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Tapio Westerlund - One of the best experts on this subject based on the ideXlab platform.

  • Comparison of Some High-performance MINLP Solvers
    Chemical engineering transactions, 2007
    Co-Authors: Toni Lastusilta, Michael R. Bussieck, Tapio Westerlund
    Abstract:

    In this paper some high-performance mixed integer Non-Linear Programming (MINLP) solvers in GAMS (General Algebraic Modeling System) are evaluated. AlphaECP, Baron, Dicopt and SBB are the MINLP (mixed integer Non-Linear Programming) solvers in focus. A large test set with 250 problems is used and special attention is given to a new GAMS solver, GAMS/AlphaECP, which has recently been included in GAMS. The results show that each solver improves the overall performance of the GAMS system. Furthermore the results reveal that the combined performance of some pairs of solvers is significantly better than other pairs.

  • solving pseudo convex mixed integer optimization problems by cutting plane techniques
    Optimization and Engineering, 2002
    Co-Authors: Tapio Westerlund, Swedish Polytechnic
    Abstract:

    In the present paper a cutting plane approach to solve Mixed-Integer Non-Linear Programming (MINLP) problems, containing pseudo-convex functions, is given. It is shown how valid cutting planes for pseudo convex functions can be obtained and, furthermore, it is shown how a class of non-convex MINLP problems with a pseudo-convex objective function and pseudo-convex constraints, can be solved to global optimality with the considered cutting plane technique. Finally the numerical efficiency of the procedure, when solving some example problems, is illustrated.

  • Mixed integer Non-Linear Programming using cutting plane techniques
    Computer Aided Chemical Engineering, 2000
    Co-Authors: Ray Pörn, Tapio Westerlund
    Abstract:

    In the present paper a modification of the extended cutting plane (ECP) method is described and illustrated. It is shown how it is possible to solve general MINLP (Mixed Integer Non-Linear Programming) problems with pseudo-convex objective as well as constraints to global optimality by a sophisticated cutting plane approach. The method relies on the ability to construct valid cutting planes for the entire feasible region of the problem. The method is illustrated on a simple test example and on some demanding practical scheduling problems. A comparison with a recently developped branch-and-bound approach is also given.

  • A cutting plane method for minimizing pseudo-convex functions in the mixed integer case
    Computers & Chemical Engineering, 2000
    Co-Authors: Ray Pörn, Tapio Westerlund
    Abstract:

    Abstract In this paper, a mixed integer non linear Programming (MINLP) algorithm for minimizing pseudo-convex functions under pseudo-convex constraints is proposed and illustrated. The solution procedure is iterative and relies on successive linear approximation of the objective function and on a line-search technique. The whole procedure is then embedded within the framework of a existing cutting plane method for mixed integer Non-Linear programs. This enables us to solve general MINLPs with pseudo-convex objective and pseudo-convex inequality constraints to global optimality.

  • Numerical and environmental considerations on a complex industrial mixed integer Non-Linear Programming (MINLP) problem
    Computers & Chemical Engineering, 1999
    Co-Authors: Iiro Harjunkoski, Tapio Westerlund, Ray Pörn
    Abstract:

    Abstract In the present paper an essential problem in the process industry, the trim-loss problem, is considered. The problem can be identified in many different industries (for instance in the paper and metal industry) but here, the main focus is on the paper industry or more precisely, the paper-converting industry. In the trim-loss problem at a paper-converting mill, an optimal strategy is sought for cutting a wide raw-paper reel into narrower, customer-specified product reels in such a way that the appearance of waste, the trim loss, is minimized. Besides being a numerically challenging non-convex mixed integer Non-Linear Programming problem, the choice of objective is of great importance and a non-trivial task in order to alter sustainable and environmentally benign solutions. Therefore, in the following some transformation techniques for overcoming bilinearity and solving the original problem into its global optimality are presented. The transformations are followed by an analysis and comparison of different ways to formulate the objective function. Finally, a set of example problems are solved in order to project the theoretical considerations to more practical level.

Ray Pörn - One of the best experts on this subject based on the ideXlab platform.

