scholarly journals MILP Formulation for Solving and Initializing MINLP Problems Applied to Retrofit and Synthesis of Hydrogen Networks

Processes ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1102
Author(s):  
Patrícia R. da Silva ◽  
Marcelo E. Aragão ◽  
Jorge O. Trierweiler ◽  
Luciane F. Trierweiler
Keyword(s):  
Linear Programming ◽  
Linear Model ◽  
Cost Reduction ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Starting Point ◽  
Good Starting Point ◽  
Cost Efficient ◽  
Hydrogen Network ◽  
The Cost

The demand for hydrogen in refineries is growing due to its importance as a sulfur capture element. Therefore, hydrogen management is critical for fulfilling demands as efficiently as possible. Through mathematical modeling, hydrogen network management can be better performed. Cost-efficient Mixed-Integer Linear Programming (MILP) and Mixed-Integer Nonlinear Programming (MINLP) optimization models for (re)designing were proposed and implemented in GAMS with two case studies. Linear programming has the limitation of no stream mixing allowed; therefore, to overcome this limitation, an algorithm-based procedure called the Virtual Compressor Approach was proposed. Based on the MILP optimal solution obtained, the streams and compressors were merged. As a result, the number of compressors was reduced, along with the inherent investment costs. An operational cost reduction of more than 28% (example 1) and 26% (example 2) was obtained with a linear model. The optimal MILP solution after rearranging compressors was then provided as a good starting point to the MINLP. The operating costs were decreased by more than 31% (example 1) and 32% (example 2). Most of the cost reduction was obtained only with the usage of the MILP model. Besides, a higher level of cost reduction was only obtained when the linear model was used as the starting point.

scholarly journals Minimising negative externalities cost using 0-1 mixed integer linear programming model in e-commerce environment

2017 ◽  
Vol 11 ◽  
Author(s):  
Akyene Tetteh ◽  
Sarah Dsane-Nsor
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Programming Model ◽  
Petroleum Products ◽  
Mixed Integer ◽  
The Internet ◽  
Negative Externalities ◽  
The Government ◽  
The Cost

Background: Although the Internet boosts business profitability, without certain activities like efficient transportation, scheduling, products ordered via the Internet may reach their destination very late. The environmental problems (vehicle part disposal, carbon monoxide [CO], nitrogen oxide [NOx] and hydrocarbons [HC]) associated with transportation are mostly not accounted for by industries.Objectives: The main objective of this article is to minimising negative externalities cost in e-commerce environments.Method: The 0-1 mixed integer linear programming (0-1 MILP) model was used to model the problem statement. The result was further analysed using the externality percentage impact factor (EPIF).Results: The simulation results suggest that (1) The mode of ordering refined petroleum products does not impact on the cost of distribution, (2) an increase in private cost is directly proportional to the externality cost, (3) externality cost is largely controlled by the government and number of vehicles used in the distribution and this is in no way influenced by the mode of request (i.e. Internet or otherwise) and (4) externality cost may be reduce by using more ecofriendly fuel system.

scholarly journals Security Constrained Unit Commitment in a Power System based on Benders Decomposition and Mixed Integer Non-linear Programming

2018 ◽  
Vol 7 (2.6) ◽  
pp. 283 ◽  
Author(s):  
Pranda Prasanta Gupta ◽  
Prerna Jain ◽  
Suman Sharma ◽  
Rohit Bhakar
Keyword(s):  
Linear Programming ◽  
Network Security ◽  
Power System ◽  
Optimal Power Flow ◽  
Benders Decomposition ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Reserve Requirement ◽  
Non Linear Programming ◽  
Non Linear

