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- Holmström, Kenneth, 1954-, et al.
(författare)
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Adaptive Radial Basis Algorithms (ARBF) for Expensive Black-Box Global MINLP Optimization
- 2008
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Ingår i: SIOPT08 - Abstracts. ; , s. 132-
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Konferensbidrag (refereegranskat)abstract
- Improvements of the adaptive radial basis function algo-rithm (ARBF) for computationally costly optimization are presented. A new target value search algorithm and modifications to improve robustness and speed are discussed. The algoritm is implemented in solver ARBFMIP in the TOM-LAB Optimization Environment (http://tomopt.com/). Solvers in TOMLAB are used to solve global and local subproblems. Results and comparisons with other solvers are presented for global optimization test problems. Performance on costly real-life applications are reported.
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| 2. |
- Holmström, Kenneth, 1954-, et al.
(författare)
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An adaptive radial basis algorithm (ARBF) for expensive black-box mixed-integer constrained global optimization
- 2008
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Ingår i: Optimization and Engineering. - : Springer US. - 1389-4420 .- 1573-2924. ; 9:4, s. 311-339
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Tidskriftsartikel (refereegranskat)abstract
- Response surface methods based on kriging and radial basis function (RBF) interpolationhave been successfully applied to solve expensive, i.e. computationally costly,global black-box nonconvex optimization problems.In this paper we describe extensions of these methods to handle linear, nonlinear, and integer constraints. In particular, algorithms for standard RBF and the new adaptive RBF (ARBF) aredescribed. Note, however, while the objective function may be expensive, we assume that any nonlinear constraints are either inexpensive or are incorporated into the objective function via penalty terms. Test results are presented on standard test problems, both nonconvexproblems with linear and nonlinear constraints, and mixed-integernonlinear problems (MINLP). Solvers in the TOMLAB OptimizationEnvironment (http://tomopt.com/tomlab/) have been compared,specifically the three deterministic derivative-free solversrbfSolve, ARBFMIP and EGO with three derivative-based mixed-integernonlinear solvers, OQNLP, MINLPBB and MISQP, as well as the GENOsolver implementing a stochastic genetic algorithm. Results showthat the deterministic derivative-free methods compare well with thederivative-based ones, but the stochastic genetic algorithm solver isseveral orders of magnitude too slow for practical use.When the objective function for the test problems is costly to evaluate, the performance of the ARBF algorithm proves to be superior.
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| 3. |
- Holmström, Kenneth, 1954-, et al.
(författare)
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AUTOPACK - Algorithms for Automated Container Loading
- 2008
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Ingår i: Journal of Numerical and Applied Mathematics. - Kyiv-4, Ukraine : Institute of Mathematics of Ukrainian National Academy of Sciences. - 0868-6912. ; 96:1, s. 105-118
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Tidskriftsartikel (refereegranskat)abstract
- The container loading problem aims at optimal packing of boxes of different dimensions into available containers with respect to some objective function. This problem arises in areas like distribution and logistics. Since the scale of distribution and amount of distributed goods grows rapidly, so does the need for more energy effective and environmentally friendly distribution methods.This paper considers a single container loading problem motivated by a real life application. The formulation includes an objective function for maximizing utilization of a container and additional constraints such as a predefined order and priorities between boxes. A short evaluation of the algorithm is presented as well as some directions for future development.
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| 6. |
- Holmström, Kenneth, 1954-, et al.
(författare)
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The influence of Experimental Designs on the Performance of Surrogate Model Based Costly Global Optimization Solvers
- 2009
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Ingår i: Studies in Informatics and Control. - : National Institute for Research & Development in Informatics. - 1220-1766 .- 1841-429X. ; 18:1, s. 87-95
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Tidskriftsartikel (refereegranskat)abstract
- When dealing with costly objective functions in optimization, one good alternative is to use a surrogate model approach. A common feature for all such methods is the need of an initial set of points, or "experimental design", in order to start the algorithm. Since the behavior of the algorithms often depends heavily on this set, the question is how to choose a good experimental design. We investigate this by solving a number of problems using different designs, and compare the outcome with respect to function evaluations and a root mean square error test of the true function versus the surrogate model produced. Each combination of problem and design is solved by 3 different solvers available in the TOMLAB optimization environment. Results indicate two designs as superior.
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