figure a

Professor Christodoulos A. Floudas (8/31/1959–8/14/2016). Photo Credit: Texas A&M University Engineering.

This special issue marks three years after the unexpected and devastating passing of Professor Christodoulos (Chris) A. Floudas, an extraordinary scholar who has since been sorely missed by the Process Systems Engineering community as well as the broader world of Mathematical Optimization. Chris Floudas was the Stephen C. Macaleer ’63 Professor in Engineering and Applied Science at Princeton University, where he served as faculty for three decades. Later in his life, Chris joined Texas A&M University as the Director of the Texas A&M Energy Institute and the Erle Nye ’59 Chair Professor for Engineering Excellence.

Chris Floudas’s scholarly contributions are captured in an excess of 10 textbooks, 30 book chapters and 400 journal papers. Collectively, these works discuss many theoretical and methodological advances in the fields of Global Optimization, Mixed-Integer Nonlinear Optimization, Grey-box Optimization, and Optimization under Uncertainty as well as apply these fields in areas as diverse as Process and Product Design, Process Synthesis, Process Operations, Multi-scale Energy Systems, Bioinformatics, and Computational Biology, among others.

Chris Floudas received many accolades for his research, teaching prowess, academic leadership, and entrepreneurial virtue. Notable moments of recognition were his induction to the National Academy of Engineering in 2011 for contributions to theory, methods, and applications of global optimization in process systems engineering, computational chemistry, and molecular biology; his induction to the National Academy of Inventors in 2015; his election as a Corresponding Member of the First Section of the Academy of Athens in 2015; his receipt of awards including the Constantin Caratheodory Prize, the AIChE Computing in Chemical Engineering Award, the AIChE Professional Progress Award, the National Award and Gold Medal of the Hellenic Operational Research Society, the Bodossaki Foundation Award in Applied Sciences, the NSF Presidential Young Investigator Award, and the Graduate Mentoring Award of Princeton University; his naming as Fellow of organizations such as AIChE, TIAS, and SIAM; and many other honors that are too many to list here.

At the same time, Chris possessed a unique gift in the way he touched the lives of the many people with whom he interacted, whether as an advisor, mentor, collaborator, colleague, and/or personal friend. Notably, Chris Floudas left behind an impressive academic tree, which to-date has grown to contain more than 140 members, including 21 faculty at major academic institutions; the full academic tree of Prof. Christodoulos A. Floudas is maintained at http://titan.engr.tamu.edu/tree/caf/tree.php.

We wish to celebrate all these scientific, professional, and interpersonal contributions of Chris Floudas via this special issue, which is dedicated to his memory. The issue features a total of 11 manuscripts whose authorship was led by students, mentees, colleagues and friends of Chris’s, discussing advances in both methodology and application-driven research. From the methodological viewpoint, the contributions can be broadly categorized in three areas, namely (a) Deterministic Global Optimization, (b) Optimization under Uncertainty, and (c) Derivative-Free Optimization and Machine Learning, which also constituted three of Chris’s core research thrusts. From the viewpoint of application areas, the focus of the contributions ranges from oil-sands production to heating and cooling in commercial buildings to large-scale packing, to name but a few examples. Indeed, the diversity of topics addressed in this issue are reminiscent of the broad range of application areas on which Chris has made a significant impact.

In the area of Deterministic Global Optimization, the paper “SUSPECT: MINLP special structure detector for Pyomo” by Ceccon et al. presents an open-source tool that performs bounds tightening, bound propagation, monotonicity and convexity detection for generic mixed-integer nonlinear optimization (MINLP) problems. The toolkit symbolically analyzes the original MINLP formulations and uses acyclic graph representations and state-of-the-art convexity detection methods to identify special structures. The tool is implemented in Python and can be used as a preprocessing step for MINLP solvers. In their paper “On the use of third-order models with fourth-order regularization for unconstrained optimization,” Birgin et al. extend previous work on worst-case complexity evaluation for unconstrained nonlinear optimization problems. Their proposed algorithm uses regularized third-order models and a step control strategy for smooth unconstrained optimization. The competitiveness of the algorithm is shown through literature benchmark problems and a large-scale packing problem.

