Multi-objective optimization aided to allocation of vertices in aesthetic drawings of special graphs

A problem of drawing specific graphs is considered emphasizing aesthetic appeal of the visualization. We focus on graphs related to the management of business processes. A particular problem of the aesthetic drawing is considered where the aesthetic allocation of vertices is aimed. The problem is stated as a problem of bi-objective optimization where the objectives are the length of connectors and the compatibility of the sequence flows with the favorable top-down, left-right direction. An algorithm based on the branch-and-bound approach is proposed

On multidimensional scaling with Euclidean and city block metrics

Experimental sciences collect large amounts of data. Different techniques are available for information elicitation from data. Frequently statistical analysis should be combined with the experience and intuition of researchers. Human heuristic abilities are developed and oriented to patterns in space of dimensionality up to 3. Multidimensional scaling (MDS) addresses the problem how objects represented by proximity data can be represented by points in low dimensional space. MDS methods are implemented as the optimization of a stress function measuring fit of the proximity data by the distances between the respective points. Since the optimization problem is multimodal, a global optimization method should be used. In the present paper a combination of an evolutionary metaheuristic algorithm with a local search algorithm is used. The experimental results show the influence of metrics defining distances in the considered spaces on the results of multidimensional scaling. Data sets with known and unknown structure and different dimensionality (up to 512 variables) have been visualized. Daugiamačių skalių su Euklido ir Manheteno metrikomis sudarymo metodai Santrauka Eksperimentiniai mokslai kaupia didelius duomenų kiekius. Sukurta daug metodų informacijai iš duomenų išgauti. Daûnai statistiniai metodai yra derinami su euristine analize pagrįsta tyrinėtojų intuicija. Tačiau euristiniai žmonių sugebėjimai gerai tinka analizuoti duomenis, kurių matavimų skaičius neviršija 3. Daugiamačių skalių metodas skirtas vaizduoti objektams mažo matavimų skaičiaus erdvėje, kai objektai apibrėžti panašumais/nepanašumais, o atstumai vaizdų erdvėje vaizduoja nepanašumus. Daugiamačių skalių metodai sudaromi kaip vaizdavimo tikslumo kriterijaus, paprastai vadinamo stresu, minimizavimo procedūros. Kadangi optimizavimo uždaviniai daugiaekstremalūs, jiems spręsti reikia globalios optimizacijos metodų. Šiame darbe pasiūlytas algoritmas, jungiantis metaeuristinę globalią paiešką ir lokalios minimizacijos metodą. Eksperimentais ištirta metrikos vaizdų erdvėje įtaka vaizdavimo tikslumui ir algoritmo efektyvumui. Eksperimentuose naudotos duomenų aibės su žinoma ir nežinoma struktūra; optimizacijos uždavinio kintamųjų yra iki 512. First Published Online: 21 Oct 2010 Reikšminiai žodžiai: daugiadimensės skalės, globalioji optimizacija, metaeuristiniai metodai, Manheteno metrika, daugiamačių duomenų vizualizacija

Operations research: Theory and applications

„Operations research: Theory and applications" Technological and Economic Development of Economy, 12(4), p. 26

Use of stabilized pressure curves in horizontal wells to evaluate the informative value determination of fluid flow parameters at production facilities

The relevance of the research is caused by the fact that the main sources of information on filtration parameters of the remote zone of the formation are well tests at unsteady regimes with the recording of pressure or level recovery curves pressure recovery curve. To determine the reliable parameters of the formation zone remote from the well, the duration of recording of the pres* sure recovery curve should be long enough, which leads to losses in oil production. To determine the filtration cha* racteristics of the formation, as well as reduce losses during hydrodynamic studies, it is possible to use the method of studying wells without stopping them - the method of stabilizing the pressure. Need to identify the filtration flow regimes for operational determination of the hydrodynamic parameters of oil reservoirs during horizontal well tests by bottomhole pressure buildup curves. However, now, the issue of analyzing and interpreting the results of measurements with the recording the pressure stabilization curves, which, like the pressure recovery curve, can give the required infor* mation about the formation, remains poorly understood

