A knowledge-based evolution strategy for the multi-objective minimum spanning tree problem

A fast Knowledge-based Evolution Strategy, KES, for the multi-objective minimum spanning tree, is presented. The proposed algorithm is validated, for the bi-objective case, with an exhaustive search for small problems (4-10 nodes), and compared with a deterministic algorithm, EPDA and NSGA-II for larger problems (up to 100 nodes) using benchmark hard instances. Experimental results show that KES finds the true Pareto fronts for small instances of the problem and calculates good approximation Pareto sets for larger instances tested. It is shown that the fronts calculated by YES are superior to NSGA-II fronts and almost as good as those established by EPDA. KES is designed to be scalable to multi-objective problems and fast due to its small complexity.

RBF equalizer design using directional evolutionary multi-objective optimization

Whilst radial basis function (RBF) equalizers have been employed to combat the linear and nonlinear distortions in modern communication systems, most of them do not take into account the equalizer's generalization capability. In this paper, it is firstly proposed that the. model's generalization capability can be improved by treating the modelling problem as a multi-objective optimization (MOO) problem, with each objective based on one of several training sets. Then, as a modelling application, a new RBF equalizer learning scheme is introduced based on the directional evolutionary MOO (EMOO). Directional EMOO improves the computational efficiency of conventional EMOO, which has been widely applied in solving MOO problems, by explicitly making use of the directional information. Computer simulation demonstrates that the new scheme can be used to derive RBF equalizers with good performance not only on explaining the training samples but on predicting the unseen samples.

Nonlinear channel equalizer design using directional evolutionary multi-objective optimization

In this paper, a new equalizer learning scheme is introduced based on the algorithm of the directional evolutionary multi-objective optimization (EMOO). Whilst nonlinear channel equalizers such as the radial basis function (RBF) equalizers have been widely studied to combat the linear and nonlinear distortions in the modern communication systems, most of them do not take into account the equalizers' generalization capabilities. In this paper, equalizers are designed aiming at improving their generalization capabilities. It is proposed that this objective can be achieved by treating the equalizer design problem as a multi-objective optimization (MOO) problem, with each objective based on one of several training sets, followed by deriving equalizers with good capabilities of recovering the signals for all the training sets. Conventional EMOO which is widely applied in the MOO problems suffers from disadvantages such as slow convergence speed. Directional EMOO improves the computational efficiency of the conventional EMOO by explicitly making use of the directional information. The new equalizer learning scheme based on the directional EMOO is applied to the RBF equalizer design. Computer simulation demonstrates that the new scheme can be used to derive RBF equalizers with good generalization capabilities, i.e., good performance on predicting the unseen samples.

The automatic layout model in the sequencing of construction activities of multi-objective diaphragm wall unit by using self-learning neural network

Foundation construction process has been an important key point in a successful construction engineering. The frequency of using diaphragm wall construction method among many deep excavation construction methods in Taiwan is the highest in the world. The traditional view of managing diaphragm wall unit in the sequencing of construction activities is to establish each phase of the sequencing of construction activities by heuristics. However, it conflicts final phase of engineering construction with unit construction and effects planning construction time. In order to avoid this kind of situation, we use management of science in the study of diaphragm wall unit construction to formulate multi-objective combinational optimization problem. Because the characteristic (belong to NP-Complete problem) of problem mathematic model is multi-objective and combining explosive, it is advised that using the 2-type Self-Learning Neural Network (SLNN) to solve the N=12, 24, 36 of diaphragm wall unit in the sequencing of construction activities program problem. In order to compare the liability of the results, this study will use random researching method in comparison with the SLNN. It is found that the testing result of SLNN is superior to random researching method in whether solution-quality or Solving-efficiency.

Modeling small-scale dairy farms in central Mexico using multi-criteria programming

Milk supply from Mexican dairy farms does not meet demand and small-scale farms can contribute toward closing the gap. Two multi-criteria programming techniques, goal programming and compromise programming, were used in a study of small-scale dairy farms in central Mexico. To build the goal and compromise programming models, 4 ordinary linear programming models were also developed, which had objective functions to maximize metabolizable energy for milk production, to maximize margin of income over feed costs, to maximize metabolizable protein for milk production, and to minimize purchased feedstuffs. Neither multicriteria approach was significantly better than the other; however, by applying both models it was possible to perform a more comprehensive analysis of these small-scale dairy systems. The multi-criteria programming models affirm findings from previous work and suggest that a forage strategy based on alfalfa, rye-grass, and corn silage would meet nutrient requirements of the herd. Both models suggested that there is an economic advantage in rescheduling the calving season to the second and third calendar quarters to better synchronize higher demand for nutrients with the period of high forage availability.