  • Mixed integer Non-Linear Programming using cutting plane techniques
    Computer Aided Chemical Engineering, 2000
    Co-Authors: Ray Pörn, Tapio Westerlund
    Abstract:

    In the present paper a modification of the extended cutting plane (ECP) method is described and illustrated. It is shown how it is possible to solve general MINLP (Mixed Integer Non-Linear Programming) problems with pseudo-convex objective as well as constraints to global optimality by a sophisticated cutting plane approach. The method relies on the ability to construct valid cutting planes for the entire feasible region of the problem. The method is illustrated on a simple test example and on some demanding practical scheduling problems. A comparison with a recently developped branch-and-bound approach is also given.

  • A cutting plane method for minimizing pseudo-convex functions in the mixed integer case
    Computers & Chemical Engineering, 2000
    Co-Authors: Ray Pörn, Tapio Westerlund
    Abstract:

    Abstract In this paper, a mixed integer non linear Programming (MINLP) algorithm for minimizing pseudo-convex functions under pseudo-convex constraints is proposed and illustrated. The solution procedure is iterative and relies on successive linear approximation of the objective function and on a line-search technique. The whole procedure is then embedded within the framework of a existing cutting plane method for mixed integer Non-Linear programs. This enables us to solve general MINLPs with pseudo-convex objective and pseudo-convex inequality constraints to global optimality.

  • Numerical and environmental considerations on a complex industrial mixed integer Non-Linear Programming (MINLP) problem
    Computers & Chemical Engineering, 1999
    Co-Authors: Iiro Harjunkoski, Tapio Westerlund, Ray Pörn
    Abstract:

    Abstract In the present paper an essential problem in the process industry, the trim-loss problem, is considered. The problem can be identified in many different industries (for instance in the paper and metal industry) but here, the main focus is on the paper industry or more precisely, the paper-converting industry. In the trim-loss problem at a paper-converting mill, an optimal strategy is sought for cutting a wide raw-paper reel into narrower, customer-specified product reels in such a way that the appearance of waste, the trim loss, is minimized. Besides being a numerically challenging non-convex mixed integer Non-Linear Programming problem, the choice of objective is of great importance and a non-trivial task in order to alter sustainable and environmentally benign solutions. Therefore, in the following some transformation techniques for overcoming bilinearity and solving the original problem into its global optimality are presented. The transformations are followed by an analysis and comparison of different ways to formulate the objective function. Finally, a set of example problems are solved in order to project the theoretical considerations to more practical level.

  • An extended cutting plane method for a class of non-convex MINLP problems
    Computers & Chemical Engineering, 1998
    Co-Authors: Tapio Westerlund, Iiro Harjunkoski, Hans Skrifvars, Ray Pörn
    Abstract:

    An extended cutting plane method is introduced. The extended method can be applied in the solution of a class of non-convex MINLP (Mixed-Integer Non-Linear Programming) problems, although the method was originally introduced for the solution of convex problems only. Global convergence properties of the method are given for pseudo-convex MINLP problems in the present paper and a numerical example from the paper-converting industry is finally provided to illustrate the numerical procedure.

Lazaros G. Papageorgiou - One of the best experts on this subject based on the ideXlab platform.

  • fair electricity transfer price and unit capacity selection for microgrids
    Energy Economics, 2013
    Co-Authors: Di Zhang, Nouri J Samsatli, Adam Hawkes, Dan J L Brett, Nilay Shah, Lazaros G. Papageorgiou
    Abstract:

    Microgrids are defined as an area of electricity distribution network that can operate autonomously from the rest of the network. In order to achieve the best economic outcomes, the participants in a microgrid can benefit from cooperation in microgrid design and operation. In this paper, a mathematical Programming formulation is presented for fair, optimised cost distribution amongst participants in a general microgrid. The proposed formulation is based on the Game-theory Nash bargaining solution approach for finding optimal multi-partner cost levels subject to given upper bounds on the equivalent annual costs. The microgrid planning problem concerning the fair electricity transfer price and unit capacity selection is first formulated as a mixed integer Non-Linear Programming model. Then, a separable Programming approach is applied to reform the resulting mixed integer Non-Linear Programming model to a mixed integer linear Programming form. The model is applied to a case study with a microgrid involving five participants.

  • An MINLP Formulation for the Synthesis of Chromatographic Protein Purification Processes with Product Loss
    Computer Aided Chemical Engineering, 2009
    Co-Authors: Eleftheria M. Polykarpou, Paul A. Dalby, Lazaros G. Papageorgiou
    Abstract:

    Abstract One of the mam challenges in the synthesis of downstream purification processes is the appropriate selection of chromatographic steps. The objective of this work is to develop a mixed integer Non-Linear Programming (MINLP) model for the synthesis of protein purification process that incorporates product losses. The methodology is validated by an illustrative example based on experimental data. The results provide an important guideline for synthesizing purification processes.

