Showing papers on "Metaheuristic published in 1973"

Algorithm 454: the complex method for constrained optimization [E4]

Abstract: s o f the papers by Daily and Lynning A Sel f -Modi fy ing Ex t rapo la t ion M e t h o d for Solving O r d i n a r y Differential Equa t ions Dar D. Dai ly Kansas State University, Manhattan, Kansas Author's address: 8133 Dearborn Drive, Prairie Village, KS 66208 This paper outl ines a p rogram that searches for the p r e d o m i n a n t terms of the a sympto t i c er ror expans ion of initial value problems in o rd ina ry differential equa t ions and uses this i n fo rma t ion in a se l f -modifying ex t rapo la t ion process. Dur ing the in tegra t ion process, using a ra t io that Carl de Boor (1971) used in an integra t ion program, the me thod seeks to recognize t rends of change in the error expans ion of the differential equat ion and to adjus t the me thod of ex t rapola t ion . A basic a lgo r i thm used in the modi fy ing process is presented a long with a br ief exp lana t ion . Also, a compa r i son made with the wel l -known ra t iona l ex t rapo la t ion m e t h o d shows ra t ional ex t rapo la t ion to be general ly less efficient in terms of funct ion eva lua t ions but also demons t ra t e s tha t the se l f -modifying me thod is general ly not able to reduce its e r ror to the level of ra t iona l ex t rapo la t ion . A note, though, shows the se l f -modifying m e t h o d to be super ior to the regular R o m b e r g ex t rapo la t ion . Key W o r d s and Phrases : se l f -modifying ex t rapo la t ion, ra t iona l ex t rapo la t ion , modif ied m i d p o i n t me thod , R o m b e r g in tegrat ion, a sympto t i c e r ror expans ion , predominan t , s ingulari ty, ini t ial value p rob lems in o rd ina ry differential equa t ions ; C R Categor ies : 5.10, 5.17 A C o m p u t e r Solut ion of Po lygona l Jigsaw Puzzles Ejv ind Lynning University of Arhus, Arhus, Denmark Author's address: Brandeis University, Waltham, M A. 02154 A p rogram to solve any j igsaw puzzle involving pieces of polygonal shape is described. An efficient solut ion has been found to depend on a number of ad hoc strategies, which are descr ibed in detail in the paper . The puzzles are solved by successively placing individual pieces in the region to be covered using a depth-f i rs t tree search a lgor i thm. A formal representa t ion of regions, pieces, and placings of pieces is defined. The main idea behind the chosen represen ta t ion is to or ient clockwise the po lygons mak ing up a region, and to or ient counter c lockwise the pieces to be placed. Placing a piece means compu t ing a valid new region, i.e. one or more c lockwise or ien ted polygons , cons t ruc ted f rom the previous one by removing the par t co r re spond ing to the piece which is placed. The da ta s t ructure and the p rocedures requi red to examine where pieces can be placed and how to pe r fo rm the placing of the pieces are also descr ibed. Al l puzzles so far presented to the p r o g r a m have been successfully solved in a r easonab le t ime. K e y W o r d s and Phrases : art if icial intelligence, p roblem solving, pa t te rn recogni t ion , puzzles, po lygona l puzzles, j igsaw puzzles, back t r ack p rog ramming , tree search a lgor i thms ; C R Categor ies : 3.6, 3.63, 3.64 482 Algor i t hms L.D. F o s d i c k and A.K. Cline, Ed i to r s Submittal of an algorithm for consideration for publication in Communications of the A C M implies unrestricted use of the algorithm within a computer is permissible. Copyright © 1973, Association for Computing Machinery, Inc. General permission to republish, but not for profit, all or part of this material is granted provided that ACM's copyright notice is given and that reference is made to the publication, to its date of issue, and to the fact that reprinting privileges were granted by permission of the Association for Computing Machinery.

A combined decomposition and coordination method in large dimension optimization problems

Abstract: In this article, the authors present a method for the decomposition of complex problems which uses as coordination magnitudes the variables of interconnection between subsystems and the associated Lagrangian parameters. This method thus uses a combined coordination by simultaneous action on the criterion function and on the model of each subsystem. The principles of the method are discussed along with static and dynamic optimization problems while defining the local lower-level optimization subproblems, proposing coordinating algorithms for the higher level, and presenting the con vergence studies relative to these algorithms.

Response Surface Optimization when Experimental Factors are Subject to Costs and Constraints

Abstract: This paper deals with problems of response surface optimization in which the control variables and responses are subject to costs and constraints. Relationships between control variables and the cost or constraint functions are treated as additional response surfaces if explicit algebraic models are unavailable. Optimization methods are suggested which are based on gradient search and nonlinear programming techniques. To assure operating conditions within the specified constraint set a method based on feasible directions is used to control the search pattern. A scale-invariant gradient search method is suggested. Because it leads to an economical path to the maximum point the method has been dubbed “cheapest ascent.” The selection of measurement scales for the control variables is also discussed.

The solution of discrete linear optimization problems by neighborhood-search techniques

Abstract: A process and apparatus for forming a wide variety of air-laid nonwoven webs, with the apparatus including plural pairs of spaced parallel oppositely rotating lickerins, each pair having a movable divider plate therebetween. The lickerins individualize fibers from separate fibrous sources, which may be similar or dissimilar, and high speed air streams are caused to flow past each individual lickerin, through a mixing zone between each pair of lickerins to form combined streams, and into a common mixing zone above a fiber collecting means to form a composite stream. The individualized fibers are doffed from the lickerins by the high speed air streams and are entrained therein, and divider plates between each pair of lickerins are adjustable through a range of positions for controlling the degree of intermixing of the entrained fibers in the combined streams. A further divider plate is mounted in adjustable relationship with respect to the common mixing zone to control the degree to which the combined streams and entrained fibers intermix in forming the composite stream. The air streams may be generated by a single suction source below the fiber collecting means, or by separate individually controlled suction sources on opposite sides of the further divider plates, which may be individually adjusted to further vary the web that is formed on the fiber collecting means. The further divider plate is preferably removably mounted so that a further material, such as a reinforcing material or an adhesive can be introduced into the composite stream and resulting web, if desired.

A minimax search plan for constrained optimization problems

Abstract: A minimax search strategy is described for locating the boundary point of a region on a line joining a feasible point to an infeasible point. Asymptotic strategies, useful when the number of experiments to be used in the search is not predetermined, are also given. These strategies are useful subroutines for many multidimensional optimization algorithms.