A Comprehensive Review of Goal Programming Problems and Constraint Handling Approaches

Goal programming (GP) is an important type of multi-criteria decision-making approach, widely used to analyze and solve problems with conflicting objectives. Originally introduced in the 1950s, the popularity and applications of GP have increased immensely due to the mathematical simplicity and modelling elegance. Over the recent decades, algorithmic developments and computational improvements have greatly contributed to the diverse applications and variants of GP models. In this work, a comprehensive review of GP concepts, history, mathematical models, problems, and solution methodologies is presented. Various constraint handling approaches are also reviewed for key features and limitations. Moreover, the GP problems from supply chain management, engineering design, and manufacturing domains are discussed in detail with mathematical formulations. Furthermore, a GP problem of an I beam design is solved with socio-inspired AI-based metaheuristics referred to as Cohort Intelligence algorithm, and solutions are compared with genetic algorithm (GA), simulated annealing (SA), and Monte Carlo simulations. Results show an improvement of 59%, 11%, and 54% for achievement of goals when compared with GA, SA, and Monte Carlo simulations, respectively. At the end of this chapter, the recent trends in GP are also discussed.