  • Safe Process Plant Layout using Mathematical Programming
    Computer-aided chemical engineering, 2007
    Co-Authors: Dimitrios I. Patsiatzis, Lazaros G. Papageorgiou
    Abstract:

    This paper presents a general mathematical Programming formulation, considering simultaneously process plant layout and safety. The proposed model determines the detailed process plant layout (coordinates and orientation of each equipment item), the number and type of protection devices in order to reduce possible accidents and the financial risk. The problem is formulated as a mixed integer Non-Linear Programming (MINLP) model and its applicability is demonstrated by a literature example.

  • Optimal design of an electrodialysis brackish water desalination plant
    DESALINATION, 2005
    Co-Authors: Lazaros G. Papageorgiou
    Abstract:

    This paper considers the optimal design and operation of electrodialysis (ED) desalination plants. In general an ED plant aims to produce potable water from a high salinity source, like brackish water or high salinity water. The system is modelled mathematically as Mixed-Integer Non-Linear Programming (MINLP) optimization problem, determining the number of desalination stages, the membrane area, the total required energy so as to minimise the total annualised cost of the investment accounting for both infrastructure and operating costs. Two examples from the literature illustrate the applicability of the proposed approach and evaluate the quality of the results obtained.

  • A Mathematical Programming Approach for the Optimal Scheduling of Heat-integrated Multipurpose Plants under Fouling Conditions
    Computer Aided Chemical Engineering, 2000
    Co-Authors: Michael C. Georgiadis, Lazaros G. Papageorgiou
    Abstract:

    This work presents a systematic mathematical framework for scheduling the operation of multipurpose plants involving heat-integrated unit operations under fouling considerations. Based on a uniform time discretization, the overall problem is formulated as a mixed integer Non-Linear Programming (MINLP) model. An iterative procedure has been developed for the solution of the resulting non-convex MINLP model, involving the solution of a series of mixed integer linear Programming (MILP) and Non-Linear Programming (NLP) subproblems. An example problem is presented to illustrate the applicability of the proposed approach.

Robert C Leachman - One of the best experts on this subject based on the ideXlab platform.

  • a supply chain optimization model of the allocation of containerized imports from asia to the united states
    Transportation Research Part E-logistics and Transportation Review, 2011
    Co-Authors: Payman Jula, Robert C Leachman
    Abstract:

    This article proposes a mixed integer Non-Linear Programming model for the optimizing supply chains of importers of waterborne containerized goods from Asia to the USA. This model determines the least-cost strategy for an importer, in terms of ports and landside transportation modes to be used, where costs considered include costs for transportation and handling, pipeline inventory, and safety-stock. We introduce a heuristic algorithm to quickly solve the mathematical model to near optimality. We assess the proposed heuristic compared to use of a commercial solver, and provide general recommendations for efficient supply-chain strategies as a function of the value of imported goods.

Rohit Bhakar - One of the best experts on this subject based on the ideXlab platform.

  • Security Constrained Unit Commitment in a Power System based on Benders Decomposition and Mixed Integer Non-Linear Programming
    International Journal of Engineering & Technology, 2018
    Co-Authors: Pranda Prasanta Gupta, Prerna Jain, Sanjeev Sharma, Rohit Bhakar
    Abstract:

    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. 

  • Reliability-Security Constrained Unit Commitment based on benders decomposition and Mixed Integer Non-Linear Programming
    2017 International Conference on Computer Communications and Electronics (Comptelix), 2017
    Co-Authors: Pranda Prasanta Gupta, Prerna Jain, S.k. Sharma, Rohit Bhakar
    Abstract:

    Reliability-Security Constrained Unit Commitment (RSCUC) with emphasis on Mixed Integer Nonlinear Programming (MINLP) and Benders Decomposition (BD) based on thermal generating units are presented in this paper. To solve unit commitment problem generalized BD along with reliability issues are considered. The approach presented in this work allows the decomposition of the whole program in quadratic mixed integer master program and network security check Non-Linear sub-problem. The case study demonstrates the effectiveness of the proposed approach.