In deregulated power markets, Independent System Operators (ISOs) maintains adequate reserve requirement in order to respond to generation and system security constraints. In order to estimate accurate reserve requirement and handling non-linearity and non-convexity of the problem, an efficient computational framework is required. In addition, ISO executes SCUC in order to reach the consistent operation. In this paper, a novel type of application which is Benders decomposition (BD) and Mixed integer non linear programming (MINLP) can be used to assess network security constraints by using AC optimal power flow (ACOPF) in a power system. It performs ACOPF in network security check evaluation with line outage contingency. The process of solving modified system would be close to optimal solution, the gap between the close to optimal and optimal solution is expected to determine whether a close to optimal solutionis accepetable for convenientpurpose. This approach drastically betters the fast computational requirement in practical power system .The numerical case studies are investigated in detail using an IEEE 118-bus system. 

scholarly journals Layout optimization of simplified trusses using mixed integer linear programming with runtime generation of constraints

2020 ◽  
Vol 61 (5) ◽  
pp. 1977-1999
Author(s):  
H. Fairclough ◽  
M. Gilbert
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Geometry Optimization ◽  
Layout Optimization ◽  
Mixed Integer ◽  
Optimal Solutions ◽  
Problem Size ◽  
Solution Quality ◽  
Starting Point

AbstractTraditional truss layout optimization employing the ground structure method will often generate layouts that are too complex to fabricate in practice. To address this, mixed integer linear programming can be used to enforce buildability constraints, leading to simplified truss forms. Limits on the number of joints in the structure and/or the minimum angle between connected members can be imposed, with the joints arising from crossover of pairs of members accounted for. However, in layout optimization, the number of constraints arising from ‘crossover joints’ increases rapidly with problem size, along with computational expense. To address this, crossover constraints are here dynamically generated and added at runtime only as required (so-called lazy constraints); speedups of more than 20 times are observed whilst ensuring that there is no loss of solution quality. Also, results from the layout optimization step are shown to provide a suitable starting point for a non-linear geometry optimization step, enabling results to be obtained that are in agreement with literature solutions. It is also shown that symmetric problems may not have symmetric optimal solutions, and that multiple distinct and equally optimal solutions may be found.

scholarly journals Demand Side Energy Management via Multiagent Coordination in Consumer Cooperatives

2014 ◽  
Vol 50 ◽  
pp. 885-922 ◽  
Author(s):  
A. Veit ◽  
Y. Xu ◽  
R. Zheng ◽  
N. Chakraborty ◽  
K. Sycara
Keyword(s):  
Cost Reduction ◽  
Energy Demand ◽  
Incentive Compatibility ◽  
Electric Energy ◽  
Optimal Solution ◽  
Convergence Time ◽  
Multiagent Coordination ◽  
Price Functions ◽  
The Cost ◽  
The Coordinator

A key challenge in creating a sustainable and energy-efficient society is to make consumer demand adaptive to the supply of energy, especially to the renewable supply. In this article, we propose a partially-centralized organization of consumers (or agents), namely, a consumer cooperative that purchases electricity from the market. In the cooperative, a central coordinator buys the electricity for the whole group. The technical challenge is that consumers make their own demand decisions, based on their private demand constraints and preferences, which they do not share with the coordinator or other agents. We propose a novel multiagent coordination algorithm, to shape the energy demand of the cooperative. To coordinate individual consumers under incomplete information, the coordinator determines virtual price signals that it sends to the consumers to induce them to shift their demands when required. We prove that this algorithm converges to the central optimal solution and minimizes the electric energy cost of the cooperative. Additionally, we present results on the time complexity of the iterative algorithm and its implications for agents' incentive compatibility. Furthermore, we perform simulations based on real world consumption data to (a) characterize the convergence properties of our algorithm and (b) understand the effect of differing demand characteristics of participants as well as of different price functions on the cost reduction. The results show that the convergence time scales linearly with the agent population size and length of the optimization horizon. Finally, we observe that as participants' flexibility of shifting their demands increases, cost reduction increases and that the cost reduction is not sensitive to variation in consumption patterns of the consumers.

scholarly journals A New Approach to Find an Optimal Solution of a Fuzzy Linear Programming Problem by Fuzzy Dynamic Programming

