Random tunneling by means of acceptance-rejection sampling for global optimization

Any global minimization algorithm is made by several local searches performed sequentially. In the classical multistart algorithm, the starting point for each new local search is selected at random uniformly in the region of interest. In the tunneling algorithm, such a starting point is required to have the same function value obtained by the last local minimization. We introduce the class of acceptance-rejection based algorithms in order to investigate intermediate procedures. A particular instance is to choose at random the new point approximately according to a Boltzmann distribution, whose temperatureT is updated during the algorithm. AsT 0, such distribution peaks around the global minima of the cost function, producing a kind of random tunneling effect. The motivation for such an approach comes from recent works on the simulated annealing approach in global optimization. The resulting algorithm has been tested on several examples proposed in the literature.     

A theoretical approximation scheme for Stackelberg problems

We consider the Stackelberg problem corresponding to a two-player game in which one of the two players has the leadership in playing the game. We present a general approach for approximating the considered hierarchical programming problem by a sequence of two-level optimization problems. From a practical point of view, we also give some results for asymptotically Stackelberg approximating sequences and for problems with perturbed constraints.This paper is based upon results first presented at Journées Fermat: Mathematics for Optimization, Toulouse, France, May 1985.     

Determination of the optimal initial function and the parameters for nonlinear time-delay systems

This paper deals with dynamic systems described by nonlinear differential-difference equations of retarded type. The problem considered is to determine the initial function and certain system parameters which minimize a given cost functional. A computational method is presented and some convergence results are given. Numerical examples of linear and nonlinear systems are also included.     

On the statistical mechanics of the traveling salesman problem

We consider the statistical mechanics of the traveling salesman problem (TSP) and develop some representations to study it. In one representation the mean field theory has a simple form and brings out some of the essential features of the problem. It shows that the system has spontaneous symmetry breaking at any nonzero temperature. In general the phase progressively changes as one decreases the temperature. At low temperatures the mean field theory solution is very sensitive to any small perturbations, due to the divergence of some local susceptibilities. This critical region extends down to zero temperature. We perform the quenched average for a nonmetric TSP in the second representation and the resulting problem is more complicated than the infinite-range spin-glass problem, suggesting that the free energy landscape may be more complex. The role played by frustration in this problem appears explicitly through the localization property of a random matrix, which resembles the tight binding matrix of an electron in a random lattice.     

A conformational analysis method for understanding the energy landscapes of clusters.

A newly developed unbiased structural optimization method, named dynamic lattice searching (DLS), is proposed as an approach for conformational analysis of atomic/molecular clusters and used in understanding the energy landscape of large clusters. The structures of clusters are described in terms of the number of basic tetrahedron (BT) units they contain. We found that the hit numbers of different structural motifs in DLS runs is proportional to the number of BTs. A parameter T(max) is defined to limit the maximal number of atoms moved in a structural transition. Results show that T(max) is a key parameter for modulating the efficiency of the DLS method and has a great influence on the hit number of different motifs in DLS runs. Finally, the effect of potential range on the conformational distribution of the (Morse)(98) cluster is also discussed with different potential-range parameters.     

Simplex-optimization with a new criterion. Applications to dual-column ion chromatography

A new optimization criterion for chromatography is presented. It was designed to evaluate the quality of chromatograms in a way similar to human estimation. Selectivity, efficiency, and time of analysis as well as the number of peaks were taken into account. The criterion has been tested in comparison with expert estimations and some modern criteria. A better agreement of the new criterion with human estimation of chromatographic quality compared to some literature criteria is shown. A number of successful optimization runs has been performed using the criterion together with simplex optimization.     

Nanostructural Approach to Proton Ordering in Gas Hydrate Cages

A nanostructural approach to analysis of proton ordering in gas hydrate cages has been worked out within the framework of the topological model of strong and weak H-bonds. The approach involves rejection of the periodic boundary conditions, decomposition of the H-bond net into spherical layers, and two-dimensional drawing of the structure of spherical (spheroidal) fragments in the form of conjugate Schlegel diagrams. To analyze proton ordering in the spherical fragments composed of gas hydrate voids, we used the simulated annealing procedure and the correlation extension method proposed earlier.     

Flow-injection chemiluminescence determination of epinephrine in pharmaceutical preparations using raw apple juice as enzyme source

Raw apple juice exhibits the activity of polyphenol oxidase which can be employed for the determination of mono-, di- and polyhydric phenols. The chemiluminescence detection in the two-channel manifold was used to develop the new procedure for determination of epinephrine. Epinephrine can be determined by this method in pharmaceutical preparations in concentration ranges 1.0–10.0 and 10.0–25.0 mg l⁻¹, with a detection limit of 0.2 mg l⁻¹. Good selectivity against typical antioxidants and other coexisting substances was achieved. Relatively slow loss of the enzyme activity was observed during 1 week. The proposed method is very simple. Fresh juice solution from one apple can be prepared in 10 min and used for at least 8 h with excellent precision. Consumption of luminol solution was 0.15 ml min⁻¹. The throughput was 20 samples per hour.     

Evaluation of a complete HPLC solvent optimization system involving piece-wise quadratic modelling

Summary Interpretive methods are accepted to give the best possible results for selectivity optimization in HPLC. However the methods are very complex, and most work so far has been detailed academic studies. This paper describes an evaluation of a complete integrated system incorporating peak labelling, modelling of retention behaviour and calculation of response surfaces, with particular emphasis on the retention modelling. The peak labelling section has been discussed previously.A piece-wise quadratic function is investigated for the modelling of retention times across an isoeluotropic plane to effect selectivity optimization in HPLC. This requires 10 data-points on the isoeluotropic plane. The predicted global optimum and local optima are evaluated by comparison of calculated and experimental retention data, for a nine component sample. Seven interstitial points, distributed across the whole plane between the data-points, are similarly evaluated for a related sample. The typical error (in retention time) is less than 2%, often 1%, and the maximum error is 4.2%. At the global optimum the error was found be less than 1.3% for all 9 peaks.     

Fitting complex potential energy surfaces to simple model potentials: application of the simplex-annealing method

A stochastic method of optimization, which combines simulated annealing with simplex, is implemented to fit the parameters of a simple model potential. The main characteristic of the method is that it explores the whole space of the parameters of the model potential, and therefore it is very efficient in locating the global minimum of the cost function, in addition to being independent of the initial guess of the parameters. The method is employed to fit the complex intermolecular potential energy surface of the dimer of water, using as a reference the spectroscopic quality anisotropic site-site potential of Feller et al. The simple model potential chosen for its reparameterization is the MCY model potential of Clementi et al. The quality of the fit is assessed by comparing the geometry of the minimum, the harmonic frequencies, and the second virial coefficients of the parameterized potential with the reference one. Finally, to prove more rigorously the robustness of this method, it is compared with standard nonstochastic methods of optimization.