In the area of Optimization under Uncertainty, the paper “Stochastic optimization in supply chain networks: Averaging robust solutions” by Bertsimas and Youssef studies the expected performance of supply chain networks that are subject to demand uncertainty. Unlike in a classical robust optimization approach, the authors introduce uncertainty sets whose variability parameter is a random variable, and they seek to maximize expected system performance in light of possible worst case realizations. By using a low-dimensional approximation to evaluate expectations, the authors showed that they can obtain base-stock levels matching those resulting from stochastic optimization at a significantly reduced computational cost. The paper “Parallel-batching Scheduling of deteriorating jobs with non-identical sizes and rejection on a single machine” by Kong et al. addresses the single-machine, parallel-batching scheduling with deteriorating jobs and option for job rejection. The authors develop a low-complexity dynamic programming algorithm to solve the special case of identical-sized jobs, as well as a hybrid algorithm combining heuristics with dynamic programming to address the general case. In their paper “Adjustable robust optimization through multi-parametric programming,” Avraamidou and Pistikopoulos propose a novel method based on multi-parametric programming to derive generalized affine decision rules for linear mixed-integer adjustable robust optimization problems. They achieve this by considering the second-stage optimization as a problem that is parametric not only on the uncertain parameters but also on the “here-and-now” decisions, yielding exact and global solutions to the full, two-stage mixed-integer linear problem. Risbeck et al. contribute “Mixed-integer optimization methods for online scheduling in large-scale HVAC systems,” where they present a mixed-integer linear programming formulation for minimizing the operating cost of large HVAC systems. The authors show that the use of simplified surrogates to describe the system during the later time points in the horizon leads to a significant increase in tractability, allowing the approach to be used in an online setting. Furthermore, they develop decompositions to separate the airside and waterside models, pushing the envelope towards handling complex systems with many temperature zones and pieces of equipment. Finally, in their paper “Generalized Hose uncertainty in single-commodity robust network design,” Gounaris and Schmidt study the robust design of single-commodity networks with uncertain demands. In this context, they generalize the commonly used Hose uncertainty polytope to include realistic correlations among network subsets. The authors also derive new closed-form expressions for the worst-case cumulative demand of any set of nodes, and they use those expressions to extend the MIP formulation for separating the robust cut-set inequalities. Via their computational experiments on benchmark instances, the authors quantify the expected cost savings by explicitly accounting for the demand correlations, when the latter exist in the network of interest.

The remaining four contributions of this issue deal with optimization using Machine Learning (ML) approximation models and/or Derivative-Free Optimization techniques for problems that are either computationally expensive or reliant on real data. The paper “Oil sands extraction plant debottlenecking: An optimization approach” by Yuan et al. proposes a novel optimization approach that combines first-principles and Gaussian Process Modeling to enable optimal capacity expansion of highly integrated process systems. The authors use real process data, parametric linear programming, and nonlinear programming to identify bottlenecks in expanding a real oil-sands production process. In their paper “A discontinuous derivative-free optimization framework for multi-enterprise supply chain,” Bhosekar and Ierapetritou propose various novel techniques for simulation-based optimization of supply-chain problems with unavailability of derivatives and discontinuities in the objective function. Their approach combines Sparse-Grid Sampling and Support Vector Machines to model discontinuities, which leads to higher optimality solutions when compared to state-of-the-art methods. The contribution by Kim and Boukouvala, “Machine learning-based surrogate modeling for data-driven optimization: A comparison of subset selection for regression techniques,” presents a comprehensive comparison of subset selection regression and interpolating surrogate methods for approximating input-output data for simulation-based optimization. The authors also present a novel adaptive sampling and surrogate modeling optimization technique for box constrained and nonlinearly constrained optimization problems. Finally, in their paper “Deterministic global derivative-free optimization of black-box problems with bounded Hessian,” Bajaj and Hasan present a novel optimization approach for problems that lack derivative information, but for which an upper bound on the diagonal Hessian elements is available. Using the Hessian bounds, the authors develop valid edge-concave underestimators and a branch-and-bound approach to globally optimize a variety of problems fitting these characteristics.

We hope that you will enjoy reading these papers, and that you shall take the opportunity to fondly reflect on Chris’s legacy in these and other areas. In conclusion, we would like to thank the authors of all submissions for contributing their original manuscripts in support of this special issue effort. Our deepest appreciation also goes to all referees that contributed valuable time and hard work to review these papers, offering constructive comments that often helped improve the overall presentation and quality of the papers. Finally, we would like to thank the Editors-in-Chief of Optimization Letters, Professors Pavlo Krokhmal and Oleg Prokopyev, both of whom embraced the idea to host this Special Issue in Memory of Professor Christodoulos A. Floudas, and who entrusted us with its editorial process.