Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new ...
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Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new century. In order to get a deep insight into this field, some notes on the direct searches for non-smooth optimization problems are made. The global convergence vs. local convergence and their influences on expected solutions for simulation-based stochastic optimization are pointed out. The sufficient and simple decrease criteria for step acceptance are analyzed, and why simple decrease is enough for globalization in direct searches is identified. The reason to introduce the positive spanning set and its usage in direct searches is explained. Other topics such as the generalization of direct searches to bound, linear and non-linear constraints are also briefly discussed.
In this Letter a new approach for solving optimal path planning problems for a single rigid and free moving object in a two and three dimensional space in the presence of stationary or moving obstacles is presented. I...
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In this Letter a new approach for solving optimal path planning problems for a single rigid and free moving object in a two and three dimensional space in the presence of stationary or moving obstacles is presented. In this approach the path planning problems have some incompatible objectives such as the length of path that must be minimized, the distance between the path and obstacles that must be maximized and etc., then a multi-objective dynamic optimization problem (MODOP) is achieved. Considering the imprecise nature of decision maker's (DM) judgment, these multiple objectives are viewed as fuzzy variables. By determining intervals for the values of these fuzzy variables, flexible monotonic decreasing or increasing membership functions are determined as the degrees of satisfaction of these fuzzy variables on their intervals. Then, the optimal path planning policy is searched by maximizing the aggregated fuzzy decision values, resulting in a fuzzy multi-objective dynamic optimization problem (FMODOP). Using a suitable t-norm, the FMODOP is converted into a non-linear dynamic optimization problem (NLDOP). By using parametrization method and some calculations, the NLDOP is converted into the sequence of conventional non-linear programming problems (NLPP). It is proved that the solution of this sequence of the NLPPs tends to a Pareto optimal solution which, among other Pareto optimal solutions, has the best satisfaction of DM for the MODOP. Finally. the above procedure as a novel algorithm integrating parametrization method and fuzzy aggregation to solve the MODOP is proposed. Efficiency of our approach is confirmed by some numerical examples. (C) 2009 Elsevier B.V. All rights reserved.
The National Collegiate Athletic Association baseball tournament involves 64 teams representing American universities and colleges in a series of win-and-advance weekend tournaments. In the first weekend, a four-team ...
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The National Collegiate Athletic Association baseball tournament involves 64 teams representing American universities and colleges in a series of win-and-advance weekend tournaments. In the first weekend, a four-team 'regional' tournament is played at a host institution. The 16 regionals are also paired a priori, with the winners of paired regionals playing in the second weekend at one of the two institutions' home sites. The eight teams remaining after the second weekend play a final tournament at a neutral location. Given a selection of 64 tournament teams and their seeding classifications, prohibited four-team groupings during the first weekend and prohibited regional pairings in the second weekend, we examine the problem of creating regionals and regional pairings in order to minimize expected team travel costs. The problem is modelled as a non-linear mixed-integer program and solved by a combinatorial cutting plane approach. We examine the performance and output of the proposed algorithm on 2006 and 2007 tournament data.
We propose an approach to model and solve the joint problem of facility location, inventory allocation and capacity investment in a two echelon, single-item, service parts supply chain with stochastic demand. The obje...
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We propose an approach to model and solve the joint problem of facility location, inventory allocation and capacity investment in a two echelon, single-item, service parts supply chain with stochastic demand. The objective of the decision problem is to minimize the total expected costs associated with (I) opening repair facilities, (2) assigning each field service location to an opened facility, (3) determining capacity levels of the opened repair facilities, and (4) optimizing inventory allocation among the locations. Due to the size of the problem, computational efficiency is essential. The accuracy of the approximations and effectiveness of the approach are analyzed with two numerical studies. The approach provides optimal results in 90% of scenarios tested and was within 2% of optimal when it did not. We explore the impact of capacity utilization, inventory availability, and lead times on the performance of the approach. We show that including tactical considerations jointly with strategic network design resulted in additional cost savings from 3% to 12%. Our contribution is the development of a practical model and approach to support the decision making process of joint facility location and multi-echelon inventory optimization. (C) 2008 Elsevier B.V. All rights reserved.
