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Decision Making via Optimization

Feb 3, 2021 | 2020 ISSUE, RESEARCH

Decision Making via Optimization

2020 ISSUE, RESEARCH

Written by Malek Succar

Whenever faced with an important decision, finding the optimal choice can be a tedious task. Sometimes referred to as the science of “making the most of what you have”, optimization is in a nutshell the search for the best solution given a set of alternatives and constraints. In practice, optimization techniques help engineers in maximizing engineering performance.
An optimization problem typically consists of modelling the problem at hand, which helps identify what needs to be optimized, using the control parameters or decision variables. The simplest single-variable optimization methods were first introduced by Pierre De Fermat and Joseph-Louis Lagrange using calculus-based techniques, whereby setting the first derivative of a continuous mathematical function to zero, yielding either its maximum, minimum, or inflection point. Back in the 1600s, however, such problems like the simplex method, steepest descent, Newton’s method, etc. needed to be done manually. Today, the optimization field has gained a lot of popularity due to the advancement of computational methods. One branch of optimization that benefited from this advancement is linear programming.
Linear programming includes the subset of problems where the objective function and constraints are all linear. As a result, typical problems can be solved in a matter of seconds, but some might take days if up-scaled or even weeks to find the optimal solution. Convex optimization, on the other hand, deals with convex sets and convex functions, which is a form of nonlinear functions, hence increasing the complexity. Furthermore, developing heuristics, such as the genetic algorithm, is an intriguing research area aimed at solving non-convex problems via these heuristics. Solving these optimization problems could take advantage of solvers and tools such as CPLEX, SNOPT, CSDP, LINDO, MATLAB, CVX, etc. Since the field of optimization is very broad, it’s easy to get confused about what it actually tackles.
For example, Dr. Sabla Alnouri, a chemical engineering professor, utilizes optimization techniques to understand and assess the performance of various complex chemical arrangements, as well as to design, control, and enhance process system performance. She also formulates and develops optimization problems that ease coordination between different elements in large complex systems.

Another area of research is applied optimization, where Dr. Hussein Tarhini, an industrial engineering professor, worked on several projects across several departments at MSFEA, from finding the best sensor placement on an aircraft surface to designing the most balanced schedule for doctors’ shifts at AUBMC.

Moreover, Dr. Dany Abou Jaoude, a mechanical engineering professor, works on designing numerical techniques to solve complex optimization problems in control theory. Another aspect of his work is control design, specifically robust control, which ensures that the designed controller will satisfy requirements in spite of disturbances.

In the grand scheme of things, the general modelling approach consists of the decision variables, the constraints, and the objective function. The key difference, however, lies in their signification and formulation. In fact, the intersection of different optimization fields is very apparent in the Convex Optimization course (MECH 691), taught by Dr. Dany, where students across multiple engineering disciplines work on various problems, ranging from path planning for robots to avoid collisions all the way to smart grid scheduling.

Despite the widespread interest in optimization, there are still challenges facing it. When modelling a problem, it is essential to preserve its conditions by adding enough information, while also preventing it from getting too complex to solve. Hence, there lies a trade-off between computational time and accuracy. Furthermore, as emphasized by renowned convex optimization expert Stephen Boyd, properly defining a problem is extremely important. The objective function to be minimized/maximized must be accurately modelled, as well as its constraints. Referring to the smart grid example, one must determine whether to minimize cost, non-renewable energy consumption, or a predetermined weighted combination of both.

The professors across the 3 MSFEA departments believe that optimization is a necessary tool in tackling any engineering problem and recommend that optimization courses be integrated as part of all engineering curricula. Therefore, these skills can help the MSFEA curricula in equipping students with effective decision-making skills. With the increasing complexity of modern problems, the continuous advances in scientific computing, both in hardware and software fields, is crucial in the quest to develop new optimization algorithms and extend the application of optimization techniques to problems that were once deemed to be unsolvable.

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