Ioannis P. Androulakis

αBB: A global optimization method for general constrained nonconvex problems

A branch and bound global optimization method,αBB, for general continuous optimization problems involving nonconvexities in the objective function and/or constraints is presented. The nonconvexities are categorized as being either of special structure or generic. A convex relaxation of the original nonconvex problem is obtained by (i) replacing all nonconvex terms of special structure (i.e. bilinear, fractional, signomial) with customized tight convex lower bounding functions and (ii) by utilizing the α parameter as defined in [17] to underestimate nonconvex terms of generic structure. The proposed branch and bound type algorithm attains finiteε-convergence to the global minimum through the successive subdivision of the original region and the subsequent solution of a series of nonlinear convex minimization problems. The global optimization method,αBB, is implemented in C and tested on a variety of example problems.

A global optimization method, αBB, for general twice-differentiable constrained NLPs—II. Implementation and computational results

Abstract Part I of this paper ( Adjiman et al., 1998a ) described the theoretical foundations of a global optimization algorithm, the α BB algorithm, which can be used to solve problems belonging to the broad class of twicedifferentiable NPLs. For any such problem, the ability to automatically generate progressively tighter convex lower bounding problems at each iteration guarantees the convergence of the branch-and-bound α BB algorithm to within e of the global optimum solution. Several methods were presented for the construction of valid convex underestimators for general nonconvex functions. In this second part, the performance of the proposed algorithm and its alternative underestimators is studied through their application to a variety of problems. An implementation of the α BB is described and a number of rules for branching variable selection and variable bound updates are shown to enhance convergence rates. A user-friendly parser facilitates problem input and provides flexibility in the selection of an underestimating strategy. In addition, the package features both automatic differentiation and interval arithmetic capabilities. Making use of all the available options, the α BB algorithm successfully identifies the global optimum solution of small literature problems, of small and medium size chemical engineering problems in the areas of reactors network design, heat exchanger network design, reactor–separator network design, of generalized geometric programming problems for design and control, and of batch process design problems with uncertainty.

Cytoskeleton-based forecasting of stem cell lineage fates

Stem cells that adopt distinct lineages cannot be distinguished based on traditional cell shape. This study reports that higher-order variations in cell shape and cytoskeletal organization that occur within hours of stimulation forecast the lineage commitment fates of human mesenchymal stem cells (hMSCs). The unique approach captures numerous early (24 h), quantitative features of actin fluororeporter shapes, intensities, textures, and spatial distributions (collectively termed morphometric descriptors). The large number of descriptors are reduced into “combinations” through which distinct subpopulations of cells featuring unique combinations are identified. We demonstrate that hMSCs cultured on fibronectin-treated glass substrates under environments permissive to bone lineage induction could be readily discerned within the first 24 h from those cultured in basal- or fat-inductive conditions by such cytoskeletal feature groupings. We extend the utility of this approach to forecast osteogenic stem cell lineage fates across a series of synthetic polymeric materials of diverse physicochemical properties. Within the first 24 h following stem cell seeding, we could successfully “profile” the substrate responsiveness prospectively in terms of the degree of bone versus nonbone predisposition. The morphometric methodology also provided insights into how substrates may modulate the pace of osteogenic lineage specification. Cells on glass substrates deficient in fibronectin showed a similar divergence of lineage fates, but delayed beyond 48 h. In summary, this high-content imaging and single cell modeling approach offers a framework to elucidate and manipulate determinants of stem cell behaviors, as well as to screen stem cell lineage modulating materials and environments.

Global optimization of MINLP problems in process synthesis and design

Abstract Two new methodologies for the global optimization of MINLP models, the Special structure Mixed Integer Nonlinear αBB,SMIN-αBB, and the General structure Mixed Integer Nonlinear αBB,GMIN-αBB, are presented. Their theoretical foundations provide guarantees that the global optimum solution of MINLPs involving twice-differentiable nonconvex functions in the continuous variables can be identified. The conditions imposed on the functionality of the binary variables differ for each method: linear and mixed bilinear terms can be treated with the SMIN-αBB; mixed nonlinear terms whose continuous relaxation is twice-differentiable are handled by the GMIN-αBB. While both algorithms use the concept of a branch & bound tree, they rely on fundamentally different bounding and branching strategies. In the GMIN-αBB algorithm, lower (upper) bounds at each node result from the solution of convex (nonconvex) MINLPs derived from the original problem. The construction of convex lower bounding MINLPs, using the techniques recently developed for the generation of valid convex underestimators for twice-differentiable functions ( Adjiman et al., 1996 ; Adjiman and Floudas, 1996 ), is an essential task as it allows to solve the underestimating problems to global optimality using the GBD algorithm or the OA algorithm, provided that the binary variables participate separably and linearly. Moreover, the inherent structure of the MINLP problem can be fully exploited as branching is performed on the binary and the continuous variables. In the case of the SMIN-αBB algorithm, the lower and upper bounds are obtained by solving continuous relaxations of the original MINLP. Using the αBB algorithm, these nonconvex NLPs are solved as global optimization problems and hence valid lower bounds are generated. Since branching is performed exclusively on the binary variables, the maximum size of the branch-and-bound tree is smaller than that for the SMIN-αBB. The two proposed approaches are used to generate computational results on various nonconvex MINLP problems that arise in the areas of Process Synthesis and Design.

