another, so that it is not possible to improve on any of the objective functions without deteriorating at least one of the other objective functions. This is known as the concept of Pareto optimality (Rao, 1991). In multiobjective optimization, as opposed to single-objective optimization, there may not exist an unambigous optimal solution (global minimum or global maximum). Characteristic of th...

Operations research applications often pose multicriteria problems. Mathematical research on multicriteria problems predominantly revolves around the set of Pareto optimal solutions, while in practice, methods that output a single solution are more widespread. In real-world multicriteria optimization, reference point methods are widely used and successful examples of such methods. A reference p...

When solving multiobjective optimization problems, there is typically a decision maker (DM) who is responsible for determining the most preferred Pareto optimal solution based on his preferences. To gain confidence that the decisions to be made are the right ones for the DM, it is important to understand the trade-offs related to different Pareto optimal solutions. We first propose a trade-off ...

1 Abstract Multi-objective optimization addresses problems with several design objectives, which are often conflicting, placing different demands on the design variables. In contradiction to traditional optimization methods, which combine all objectives into a single figure of merit, parallel optimization strategies such as evolutionary algorithms allow direct convergence to the Pareto front. T...

We obtain sufficient and/or necessary conditions for global/local error bounds for the distances to some sets appeared in set optimization studied with both the set approach and vector approach (sublevel sets, constraint sets, sets of all Pareto efficient/ Henig proper efficient/super efficient solutions, sets of solutions corresponding to one Pareto efficient/Henig proper efficient/super effic...

We consider Multi Criteria Decision Making (MCDM) as the conjunction of three components: search, preference tradeoffs, and interactive visualization. The first MCDM component is the search process over the space of possible solutions to identify the nondominated solutions that compose the Pareto set. The second component is the preference tradeoff process to select a single solution (or a smal...

Many robotic tasks require solutions that maximize multiple performance objectives. For example, in path-planning, these objectives often include finding short paths that avoid risk and maximize the information obtained by the robot. Although there exist many algorithms for multi-objective optimization, few of these algorithms apply directly to robotic path-planning and fewer still are capable ...

This paper presents a multi-objective differential evolution algorithm, called MODE, to search for a set of non-dominated solutions on the Pareto front. During the iterative search process, the non-dominated solutions found are stored as the ‘Elite group’ of solutions. The study focuses on utilising the solutions in the Elite group to guide the movement of the search. Several potential mutation...

In this paper we study the Pareto-optimal solutions in convex multi-objective optimization with compact and convex feasible domain. One of the most important problems in multi-objective optimization is the investigation of the topological structure of the Pareto sets. We present the problem of construction of a retraction function of the feasible domain onto Paretooptimal set, if the objective ...

When we try to implement a multi-objective genetic algorithm (MOGA) with variable weights for finding a set of Pareto optimal solutions, one difficulty lies in determining appropriate search directions for genetic search. In our MOGA, a weight value for each objective in a scalar fitness function was randomly specified. Based on the fitness function with the randomly specified weight values, a ...