Abstract
This paper addresses group multi-objective optimization under a new perspective. For each point in the feasible decision set, satisfaction or dissatisfaction from each group member is determined by a multi-criteria ordinal classification approach, based on comparing solutions with a limiting boundary between classes “unsatisfactory” and “satisfactory”. The whole group satisfaction can be maximized, finding solutions as close as possible to the ideal consensus. The group moderator is in charge of making the final decision, finding the best compromise between the collective satisfaction and dissatisfaction. Imperfect information on values of objective functions, required and available resources, and decision model parameters are handled by using interval numbers. Two different kinds of multi-criteria decision models are considered: (i) an interval outranking approach and (ii) an interval weighted-sum value function. The proposal is more general than other approaches to group multi-objective optimization since (a) some (even all) objective values may be not the same for different DMs; (b) each group member may consider their own set of objective functions and constraints; (c) objective values may be imprecise or uncertain; (d) imperfect information on resources availability and requirements may be handled; (e) each group member may have their own perception about the availability of resources and the requirement of resources per activity. An important application of the new approach is collective multi-objective project portfolio optimization. This is illustrated by solving a real size group many-objective project portfolio optimization problem using evolutionary computation tools.
Highlights
Introduction iationsFrequently, real-life decision problems need several or many decision-makers
The criticisms to group decision-making problem (GDM)-MOP approaches discussed in the introduction have been basically overcome
This paper has presented one of the most comprehensive approaches to group multi-objective optimization under imperfect information
Summary
In the GDM-MOP field, some approaches obtain a representative Pareto sample and apply a method to aggregate individual preferences in a model of collective preference, which is used to find a final solution (e.g., [22,23]). The NEMO-GROUP, a set of interactive evolutionary multi-objective optimization (MOO) methods, was developed by Kadzinski and Tomczyk in [34]. In these approaches, an evolutionary algorithm is modified with the introduction of pairwise comparisons of several DMs. Solutions are evaluated using utilitarian and egalitarian additive group value functions; the evolutionary algorithms accept weights assigned to the DMs. Borissova and Mustakerov in [35] presented a two-step placement algorithm, which combines MOO and GDM. Projects are described by several (or many) conflicting criteria, and the selection of the “best” portfolio should be made by a collective entity This group may be composed of experts in different/complementary fields or members of the top level management. Imperfect information concerning weights and criterion scores has been addressed by Liesio et al in [39,40], Fliedner and Liesio in [41], Toppila and Salo in [42], and Balderas et al in [43] using interval mathematics, no one of these papers concern the specific characteristics of GDM
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