A Co-evolutionary, Nature-Inspired Algorithm for the Concurrent Generation of Alternatives

Engineering optimization problems usually contain multifaceted performance requirements that can be riddled with unquantifiable specifications and incompatible performance objectives. Such problems typically possess competing design requirements which are very difficult – if not impossible – to quantify and capture at the time of model formulation. There are invariably unmodelled design issues, not apparent at the time of model construction, which can greatly impact the acceptability of the model’s solutions. Consequently, when solving many “real life” mathematical programming applications, it is generally preferable to formulate several quantifiably good alternatives that provide very different perspectives to the problem. These alternatives should possess near-optimal objective measures with respect to all known modelled objective(s), but be fundamentally different from each other in terms of the system structures characterized by their decision variables. This solution approach is referred to as modelling-to-generate-alternatives (MGA). This study demonstrates how the nature-inspired, Firefly Algorithm can be used to concurrently create multiple solution alternatives that both satisfy required system performance criteria and yet are maximally different in their decision spaces. This new co-evolutionary approach is very computationally efficient, since it permits the concurrent generation of multiple, good solution alternatives in a single computational run rather than the multiple implementations required in previous MGA procedures

Stochastic Modelling to Generate Alternatives Using the Firefly Algorithm: A Simulation- Optimization Approach

In solving many practical mathematicalprogramming applications, it is generally preferable to formulateseveral quantifiably good alternatives that provide very differentapproaches to the particular problem. This is because decisionmakingtypically involves complex problems that are riddled withincompatible performance objectives and possess competingdesign requirements which are very difficult – if not impossible –to quantify and capture at the time that the supporting decisionmodels are constructed. There are invariably unmodelled designissues, not apparent at the time of model construction, which cangreatly impact the acceptability of the model’s solutions.Consequently, it is preferable to generate several alternativesthat provide multiple, disparate perspectives to the problem.These alternatives should possess near-optimal objectivemeasures with respect to all known modelled objective(s), but befundamentally different from each other in terms of the systemstructures characterized by their decision variables. This solutionapproach is referred to as modelling to generate-alternatives(MGA). This paper provides a biologically-inspired simulationoptimizationMGA approach that uses the Firefly Algorithm toefficiently create multiple solution alternatives to stochasticproblems that satisfy required system performance criteria andyet remain maximally different in their decision spaces. Theefficacy of this stochastic MGA method is demonstrated using awaste facility expansion case study

On the Predictive Uncertainty of a Distributed Hydrologic Model

We use models to simulate the real world mainly for prediction purposes. However, since any model is a simplification of reality, there remains a great deal of uncertainty even after the calibration of model parameters. The model’s identifiability of realistic model parameters becomes questionable when the watershed of interest is small, and its time of concentration is shorter than the computational time step of the model. To improve the discovery of more reliable and more realistic sets of model parameters instead of mathematical solutions, a new algorithm is needed. This algorithm should be able to identify mathematically inferior but more robust solutions as well as to take samples uniformly from high-dimensional search spaces for the purpose of uncertainty analysis. Various watershed configurations were considered to test the Soil and Water Assessment Tool (SWAT) model’s identifiability of the realistic spatial distribution of land use, soil type, and precipitation data. The spatial variability in small watersheds did not significantly affect the hydrographs at the watershed outlet, and the SWAT model was not able to identify more realistic sets of spatial data. A new populationbased heuristic called the Isolated Speciation-based Particle Swarm Optimization (ISPSO) was developed to enhance the explorability and the uniformity of samples in high-dimensional problems. The algorithm was tested on seven mathematical functions and outperformed other similar algorithms in terms of computational cost, consistency, and scalability. One of the test functions was the Griewank function, whose number of minima is not well defined although the function serves as the basis for evaluating multi-modal optimization algorithms. Numerical and analytical methods were proposed to count the exact number of minima of the Griewank function within a hyperrectangle. The ISPSO algorithm was applied to the SWAT model to evaluate the performance consistency of optimal solutions and perform uncertainty analysis in the Generalized Likelihood Uncertainty Estimation (GLUE) framework without assuming a statistical structure of modeling errors. The algorithm successfully found hundreds of acceptable sets of model parameters, which were used to estimate their prediction limits. The uncertainty bounds of this approach were comparable to those of the typical GLUE approach