Solving interval multi-objective optimization problems using evolutionary algorithms with preference polyhedron

Abstract

Multi-objective optimization (MOO) problems with interval parameters are popular and important in real-world applications. Previous evolutionary optimization methods aim to find a set of well-converged and evenly-distributed Pareto-optimal solutions. We present a novel evolutionary algorithm (EA) that interacts with a decision maker (DM) during the optimization process to obtain the DMÊs most preferred solution. First, the theory of a preference polyhedron for an optimization problem with interval parameters is built up. Then, an interactive evolutionary algorithm (IEA) for MOO problems with interval parameters based on the above preference polyhedron is developed. The algorithm periodically provides a part of non-dominated solutions to the DM, and a preference polyhedron, based on which optimal solutions are ranked, is constructed with the worst solution chosen by the DM as the vertex. Finally, our method is tested on two biobjective optimization problems with interval parameters using two different value function types to emulate the DMÊs responses. The experimental results show its simplicity and superiority to the posteriori method.

Robot path planning in an environment with many terrains based on interval multi-objective PSO

“…It can be seen from TABLE II that, (1) for the path length, the experimental result is 62.42m, slightly longer than the simulation result(58.57m), the reason is that the change of terrains makes the path increase in the turn corner and the terrain border; another reason is that the robot cannot move in the straight line; (2) for the danger degree, the experimental result is 0.3992, a bit smaller than the simulation result(0.4039), because there is some deviation between the actual moving trajectory and the planned path; (3) for passing time, the experimental result is 72.64s, in the range of [50. 18,79.27](s). The above simulation and experimental results suggest that using the proposed method, the robot can reach to the end point from the starting point with small passing time, low danger degree and short path length, which verifies the effectiveness of the proposed method.…”

“…Aiming at the multi-objective optimization problem, we can gain the Pareto domination relationship between optimal solutions, for more details, please refer to [18].…”

A Similarity-Based Cooperative Co-Evolutionary Algorithm for Dynamic Interval Multiobjective Optimization Problems

“…Using them, we selected the optimal solutions to an interval MOP. Sun et al presented an interval Pareto dominance relation based on the lower limit of a possibility, and employed it to modify NSGA-II to cope with interval MOPs [36]. Zhang et al evaluated solutions using a probability dominance relation [37].…”

Solving Multi-Objective Matrix Games with Fuzzy Payoffs through the Lower Limit of the Possibility Degree

“…Inspired by [3,4], Aggarwal et al [29] applied the notions of POSS and security levels of apiece players to research the multicriteria matrix game in terms of fuzzy goals and demonstrated that this game problem and fuzzy multiple objective linear optimization problems are of equal value. Taking elicitation from [29,33,34], we can take inspiration and put forward a new model of the multiple objective matrix game based on fuzzy payoffs according to the lower limit− 1 2 of the possibility degree.…”