Luis B. Morales

BWR fuel reloads design using a Tabu search technique

Abstract We have developed a system to design optimized boiling water reactor fuel reloads. This system is based on the Tabu Search technique along with the heuristic rules of Control Cell Core and Low Leakage. These heuristic rules are a common practice in fuel management to maximize fuel assembly utilization and minimize core vessel damage, respectively. The system uses the 3-D simulator code CM-PRESTO and it has as objective function to maximize the cycle length while satisfying the operational thermal limits and cold shutdown constraints. In the system tabu search ideas such as random dynamic tabu tenure, and frequency-based memory are used. To test this system an optimized boiling water reactor cycle was designed and compared against an actual operating cycle. Numerical experiments show an improved energy cycle compared with the loading patterns generated by engineer expertise and genetic algorithms.

A practical optimization procedure for radial BWR fuel lattice design using tabu search with a multiobjective function

Abstract An optimization procedure based on the tabu search (TS) method was developed for the design of radial enrichment and gadolinia distributions for boiling water reactor (BWR) fuel lattices. The procedure was coded in a computing system in which the optimization code uses the tabu search method to select potential solutions and the HELIOS code to evaluate them. The goal of the procedure is to search for an optimal fuel utilization, looking for a lattice with minimum average enrichment, with minimum deviation of reactivity targets and with a local power peaking factor (PPF) lower than a limit value. Time-dependent-depletion (TDD) effects were considered in the optimization process. The additive utility function method was used to convert the multiobjective optimization problem into a single objective problem. A strategy to reduce the computing time employed by the optimization was developed and is explained in this paper. An example is presented for a 10×10 fuel lattice with 10 different fuel compositions. The main contribution of this study is the development of a practical TDD optimization procedure for BWR fuel lattice design, using TS with a multiobjective function, and a strategy to economize computing time.

A parallel tabu search for conformational energy optimization of oligopeptides

We have developed and implemented a tabu search heuristic (TS) to determine the best energy minimum for oligopeptides. Our test molecule was Met‐enkephalin, a pentapetide that over the years has been used as a validation model for many global optimizers. The test potential energy function was ECEPP/3. Our tabu search implementation is based on assigning integer values to the variables to be optimized, and in facilitating the diversification and intensification of the search. The final output from the TS is treated with a local optimizer, and our best result competes both in quality and CPU time with those reported in the literature. The results indicate that TS is an efficient algorithm for conformational searches. We present a parallel TS version along with experimental results that show that this algorithm allows significant increases in speed.

The Multiple-Minima Problem in Small Peptides Revisited. The Threshold Accepting Approach

A recently reported optimization method, known as Threshold Accepting, was tested for the purpose of locating the structure of several peptide molecules with the lowest conformational energy. A comparison with previous results obtained with the Simulated Annealing technique was made. Our study indicate Threshold Accepting as a better technique in locating such structures.

A genetic algorithm with conformational memories for structure prediction of polypeptides.

Abstract We have developed an iterative hybrid algorithm (HA) to predict the 3D structure of peptides starting from their amino acid sequence. The HA is made of a modified genetic algorithm (GA) coupled to a local optimizer. Each HA iteration is carried out in two phases. In the first phase several GA runs are performed upon the entire peptide conformational space. In the second phase we used the manifestation of what we have called conformational memories, that arises at the end of the first phase, as a way of reducing the peptide conformational space in subsequent HA iterations. Use of conformational memories speeds up and refines the localization of the structure at the putative Global Energy Minimum (GEM) since conformational barriers are avoided. The algorithm has been used to predict successfully the putative GEM for Met- and Leu-enkephalin, and to obtain useful information regarding the 3D structure for the 8mer of polyglycine and the 16 residue (AAQAA)3Y peptide. The number of fitness function evaluations needed to locate the putative GEMs are fewer than those reported for other heuristic methods. This study opens the possibility of using Genetic Algorithms in high level predictions of secondary structure of polypeptides.

Boiling Water Reactor Fuel Assembly Axial Design Optimization Using Tabu Search

Abstract In this paper the implementation of the tabu search (TS) optimization method to a boiling water reactor’s (BWR’s) fuel assembly (FA) axial design is described. The objective of this implementation is to test the TS method for the search of optimal FA axial designs. This implementation has been linked to the reactor core simulator CM-PRESTO in order to evaluate each design proposed in a reactor cycle operation. The evaluation of the proposed fuel designs takes into account the most important safety limits included in a BWR in-core analysis based on the Haling principle. Results obtained show that TS is a promising method for solving the axial design problem. However, it merits further study in order to find better adaptation of the TS method for the specific problem.

An enlarged family of packing polynomials on multidimensional lattices

HereN = {0, 1, 2, ...}, while a functionf onNm or a larger domain is apacking function if its restrictionf¦Nm is a bijection ontoN. (Packing functions generalize Cantors [1]pairing polynomials, and yield multidimensional-array storage schemes.) We call two functionsequivalent if permuting arguments makes them equal. Alsos(x) =x1 + ... +xm when x = (x1,...,xm); and such anf is adiagonal mapping iff(x) <f(y) whenever x, y εNm ands(x) <s(y). Lew [7] composed Skolems [14], [15] diagonal packing polynomials (essentially one for eachm) to constructc(m) inequivalent nondiagonal packing polynomials on eachNm. For eachm > 1 we now construct 2m−2 inequivalent diagonal packing polynomials. Then, extending the tree arguments of the prior work, we obtaind(m) inequivalent nondiagonal packing polynomials, whered(m)/c(m) → ∞ asm → ∞. Among these we count the polynomials of extremal degree.

Diagonal polynomials and diagonal orders on multidimensional lattices

HereR andN denote the real numbers and the nonnegative integers, respectively. Alsos(x)=x1+···+xn whenx=(x1, …,xn) inRn. A mapf:Rn →R is call adiagonal function of dimensionn iff|Nn is a bijection ontoN and, for allx, y inNn, f(x)<f(y) whens(x)<s(y). Morales and Lew [6] constructed 2n−2 inequivalent diagonal polynomial functions of dimensionn for eachn>1. Here we use new combinatorial ideas to show that numberdn of such functions is much greater than 2n−2 forn>3. These combinatorial ideas also give an inductive procedure to constructdn+1diagonal orderings of {1, …,n}.

Diagonal polynomials for small dimensions

HereR andN denote respectively the real numbers and the nonnegative integers. Also 0 <n εN, ands(x) =x1+...+xn when x = (x1,...,xn) εRn. Adiagonal function of dimensionn is a mapf onNn (or any larger set) that takesNn bijectively ontoN and, for all x, y inNn, hasf(x) <f(y) whenevers(x) <s(y). We show that diagonalpolynomials f of dimensionn all have total degreen and have the same terms of that degree, so that the lower-degree terms characterize any suchf. We call two polynomialsequivalent if relabeling variables makes them identical. Then, up to equivalence, dimension two admits just one diagonal polynomial, and dimension three admits just two.

A General Description for the Weight Distribution of Some Reducible Cyclic Codes

A remarkably general result which provides the evaluation of a family of exponential sums was presented by Moisio in 2000. In this work, we use such a general result in order to determine the value distribution of a particular kind of exponential sum. Then, motivated by some new ideas of Ma, , we use this value distribution in order to formulate a general description for the weight distribution of a particular kind of reducible cyclic codes that has been recently studied. As will be shown, such a general description not only gives a unified explanation for these families of codes, but also gives the weight distribution for other reducible cyclic codes that have not been studied so far. In addition, among the kind of codes studied here, we will characterize those that are projective.