This paper studies linear programming (LP) relaxations for solving polynomial programming problems. A polynomial programming problem can be equivalently formulated as a quadratically constrained quadratic program (QCQP) by introducing new variables that represent nonlinear monomials and substituting them within the original formulation. Whereas Reformulation-Linearization Technique (RLT)-based LP relaxations constructed for the original formulation are tight, the relaxations generated using the equivalent lower degree formulations are smaller and require less computational effort to optimize in comparison to the effort the former requires.
In this study, we analyze the strength and tractability of the standard RLT, the J-set, and recursive McCormick relaxations for polynomial programming problems, and identify the superior relaxation depending on the problem characteristics. Extensive computational results are provided to demonstrate the relative effectiveness of the standard RLT, J-set, and recursive McCormick algorithms using problems from the literature and randomly generated test instances.

Artificial intelligence (AI) is proving to be an efficient alternative approach to classical modeling techniques. AI refers to the branch of computer science that develops machines and software with human-like intelligence. Compared to traditional methods, AI offers advantages to deal with problems associated with uncertainties and is an effective aid to solve such complex problems. In addition, AI-based solutions are good alternatives to determine engineering design parameters when testing is not possible, thus resulting in significant savings in terms of human time and effort spent in experiments. AI is also able to make the process of decision making faster, decrease error rates, and increase computational efficiency. Among the different AI techniques, machine learning (ML), pattern recognition (PR), and deep learning (DL) have recently acquired considerable attention and are establishing themselves as a new class of intelligent methods for use in structural engineering. The objective of this review paper is to summarize techniques concerning applications of the noted AI methods in structural engineering developed over the last decade. First, a general introduction to AI is presented and the importance of AI in structural engineering is described. Thereafter, a review of recent applications of ML, PR, and DL in the field is provided, and the capability of such methods to address the restrictions of conventional models are discussed. Further, the advantages of employing such algorithmic methods are discussed in detail. Finally, potential research avenues and emerging trends for employing ML, PR, and DL are presented, and their limitations are discussed.