Implications of recent Australian wheat industry developments for overseas and domestic prices

This study is motivated by the proposition that the objectives of the AWB Ltd have changed since semi-privatisation of the Australian Wheat Board under the Wheat Marketing Act, 1989. Conceptualising this change of objectives as a shift from revenue maximization to profit maximization, this study examines the impact of such a change on the pricing policies of a multi-market price-setting firm. More specifically, this paper investigates, using two hypothetical objective functions, a risk averse AWB�s price-setting behaviour in an �overseas� and a �domestic� market in response to recent wheat industry developments. In the analysis these developments manifest themselves as differing price elasticities, differing transport costs and uncertain demand functions, and their implications particularly for the prices paid by domestic consumers are explored.

Past, present and future mathematical models for buildings (i)

This is the first of two articles presenting a detailed review of the historical evolution of mathematical models applied in the development of building technology, including conventional buildings and intelligent buildings. After presenting the technical differences between conventional and intelligent buildings, this article reviews the existing mathematical models, the abstract levels of these models, and their links to the literature for intelligent buildings. The advantages and limitations of the applied mathematical models are identified and the models are classified in terms of their application range and goal. We then describe how the early mathematical models, mainly physical models applied to conventional buildings, have faced new challenges for the design and management of intelligent buildings and led to the use of models which offer more flexibility to better cope with various uncertainties. In contrast with the early modelling techniques, model approaches adopted in neural networks, expert systems, fuzzy logic and genetic models provide a promising method to accommodate these complications as intelligent buildings now need integrated technologies which involve solving complex, multi-objective and integrated decision problems.

Entropy application to improve construction finance decisions

In financial decision-making processes, the adopted weights of the objective functions have significant impacts on the final decision outcome. However, conventional rating and weighting methods exhibit difficulty in deriving appropriate weights for complex decision-making problems with imprecise information. Entropy is a quantitative measure of uncertainty and has been useful in exploring weights of attributes in decision making. A fuzzy and entropy-based mathematical approach is employed to solve the weighting problem of the objective functions in an overall cash-flow model. The multiproject being undertaken by a medium-size construction firm in Hong Kong was used as a real case study to demonstrate the application of entropy. Its application in multiproject cash flow situations is demonstrated. The results indicate that the overall before-tax profit was HK$ 0.11 millions lower after the introduction of appropriate weights. In addition, the best time to invest in new projects arising from positive cash flow was identified to be two working months earlier than the nonweight system.

Application of the entropy technique and genetic algorithms to construction site layout planning of medium-size projects

Genetic algorithms (GAs) have been introduced into site layout planning as reported in a number of studies. In these studies, the objective functions were defined so as to employ the GAs in searching for the optimal site layout. However, few studies have been carried out to investigate the actual closeness of relationships between site facilities; it is these relationships that ultimately govern the site layout. This study has determined that the underlying factors of site layout planning for medium-size projects include work flow, personnel flow, safety and environment, and personal preferences. By finding the weightings on these factors and the corresponding closeness indices between each facility, a closeness relationship has been deduced. Two contemporary mathematical approaches - fuzzy logic theory and an entropy measure - were adopted in finding these results in order to minimize the uncertainty and vagueness of the collected data and improve the quality of the information. GAs were then applied to searching for the optimal site layout in a medium-size government project using the GeneHunter software. The objective function involved minimizing the total travel distance. An optimal layout was obtained within a short time. This reveals that the application of GA to site layout planning is highly promising and efficient.

A robust controller design method for feedback substitution schemes using genetic algorithms

Controllers for feedback substitution schemes demonstrate a trade-off between noise power gain and normalized response time. Using as an example the design of a controller for a radiometric transduction process subjected to arbitrary noise power gain and robustness constraints, a Pareto-front of optimal controller solutions fulfilling a range of time-domain design objectives can be derived. In this work, we consider designs using a loop shaping design procedure (LSDP). The approach uses linear matrix inequalities to specify a range of objectives and a genetic algorithm (GA) to perform a multi-objective optimization for the controller weights (MOGA). A clonal selection algorithm is used to further provide a directed search of the GA towards the Pareto front. We demonstrate that with the proposed methodology, it is possible to design higher order controllers with superior performance in terms of response time, noise power gain and robustness.