Greed Is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation

The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement (EI) and the Upper Confidence Bound (UCB) always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is not guaranteed to do so and Weighted Expected Improvement does so only for a restricted range of weights. We introduce two novel ϵ-greedy acquisition functions. Extensive empirical evaluation of these together with random search, purely exploratory, and purely exploitative search on 10 benchmark problems in 1 to 10 dimensions shows that ϵ-greedy algorithms are generally at least as effective as conventional acquisition functions (e.g. EI and UCB), particularly with a limited budget. In higher dimensions ϵ-greedy approaches are shown to have improved performance over conventional approaches. These results are borne out on a real world computational fluid dynamics optimisation problem and a robotics active learning problem. Our analysis and experiments suggest that the most effective strategy, particularly in higher dimensions, is to be mostly greedy, occasionally selecting a random exploratory solution

On visualization of multidimensional data using three‐dimensional embedding space

Multidimensional scaling addresses the problem of representation of objects specified by proximity data by points in low dimensional embedding space. The problem is reduced to optimization of an accuracy measure of fit of the proximity data by the distances between the respective points. Three‐dimensional embedding space is considered in the present paper. Images of data of different dimensionality are discussed as well as dependence of visualization accuracy on dimensionality of embedding space and complexity of data. On visualization of multidimensional data using three-dimensional embedding space Santrauka Daugiamatės skalės naudojamos artimumu apibrėžtiems duomenims atvaizduoti taškais mažo mato erdvėje. Uždavinys sprendžiamas optimizuojant atstumo tarp atitinkančių taškų atitikties duotiems artimumams įvertį. Vaizdavimo tikslumo priklausomybė nuo skalės ir duomenų mato yra aptarta ir pasiūlyta naudoti trimates skales. Įvairių duomenų trimatės skalės pavaizduotos projekcijomis ir aptartos. Reikšminiai žodžiai: daugiamatės skalės, globali optimizacija, metaeuristika, miesto kvartalo metrika, daugiamačių duomenų vizualizavimas. First Published Online: 21 Oct 201

A global optimization method based on the reduced simplicial statistical model

A simplicial statistical model of multimodal functions is used to construct a global optimization algorithm. The search for the global minimum in the multidimensional space is reduced to the search over the edges of simplices covering the feasible region combined with the refinement of the cover. The refinement is performed by subdivision of selected simplices taking into account the point where the objective function value has been computed at the current iteration. For the search over the edges the one-dimensional P-algorithm based on the statistical smooth function model is adapted. Differently from the recently proposed algorithm here the statistical model is used for modelling the behaviour of the objective function not over the whole simplex but only over its edges. Testing results of the proposed algorithm are included

Daugiamačių skalių su Euklido ir Manheteno metrikomis sudarymo metodai

Experimental sciences collect large amounts of data. Different techniques are available for information elicitation from data. Frequently statistical analysis should be combined with the experience and intuition of researchers. Human heuristic abilities are developed and oriented to patterns in space of dimensionality up to 3. Multidimensional scaling (MDS) addresses the problem how objects represented by proximity data can be represented by points in low dimensional space. MDS methods are implemented as the optimization of a stress function measuring fit of the proximity data by the distances between the respective points. Since the optimization problem is multimodal, a global optimization method should be used. In the present paper a combination of an evolutionary metaheuristic algorithm with a local search algorithm is used. The experimental results show the influence of metrics defining distances in the considered spaces on the results of multidimensional scaling. Data sets with known and unknown structure and different dimensionality (up to 512 variables) have been visualized

P-algorithm based on a simplicial statistical model of multimodal functions

Statistical models of multimodal functions, Global optimization, Simplicial partition, 90C26,