The yield curve is a very important financial tool used in investment and policy decisions. Its estimation from market data is essentially a non-linear optimization problem. In this paper, we compare a diversity of no...
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The yield curve is a very important financial tool used in investment and policy decisions. Its estimation from market data is essentially a non-linear optimization problem. In this paper, we compare a diversity of non-linear optimization algorithms for estimating yield curves based on actual bond market data and conclude that certain classes of algorithms are more effective due to the nature of the problem. (C) 2007 Elsevier B.V. All rights reserved.
Share of power generation from renewable energy sources has been steadily increasing all over the world, mainly due to the concern about clean environment. Cost of renewable power generation has reduced considerably d...
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Share of power generation from renewable energy sources has been steadily increasing all over the world, mainly due to the concern about clean environment. Cost of renewable power generation has reduced considerably during the last two decades due to technological advancements and at present some of the renewable energy sources can generate power at costs comparable with that of fossil fuels. In this paper, application of renewable energy-based power generation is proposed, for load management. The formulation utilizes non-linear programming technique for minimizing the electricity cost and reducing the peak demand, by supplementing power by renewable energy sources, satisfying the system constraints. Case study of twenty-two large-scale industries showed that, significant reduction in peak demand (about 34%) and electricity cost (about 14%) can be achieved, by the optimal utilization of the renewable energy from independent power producers (IPPs). (C) 2009 Elsevier Ltd. All rights reserved
In this paper, the optimisation of pipe network with hot water is presented. The mathematical model, consisting of the nonlinear objective function and system of nonlinear equations for the hydraulics limitations is d...
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In this paper, the optimisation of pipe network with hot water is presented. The mathematical model, consisting of the nonlinear objective function and system of nonlinear equations for the hydraulics limitations is developed. On its basis, the computer program for determination optimal tree path with the use of simplex method was solved. For economic estimation the capitalised value method, which consider all costs of investment and operation was used. The results are presented for real case study network with 24 nodes and 33 pipe sectors. (C) 2008 Elsevier Ltd. All rights reserved.
In this paper, a multi-objective production planning model has been presented for a captive plant. The model includes multi-products, multi-plants, and multi-objective with some probabilistic constraints. The probabil...
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In this paper, a multi-objective production planning model has been presented for a captive plant. The model includes multi-products, multi-plants, and multi-objective with some probabilistic constraints. The probabilistic constraints have been transformed into deterministic constraints assuming the parameters as independent normal random variables. The deterministic problem has been computed with two different methods, namely weighting method and fuzzy programming method. Finally, the integral solution obtained by these two methods have been compared.
The generation of Pareto optimal solutions for complex systems with multiple conflicting objectives can be easier if the problem can be decomposed and solved as a set of smaller coordinated subproblems. In this paper,...
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The generation of Pareto optimal solutions for complex systems with multiple conflicting objectives can be easier if the problem can be decomposed and solved as a set of smaller coordinated subproblems. In this paper, a new decomposition-coordination method is proposed, where the global problem is partitioned into subsystems on the basis of the connection structure of the mathematical model, assigning a relative importance to each of them. In order to obtain Pareto optimal solutions for the global system, the aforementioned subproblems are coordinated taking into account their relative importance. The scheme that has been developed is an iterative one, and the global efficient solutions are found through a continuous information exchange process between the coordination level (upper level) and the subsystem level (lower level). Computational experiments on several randomly generated problem instances show that the suggested algorithm produces efficient solutions within reasonable computational times.
The problem of optimizing the location and size of buffers in semi-continuous manufacturing processes is considered. This problem is formulated as a non-linear integer program that determines the optimal buffer size f...
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The problem of optimizing the location and size of buffers in semi-continuous manufacturing processes is considered. This problem is formulated as a non-linear integer program that determines the optimal buffer size for individual stages and allocates tanks to those stages in order to minimize total tank inclusion, holding, quality, process overshoot and undershoot costs. Heuristics are developed to solve the problem and bounds are derived to evaluate the quality of the heuristics. This method has been implemented at three glucose and three sorbitol production processes at a leading food processing company. This has resulted in total annual cost savings of around 6.4% or $9000 000. In addition, this work has had a significant impact on several strategic operational decisions at this company.
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