2018 ◽  
Vol 7 (4.10) ◽  
pp. 360
Author(s):  
T. Nagalakshmi ◽  
G. Uthra
Keyword(s):  
Dynamic Programming ◽  
Linear Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
New Approach ◽  
The Cost ◽  
Recursive Equations

This paper mainly focuses on a new approach to find an optimal solution of a fuzzy linear programming problem with the help of Fuzzy Dynamic Programming. Linear programming deals with the optimization of a function of variables called an objective function, subject to a set of linear inequalities called constraints. The objective function may be maximizing the profit or minimizing the cost or any other measure of effectiveness subject to constraints imposed by supply, demand, storage capacity, etc., Moreover, it is known that fuzziness prevails in all fields. Hence, a general linear programming problem with fuzzy parameters is considered where the variables are taken as Triangular Fuzzy Numbers. The solution is obtained by the method of FDP by framing fuzzy forward and fuzzy backward recursive equations. It is observed that the solutions obtained by both the equations are the same. This approach is illustrated with a numerical example. This feature of the proposed approach eliminates the imprecision and fuzziness in LPP models. The application of Fuzzy set theory in the field of dynamic Programming is called Fuzzy Dynamic Programming. 

scholarly journals Road network optimization using heuristic and linear programming

2010 ◽  
Vol 56 (No. 3) ◽  
pp. 137-145 ◽  
Author(s):  
R. Ghaffariyan M ◽  
K. Stampfer ◽  
J. Sessions ◽  
T. Durston ◽  
CH. Kanzian ◽  
...  
Keyword(s):  
Network Analysis ◽  
Optimal Solution ◽  
Road Construction ◽  
Mixed Integer ◽  
Shortest Path Algorithm ◽  
Road Density ◽  
The Road ◽  
Constant Cost ◽  
The Cost ◽  
Installation Cost

&nbsp;To minimize the cost of logging, it is necessary to optimize the road density. The aim of this study was to determine optimal road spacing (ORS) in Northern Austria. The stepwise regression method was used in modelling. The production rate of tower yarder was 10.4 m<SUP>3</SUP>/PSHo (Productive system hours) and cost of 19.71 €.m<SUP>–3</SUP>. ORS was studied by calculating road construction cost, installation cost and yarding cost per m<SUP>3</SUP> for different road spacing. The minimum total cost occurred at 39.15 €.m<SUP>–3</SUP> and ORS would be 474 m assuming uphill and downhill yarding. The optimal road density and yarding distance are 21.1 m.ha<SUP>–1</SUP> and 90 m, respectively. A sample logging area was used to plan different roads and, using network analysis, the best solution was found based on a modified shortest path algorithm. The network analysis results were very different from the optimal road spacing results that assumed roads and logging corridors could be located anywhere in the planning area at a constant cost. Mixed integer programming was also used to get a real optimal solution.

A Sequential Linear Programming Matrix Method to Insensitive H∞ Output Feedback for Linear Discrete-Time Systems

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Xiang-Gui Guo ◽  
Guang-Hong Yang
Keyword(s):  
Linear Programming ◽  
Discrete Time ◽  
Output Feedback ◽  
Matrix Method ◽  
Design Method ◽  
Sequential Linear Programming ◽  
Discrete Time Systems ◽  
Starting Point ◽  
Good Starting Point ◽  
Time Systems

This paper studies the problem of designing insensitive H∞ output-feedback controllers for linear discrete-time systems. The designed controllers are insensitive to additive/multiplicative controller coefficient variations. An LMI-based procedure, which is a sequential linear programming matrix method (SLPMM), is proposed to solve the considered problem which is a nonconvex problem itself. It is worth mentioning that the nonfragile control design method is adopted to obtain an effective solution for accelerating convergence of SLPMM algorithm due to the fact that a good starting point for the iteration is very important.

