Abstract
The Maximum Diversity (MD) problem is the process of selecting a subset of elements where the diversity among selected elements is maximized. Several diversity measures were already studied in the literature, optimizing the problem considered in a pure mono-objective approach. This work presents for the first time multi-objective approaches for the MD problem, considering the simultaneous optimization of the following five diversity measures: (i) Max-Sum, (ii) Max-Min, (iii) Max-MinSum, (iv) Min-Diff and (v) Min-P-center. Two different optimization models are proposed: (i) Multi-Objective Maximum Diversity (MMD) model, where the number of elements to be selected is defined a-priori, and (ii) Multi-Objective Maximum Average Diversity (MMAD) model, where the number of elements to be selected is also a decision variable. To solve the formulated problems, a Multi-Objective Evolutionary Algorithm (MOEA) is presented. Experimental results demonstrate that the proposed MOEA found good quality solutions, i.e. between 98.85% and 100% of the optimal Pareto front when considering the hypervolume for comparison purposes.
Highlights
In multiple contexts, the process of selecting objects, ideas, people, projects or resources is an activity frequently performed by individuals, companies or governments and in many cases it is required that the selected elements have different characteristics, so they can represent diversity
Clearly M2 is better than M1 and it can be seen that M2 dominates M1 (M2 M1) or equivalently, it can be said that M1 is dominated by M2 (22)
This work proposes an efficient Multi-Objective Evolutionary Algorithm (MOEA) inspired in the Non-dominated Sorting Genetic Algorithm II (NSGA-II), which according to the specialized literature, is currently a reference algorithm even used for comparison with new multi-objective methods (24)
Summary
The process of selecting objects, ideas, people, projects or resources is an activity frequently performed by individuals, companies or governments and in many cases it is required that the selected elements have different characteristics, so they can represent diversity. In the design of new drugs, through the process known as High Throughput Screening, companies have a large library of molecules (in the millions) that they use repeatedly for each new project in order to identify successes, while the selection of a diverse subset would ensure that the cost of this process does not become excessive In this context, Meinl proposed in (8) some diversity measures for this case. In the analysis of a social group, one might be interested in studying its diversity by means of a detailed study of some representative individuals; these selected individuals should have diverse characteristics which must be observed across the whole group, while being the best for the objective of the team Recent studies, such as that of Castillo et al (9), have determined that diversity in a group of people increases the ability of these groups to solve problems, and contributes to obtaining more efficient working groups in companies, schools, government, etc.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
