freezer, dishwasher, washer and dryer, stove, water heater, hot tub, and pool pumps are formulated. Also, mathematical models of other components of a residential energy system including lighting, heating, and air-conditioning are developed, and generic models for solar PV panels and energy storage/generation devices are proposed. The developed mathematical models result in Mixed Integer Linear Programming (MILP) optimization problems with the objective functions of minimizing energy consumption, total cost of electricity and gas, emissions, peak load, and/or any combination of these objectives, while considering end-user preferences. Several realistic case studies are carried out to examine the performance of the mathematical model, and experimental tests are carried out to find practical procedures to determine the parameters of the model. The application of the proposed model to a real household in Ontario, Canada is presented for various objective functions. The simulation results show that savings of up to 20% on energy costs and 50% on peak demand can be achieved, while maintaining the household owner's desired comfort levels.

An improvement-based MILP optimization approach to complex AWS scheduling

The automated wet-etch station (AWS) is one of the most critical stages of a modern semiconductor manufacturing system (SMS), which has to simultaneously deal with many complex constraints and limited resources. Due to its inherent complexity, industrial-sized automated wet-etch station scheduling problems are rarely solved through full rigorous mathematical formulations. Decomposition techniques based on heuristic, meta-heuristics and simulation-based methods have been traditionally reported in literature to provide feasible solutions with reasonable CPU times.This work introduces an improvement MILP-based decomposition strategy that combines the benefits of a rigorous continuous-time MILP (mixed integer linear programming) formulation with the flexibility of heuristic procedures. The schedule generated provides enhanced solutions over time to challenging real-world automated wet etch station scheduling problems with moderate computational cost. This methodology was able to provide more than a 7% of improvement in comparison with the best results reported in literature for the most complex problem instances analyzed.

Applying an integrated logistics network design and optimisation model: the Pirelli Tyre case

The aim of the present paper is to provide an application to a real-life supply-chain context (i.e. the Pirelli Tyre European logistics network) of an integrated logistics network design and optimisation model. Starting from the analysis of supply chain under study and of the configuration problem to be solved, we identified the most suitable approach: a mixed integer linear programming optimisation model endowed with a series of guidelines for gathering and processing all the data necessary to set-up and run the model. The application of the selected integrated design and optimisation model to the Pirelli Tyre case led to significant cost savings related to three different service-level scenarios. Thus, the applied model could be profitably implemented by supply chain and logistics managers for optimising various operating contexts. Moreover, the exemplified data-mapping section represents a useful guideline, which can be applied by practitioners to gather and handle the high volume of data necessary for running the model in a real-life context. In conclusion, since the current state of the art is particularly lacking exhaustive supply-chain design models, the implemented integrated approach represents a significant contribution to the existing body of knowledge on supply chain configuration.