Stochastic optimization approaches are achieving growing interest in application to difficult optimization problems common in chemical and process engineering. They are easy to use especially in cases where there are ...
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Stochastic optimization approaches are achieving growing interest in application to difficult optimization problems common in chemical and process engineering. They are easy to use especially in cases where there are disjunctive functions and logical conditions. M-LI optimization algorithm from adaptive random search (ARS) strategy has been developed for most advantageous optimization problems, i.e. MINLP ones. This method is an extension of LJ algorithm developed by Jaakola and Luus (1974) for problems with continuous variables. The main modification in M-LJ method is the change of distribution function for integer variables. The results of tests are presented and the comparison with the performance of other stochastic methods as e.g. MSIMPSA algorithm from Cardoso et al. (1997). M-LJ has shown high robustness and can be seen easy to use optimization tool for certain MINLP problems. Also, the re-formulation of difficult optimization MINLP problem for batch processes from Kocis and Grossmann (1988) has been developed which allows for solving it as NLP task.
In this paper, a general method for handling disjunctive constraints in a MINLP optimization problem is presented. This method automates the reformulation of an, in a abstract modeling language given, optimization pro...
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In this paper, a general method for handling disjunctive constraints in a MINLP optimization problem is presented. This method automates the reformulation of an, in a abstract modeling language given, optimization problem into a mathematical problem that is solvable with existing optimization tools. This implementation can use common MILP solvers for linear problems and nonlinear methods for quasi-convex optimization problems. It also includes the possibility to use the logics in the system and solve the system logically using subproblems.
The present paper deals with a production optimization problem connected with the paper-converting industry. The problem considered is to produce a set of product paper reels from larger raw paper reels such that a co...
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The present paper deals with a production optimization problem connected with the paper-converting industry. The problem considered is to produce a set of product paper reels from larger raw paper reels such that a cost function is minimized. The problem is generally non-convex due to a bilinear objective function and some bilinear constraints, both of which give rise to certain problems. The problem can, however, be solved as a two-step optimization procedure, in which the latter step is a mixedintegerlinearprogramming problem. A numerical example is introduced to illustrate the proposed procedure. The example is taken from a real-life daily production optimization problem encountered at a Finnish paper-converting mill, Wisapak Oy, having an annual production of just over 100,000 tons of printed paper. (C) 1998 Elsevier Science Ltd. All rights reserved.
In this paper a two-dimensional trim-loss problem connected to the paper-converting industry is considered. The problem is to produce a set of product paper rolls from larger raw paper rolls such that the cost for was...
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In this paper a two-dimensional trim-loss problem connected to the paper-converting industry is considered. The problem is to produce a set of product paper rolls from larger raw paper rolls such that the cost for waste and the cutting time is minimized. The problem is generally non-convex due to a bilinear objective function and some bilinear constraints, which give rise to difficulties in finding efficient numerical procedures for the solution. The problem can, however, be solved as a two-step procedure, where the latter step is a mixedintegerlinearprogramming (MILP) problem. In the present formulation, both the width and length of the raw paper rolls as well as the lengths of the product paper roils are considered variables. All feasible cutting patterns are included in the problem and global optimal cutting patterns are obtained as the solution from the corresponding MILP problem. A numerical example is included to illustrate the proposed procedure. (C) 1998 Elsevier Science B.V.
In the present paper trim-loss problems, often named the cutting stock problem, connected to the paper industry are considered. The problem is to cut out a set of product paper rolls from raw paper rolls such that the...
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In the present paper trim-loss problems, often named the cutting stock problem, connected to the paper industry are considered. The problem is to cut out a set of product paper rolls from raw paper rolls such that the cost function, including the trim loss as well as the costs for the over production, is minimized. The problem is non-convex due to certain bilinear constraints. The problem can, however, be transformed into linear or convex form. The resulting transformed problems can, thereafter, be solved as mixed-integerlinearprogramming problems or convex mixed-integernon-linearprogramming problems. The linear and convex formulations are attractive from a formal point of view, since global optimal solutions to the originally non-convex problem can be obtained. However, as the examples considered will show, the numerical efficiency of the solutions from the different transformed formulations varies considerably. An example based on a trim optimization problem encountered daily at a Finnish paper converting mill is, finally, presented in order to demonstrate differences in the numerical solutions. (C) 1998 Elsevier Science B.V.
An algorithm (M-SIMPSA) suitable for the optimization of mixed integer non-linear programming (MINLP) problems is presented. A recently proposed continuous non-linear solver (SIMPSA) is used to update the continuous p...
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An algorithm (M-SIMPSA) suitable for the optimization of mixed integer non-linear programming (MINLP) problems is presented. A recently proposed continuous non-linear solver (SIMPSA) is used to update the continuous parameters, and the Metropolis algorithm is used to update the complete solution vector of decision variables. The M-SIMPSA algorithm, which does not require feasible initial points or any problem decomposition, was tested with several functions published in the literature, and results were compared with those obtained with a robust adaptive random search method. For ill-conditioned problems, the proposed approach is shown to be more reliable and more efficient as regards the overcoming of difficulties associated with local optima and in the ability to reach feasibility. The results obtained reveal its adequacy for the optimization of MINLP problems encountered in chemical engineering practice. (C) 1997 Elsevier Science Ltd.
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