Does increased hydrochemical model complexity decrease robustness?

The aim of this study was, within a sensitivity analysis framework, to determine if additional model complexity gives a better capability to model the hydrology and nitrogen dynamics of a small Mediterranean forested catchment or if the additional parameters cause over-fitting. Three nitrogen-models of varying hydrological complexity were considered. For each model, general sensitivity analysis (GSA) and Generalized Likelihood Uncertainty Estimation (GLUE) were applied, each based on 100,000 Monte Carlo simulations. The results highlighted the most complex structure as the most appropriate, providing the best representation of the non-linear patterns observed in the flow and streamwater nitrate concentrations between 1999 and 2002. Its 5% and 95% GLUE bounds, obtained considering a multi-objective approach, provide the narrowest band for streamwater nitrogen, which suggests increased model robustness, though all models exhibit periods of inconsistent good and poor fits between simulated outcomes and observed data. The results confirm the importance of the riparian zone in controlling the short-term (daily) streamwater nitrogen dynamics in this catchment but not the overall flux of nitrogen from the catchment. It was also shown that as the complexity of a hydrological model increases over-parameterisation occurs, but the converse is true for a water quality model where additional process representation leads to additional acceptable model simulations. Water quality data help constrain the hydrological representation in process-based models. Increased complexity was justifiable for modelling river-system hydrochemistry. Increased complexity was justifiable for modelling river-system hydrochemistry.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.

Variability of the Atlantic thermohaline circulation described by three-dimensional empirical orthogonal functions

We describe the use of bivariate 3d empirical orthogonal functions (EOFs) in characterising low frequency variability of the Atlantic thermohaline circulation (THC) in the Hadley Centre global climate model, HadCM3. We find that the leading two modes are well correlated with an index of the meridional overturning circulation (MOC) on decadal timescales, with the leading mode alone accounting for 54% of the decadal variance. Episodes of coherent oscillations in the sub-space of the leading EOFs are identified; these episodes are of great interest for the predictability of the THC, and could indicate the existence of different regimes of natural variability. The mechanism identified for the multi-decadal variability is an internal ocean mode, dominated by changes in convection in the Nordic Seas, which lead the changes in the MOC by a few years. Variations in salinity transports from the Arctic and from the North Atlantic are the main feedbacks which control the oscillation. This mode has a weak feedback onto the atmosphere and hence a surface climatic influence. Interestingly, some of these climate impacts lead the changes in the overturning. There are also similarities to observed multi-decadal climate variability.

Quality of medicines stored together in multi-compartment compliance aids

Background and Objective: Dispensing medicines into compliance aids is a common practice in pharmacy contrary to manufacturers’ advice and studies have shown the appearance of light-sensitive tablets is compromised by such storage; we previously found evidence of reduced bioavailability at elevated temperature and humidity. Our objective was to examine the physicochemical stability of two generic atenolol tablets in different compliance aids and with aspirin co-storage at room temperature and at 40 °C/75% relative humidity. Methods: The physicochemical stability of atenolol tablets was evaluated after 28 days of storage and compared with controls by examining visual appearance, weight, disintegration, dissolution, friability and hardness to accepted standards and using a previously validated HPLC method for chemical assay. Results and Discussion: The response to storage was brand-dependent and not straightforward. With one make of atenolol (Alpharma), storage in compliance aids even at room temperature impacted on physical stability, reducing tablet hardness, with storage in Dosett® exerting a greater impact than storage in Medidos® (t-test P < 0·001). Co-storage at elevated temperature and humidity also impacted on the appearance of non-coated aspirin tablets (Angette™). The chemical stability of atenolol was not affected and we did not find evidence of changes to bioavailability with either make. Certainly data for one atenolol make (CP Pharmaceuticals) co-stored with aspirin (Angette™ and Nu-Seals) in both compliance aids at room temperature provided evidence of short-term stability. But medicines are dispensed into compliance aids in multi-factorial ways so our study highlights not only the lack of evidence but also a realization that evidence to support real practice may not be accomplished through research. Conclusion: Reassuring practitioners of the continued stability of medicines in compliance aids under the countless condition in which they are dispensed in practice may requires a different approach involving medical device regulators and more definitive professional guidance.