scholarly journals A mixed-integer linear programming model for harvesting, loading and transporting sugarcane. A case study in Peru

DYNA ◽  
2016 ◽  
Vol 83 (195) ◽  
pp. 173-179 ◽  
Author(s):  
Marcela María Morales-Chávez ◽  
José A. Soto-Mejía ◽  
William Ariel Sarache
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Programming Model ◽  
Raw Material ◽  
Linear Programming Model ◽  
Mixed Integer ◽  
Production Plant ◽  
Integer Linear Programming Model ◽  
The Cost

Due to opportunities for economic and social development in the biofuels market, improvement to the supply chain has become a relevant matter. In agro-industrial supply chains, procurement costs are highly relevant. Since sugarcane is a high performance raw material for ethanol production, this paper proposes a Mixed-Integer Linear Programming Model for cost optimization for harvesting, loading and transportation operations. The model determines the quantity of machines and workers to meet the biofuel plant requirements. Costs of resources for harvesting and loading as well as transportation costs from the land parcel to the production plant are minimized. Also, the model calculates the cost of penalties for shortages (unmet demand) and the cost of equipment idle time. The implementation of the model in a Peruvian biofuels company, showed a cost reduction of around 11 % when compared to the current costs.

STUDY OF THE UNEQUAL SPHERES PACKING PROBLEM: AN APPLICATION TO RADIOSURGERY TREATMENT

2003 ◽  
Vol 14 (06) ◽  
pp. 815-823 ◽  
Author(s):  
S. P. LI ◽  
KA-LOK NG
Keyword(s):  
Treatment Planning ◽  
Hard Spheres ◽  
Computing Time ◽  
Gamma Knife Radiosurgery ◽  
Optimal Solution ◽  
Packing Problem ◽  
The Monte Carlo Method ◽  
Starting Point ◽  
Good Starting Point ◽  
Selection Of

We employ the Monte Carlo method to study a constrained optimization problem — packing hard spheres with unequal radii (r2 > r1) into a 3D bounded region and discuss its connection with the Gamma Knife radiosurgery treatment planning. Selection of the best fit solution is based on the Boltzmann factor, e-ΔE/T, which allows us to search for the global optimal solution. As an illustration we determined the least number (≤15) of packed spheres that will occupy the largest volume for three different hypothetical tumor sizes (4115, 10 000 and 36 000 voxels). For the bounded regions and the sizes of the packed spheres that we studied here, the optimal volume packing ratio ranges from 41.3 to 48.7%. From our study, using a lower r2/r1 ratio is more desirable due to the ≤15 radiation shots constraint. The optimal volume packing ratio can be obtained within a relative short CPU computing time and could provide a good starting point for the radiosurgery treatment planning.

scholarly journals Stope boundary optimization for an underground copper deposit using mixed integer linear programming based algorithm

2021 ◽  
Vol 69 (3) ◽  
pp. 73
Author(s):  
Gopinath Samanta ◽  
Tapan Dey ◽  
Biswajit Samanta ◽  
Suranjan Sinha
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Underground Mining ◽  
Optimal Solution ◽  
Copper Deposit ◽  
Mixed Integer ◽  
Selling Price ◽  
Ore Body ◽  
Boundary Optimization

Optimal ore body boundary and production area geometry (Stope) are essential to maximize the profit from an underground mining project subject to inherent physical, geotechnical and geological constraints. Number of researches have been introduced for stope boundary optimization but true optimal solution in three dimensional spaces is still out of reach. This article proposed a computer programming based optimization model using mixed integer linear programming based algorithm that incorporate stope boundary optimization with varying cost of mining and selling price of the metal. An actual ore body model was taken as case study to implement the algorithm in real mining scenario. In validation study, it is observed that, by using proposed model, the profit can be increased by 10% - 15% as compared to the present stoping practice. Simulating the optimal stope boundary by changing the various cost and price parameters helps to opt the best possible option for a given mining scenario to make most realistic plan.

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