Scatter tabu search for multiobjective clustering problems

Abstract

We propose a hybrid heuristic procedure based on scatter search and tabu search for the problem of clustering objects to optimize multiple criteria. Our goal is to search for good approximations of the efficient frontier for this class of problems and provide a means for improving decision making in multiple application areas. Our procedure can be viewed as an extension of SSPMO (a scatter search application to nonlinear multiobjective optimization) to which we add new elements and strategies specially suited for combinatorial optimization problems. Clustering problems have been the subject of numerous studies; however, most of the work has focused on single-objective problems. Clustering using multiple criteria and/ or multiple data sources has received limited attention in the operational research literature. Our scatter tabu search implementation is general and tackles several problems classes within this area of combinatorial data analysis. We conduct extensive experimentation to show that our method is capable of delivering good approximations of the efficient frontier for improved analysis and decision making.

A Scatter Search Algorithm for Multi-Criteria Inventory Classification considering Multi-Objective Optimization

“…In the GA, he creates new solutions by applying crossover and mutation to two randomly selected solutions from the population. The SSA approach was used for scheduling problems (Fan, Wang, Zhai, & Li, 2019;Riahi, Khorramizadeh, Hakim Newton, & Sattar, 2017), for the uncapacitated facility location problem Hakli and Ortacay (2019), for the economic lot sizing problem (Khojaste Sarakhsi, Fatemi Ghomi, & Karimi, 2016) and for the multiobjective clustering problem (Caballero et al, 2011)). SSA can basically be defined with 5 basic components (Martí, Laguna, & Glover, 2006).…”

Mixed integer linear programming and heuristic methods for feature selection in clustering

“…Moreover, the total number of local assignments (i, k) is exactly q. Constraint (4) establishes that every unit i must be assigned to exactly one cluster k. Constraint (5) imposes that a local assignment (i, k) that uses variable j is feasible only if variable j has been selected. Constraint (6) sets the number of variables to q. Constraint (8) imposes binary values to the x assignment variables, while constraints (7) and (9)can be weakened to require that the variables are continuous (see Theorem 3).…”

“…Other constraints that can be imposed to clustering are discussed in [8]. All the constraints proposed here are linear and can be added to P 1 without increasing its theoretical difficulty.…”

Scatter Search

“…In particular, Caballero et al (2011) tackled partitioning problems for cluster analysis that requires the simultaneous optimization of more than one objective function. They considered two main classes of multiobjective partitioning problems: (1) partitioning of objects using one partitioning criterion but multiple dissimilarity matrices and (2) partitioning of objects using one dissimilarity matrix but more than one partitioning criteria.…”