This paper presents a new procedure to solve multiobjective problems, where the objectives are distributed to various working groups and the decision process is centralized. The approach is interactive and considers the preferences of the working groups. It is based on two techniques: an interactive technique that solves multi-objective problems based on goal programming, and a technique called “linear physical programming” which considers the preferences of the working groups. The approach generates Pareto-optimal solutions. It guides the director in the determination of target values for the objective functions. The approach was tested on two problems that present its capacity to generate Pareto-optimal solutions and to show the convergence to compromise solutions for all the working groups. 1. Introduction The process of product design is often organized in a hierarchical structure where the specialists are separated by discipline in several working groups. As shown in Figure 1, the working groups are supervised by a director who coordinates the design activities. The role of the director is to collect information provided by the groups and to use computational method to finding an optimal design. The working groups are considered as experts that have the technical knowledge in their proper discipline. Figure 1: Organizational structure in product design. According to their competencies, each working group is responsible of achieving specific design objectives expressing the customer’s requirements. Often these objectives are functions of the same set of design variables and in certain cases, they may be conflicting. For that reason, it is necessary to find an optimization procedure that takes into consideration that knowledge and includes it in the solution. In this paper, we develop a new Interactive Multiobjective approach taking into account the working group’s Preferences (IMOP). The original contributions of the IMOP algorithm are the as follows.(i)It has the ability to define a reduced set of target values that can be divided into degrees of desirability to capture the working groups’ preferences. This is an important contribution because it is a challenging issue in multi-objective optimization.(ii)It generates Pareto-optimal solutions corresponding to the working groups’ preferences.(iii)It subtracts the stability set from the reduced set of target values at each iteration, thus ensuring a different Pareto-optimal solution each time. The proposed approach is particularly interesting when the decision process is centralized and involves many
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