The Nelder-Mead simplex method is an optimization routine that works well with irregular objective functions. For a function of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$n$$</EquationSource> </InlineEquation> parameters, it compares the objective function at the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$n+1$$</EquationSource> </InlineEquation> vertices of a simplex and updates the worst vertex through simplex search steps. However, a...</equationsource></inlineequation></equationsource></inlineequation>

In part I of this paper, we proposed a Mixed-Integer Linear Program (MILP) to analyze imperfect competition of oligopoly producers in two-stage zonal power markets. In part II of this paper, we propose a solution algorithm which decomposes the proposed MILP model into several subproblems and...

The rapid development of artificial intelligence methods contributes to their wide applications for forecasting various financial risks in recent years. This study introduces a novel explainable case-based reasoning (CBR) approach without a requirement of rich expertise in financial risk....

Since the advent of Markov chain Monte Carlo (MCMC) methods in the early 1990s, Bayesian methods have been proposed for a large and growing number of applications. One of the main advantages of Bayesian inference is the ability to deal with many different sources of uncertainty, including data,...

We implement a dynamic programming algorithm on a computational grid consisting of loosely coupled processors, possibly including clusters and individual workstations. The grid changes dynamically during the computation, as processors enter and leave the pool of workstations. The algorithm is...

Modeling diffusion processes, such as drug deliver, bio-heat transfer, and the concentration change of cytokine for computational biology research, requires intensive computing resources as one must employ sequential numerical algorithms to obtain accurate numerical solutions, especially for...

Central composite discrepancy (CCD) has been proposed to measure the uniformity of a design over irregular experimental region. However, how CCD-based optimal uniform designs can be efficiently computed remains a challenge. Focusing on this issues, we proposed a particle swarm optimization-based...

We present a parallelization of the revised simplex method for large extensive forms of two-stage stochastic linear programming (LP) problems. These problems have been considered too large to solve with the simplex method; instead, decomposition approaches based on Benders decomposition or, more...