A genetic algorithmic framework for process design and optimization

Abstract A general optimization framework for discrete and continuous problems based on genetic algorithmic techniques is presented. The proposed framework exhi

Sepsis: Something old, something new, and a systems view

Sepsis is a clinical syndrome characterized by a multisystem response to a microbial pathogenic insult consisting of a mosaic of interconnected biochemical, cellular, and organ-organ interaction networks. A central thread that connects these responses is inflammation that, while attempting to defend the body and prevent further harm, causes further damage through the feed-forward, proinflammatory effects of damage-associated molecular pattern molecules. In this review, we address the epidemiology and current definitions of sepsis and focus specifically on the biologic cascades that comprise the inflammatory response to sepsis. We suggest that attempts to improve clinical outcomes by targeting specific components of this network have been unsuccessful due to the lack of an integrative, predictive, and individualized systems-based approach to define the time-varying, multidimensional state of the patient. We highlight the translational impact of computational modeling and other complex systems approaches as applied to sepsis, including in silico clinical trials, patient-specific models, and complexity-based assessments of physiology.

A global optimization method, αBB, for process design

A global optimization algorithm, αBB, for twice-differentiable NLPs is presented. It operates within a branch-and-bound framework and requires the construction of a convex lower bounding problem. A technique to generate such a valid convex underestimator for arbitrary twice-differentiable functions is described. The αBB has been applied to a variety of problems and a summary of the results obtained is provided.

Modeling the influence of circadian rhythms on the acute inflammatory response.

A wide variety of modeling techniques have been applied towards understanding inflammation. These models have broad potential applications, from optimizing clinical trials to improving clinical care. Models have been developed to study specific systems and diseases, but the effect of circadian rhythms on the inflammatory response has not been modeled. Circadian rhythms are normal biological variations obeying the 24-h light/dark cycle and have been shown to play a critical role in the treatment and progression of many diseases. Several of the key components of the inflammatory response, including cytokines and hormones, have been observed to undergo significant diurnal variations in plasma concentration. It is hypothesized that these diurnal rhythms are entrained by the cyclic production of the hormones cortisol and melatonin, as stimulated by the central clock in the suprachiasmatic nucleus. Based on this hypothesis, a mathematical model of the interplay between inflammation and circadian rhythms is developed. The model is validated by its ability to reproduce diverse sets of experimental data and clinical observations concerning the temporal sensitivity of the inflammatory response.

Solving long-term financial planning problems via global optimization

Abstract A significant multi-stage financial planning problem is posed as a stochastic program with decision rules. The decision rule — called dynamically balanced — requires the purchase and sale of assets at each time stage so as to keep constant asset proportions in the portfolio composition. It leads to a nonconvex objective function. We show that the rule performs well as compared with other dynamic investment strategies. We specialize a global optimization algorithm for this problem class — guaranteeing finite e-optimal convergence. Computational results demonstrate the procedures efficiency on a real-world financial planning problem. The tests confirm that local optimizers are prone to erroneously underestimate the efficient frontier. The concepts can be readily extended for other classes of long-term investment strategies.

Modeling endotoxin-induced systemic inflammation using an indirect response approach.

A receptor mediated model of endotoxin-induced human inflammation is proposed. The activation of the innate immune system in response to the endotoxin stimulus involves the interaction between the extracellular signal and critical receptors driving downstream signal transduction cascades leading to transcriptional changes. We explore the development of an in silico model that aims at coupling extracellular signals with essential transcriptional responses through a receptor mediated indirect response model. The model consists of eight (8) variables and is evaluated in a series of biologically relevant scenarios indicative of the non-linear behavior of inflammation. Such scenarios involve a self-limited response where the inflammatory stimulus is cleared successfully; a persistent infectious response where the inflammatory instigator is not eliminated, leading to an aberrant inflammatory response, and finally, a persistent non-infectious inflammatory response that can be elicited under an overload of the pathogen-derived product; as such high dose of the inflammatory insult can disturb the dynamics of the host response leading to an unconstrained inflammatory response. Finally, the potential of the model is demonstrated by analyzing scenarios associated with endotoxin tolerance and potentiation effects.