GAMBIT - Genetic Algorithm for Model-Based mixed-Integer opTimization

Abstract

Key to defining effective and efficient optimization algorithms is exploiting problem structure and other problem-specific information. Sometimes, such problem-specific knowledge is well-defined and known a-priori. This is referred to as white-box optimization. While a white-box setting approach can be very efficient, algorithms exploiting problem-specific information are very often highly-tailored to deal with only the problem at hand making it difficult to generalize them to other problems. Additionally, problem information may be unknown, incomplete, or incomprehensible prior to optimization. This is referred to as the black-box setting. In order to exploit the structure of problems in a black-box setting, this information needs to be extracted, learned and processed during execution. While more challenging, approaching a problem in the black-box setting allows for the creation of more generic methodologies that can be applied to variety of problems and does not require the understanding or specification of the problem structure a-priori. Such problems are common in many real-world settings, making black-box algorithms potentially very powerful and desirable.

In this thesis, we design a methodology for solving mixed-integer problems in the black-box setting. In order to accomplish this, we take an in-depth look at some existing algorithmic solutions and consider their applicability to the mixed integer domain. We specifically turn to the field of model-based Evolutionary Algorithms (EAs). EAs are optimization algorithms that are loosely based on general concepts of natural evolution. These algorithms, pertaining to the research field known as evolutionary computation, iteratively generate better solutions to a problem through interleaving the selection of better solutions and creating variations of solutions that are maintained in a population. Competent EAs exist in both, discrete and continuous optimization domains, achieve efficient and scalable results on many well-known benchmark problems. In this thesis we aim to see if the abilities of such EAs in their individual fields can be retained when expanding the scope to mixed-integer optimization.

Furthermore, much optimization literature focuses on solving a single, potentially constrained, objective. This often does not represent problems in the real world, where multiple objectives are often present that need to be optimized simultaneously. In many such cases, different objectives may directly oppose each other, introducing an additional layer of difficulty. As EAs are well-suited for multi-objective optimization in a black-box setting, this further motivates our decision to study them in our work.