Generalized multiobjective evolutionary algorithm guided by descent directions

This paper proposes a generalized descent directions-guided multiobjective algorithm (DDMOA2). DDMOA2 uses the scalarizing fitness assignment in its parent and environmental selection procedures. The population consists of leader and non-leader individuals. Each individual in the population is represented by a tuple containing its genotype as well as the set of strategy parameters. The main novelty and the primary strength of our algorithm is its reproduction operator, which combines the traditional local search and stochastic search techniques. To improve efficiency, when the number of objective is increased, descent directions are found only for two randomly chosen objectives. Furthermore, in order to increase the search pressure in high-dimensional objective space, we impose an additional condition for the acceptance of descent directions found for leaders during local search. The performance of the proposed approach is compared with those produced by representative state-of-the-art multiobjective evolutionary algorithms on a set of problems with up to 8 objectives. The experimental results reveal that our algorithm is able to produce highly competitive results with well-established multiobjective optimizers on all tested problems.Moreover, due to its hybrid reproduction operator, DDMOA2 demonstrates superior performance on multimodal problems.This work has been supported by FCT Fundação para a Ciência e Tecnologia in the scope of the project: PEst-OE/EEI/UI0319/2014

Multiobjective evolutionary algorithm based on vector angle neighborhood

Selection is a major driving force behind evolution and is a key feature of multiobjective evolutionary algorithms. Selection aims at promoting the survival and reproduction of individuals that are most fitted to a given environment. In the presence of multiple objectives, major challenges faced by this operator come from the need to address both the population convergence and diversity, which are conflicting to a certain extent. This paper proposes a new selection scheme for evolutionary multiobjective optimization. Its distinctive feature is a similarity measure for estimating the population diversity, which is based on the angle between the objective vectors. The smaller the angle, the more similar individuals. The concept of similarity is exploited during the mating by defining the neighborhood and the replacement by determining the most crowded region where the worst individual is identified. The latter is performed on the basis of a convergence measure that plays a major role in guiding the population towards the Pareto optimal front. The proposed algorithm is intended to exploit strengths of decomposition-based approaches in promoting diversity among the population while reducing the user's burden of specifying weight vectors before the search. The proposed approach is validated by computational experiments with state-of-the-art algorithms on problems with different characteristics. The obtained results indicate a highly competitive performance of the proposed approach. Significant advantages are revealed when dealing with problems posing substantial difficulties in keeping diversity, including many-objective problems. The relevance of the suggested similarity and convergence measures are shown. The validity of the approach is also demonstrated on engineering problems.This work was supported by the Portuguese Fundacao para a Ciencia e Tecnologia under grant PEst-C/CTM/LA0025/2013 (Projecto Estrategico - LA 25 - 2013-2014 - Strategic Project - LA 25 - 2013-2014).info:eu-repo/semantics/publishedVersio

A Pareto-metaheuristic for a bi-objective winner determination problem in a combinatorial reverse auction

The bi-objective winner determination problem (2WDP-SC) of a combinatorial procurement auction for transport contracts comes up to a multi-criteria set covering problem. We are given a set B of bundle bids. A bundle bid b in B consists of a bidding carrier c_b, a bid price p_b, and a set tau_b of transport contracts which is a subset of the set T of tendered transport contracts. Additionally, the transport quality q_t,c_b is given which is expected to be realized when a transport contract t is executed by a carrier c_b. The task of the auctioneer is to find a set X of winning bids (X is subset of B), such that each transport contract is part of at least one winning bid, the total procurement costs are minimized, and the total transport quality is maximized. This article presents a metaheuristic approach for the 2WDP-SC which integrates the greedy randomized adaptive search procedure, large neighborhood search, and self-adaptive parameter setting in order to find a competitive set of non-dominated solutions. The procedure outperforms existing heuristics. Computational experiments performed on a set of benchmark instances show that, for small instances, the presented procedure is the sole approach that succeeds to find all Pareto-optimal solutions. For each of the large benchmark instances, according to common multi-criteria quality indicators of the literature, it attains new best-known solution sets.Pareto optimization; multi-criteria winner determination; combinatorial auction; GRASP; LNS

Computing the set of Epsilon-efficient solutions in multiobjective space mission design

In this work, we consider multiobjective space mission design problems. We will start from the need, from a practical point of view, to consider in addition to the (Pareto) optimal solutions also nearly optimal ones. In fact, extending the set of solutions for a given mission to those nearly optimal significantly increases the number of options for the decision maker and gives a measure of the size of the launch windows corresponding to each optimal solution, i.e., a measure of its robustness. Whereas the possible loss of such approximate solutions compared to optimal—and possibly even ‘better’—ones is dispensable. For this, we will examine several typical problems in space trajectory design—a biimpulsive transfer from the Earth to the asteroid Apophis and two low-thrust multigravity assist transfers—and demonstrate the possible benefit of the novel approach. Further, we will present a multiobjective evolutionary algorithm which is designed for this purpose

Interval-based ranking in noisy evolutionary multiobjective optimization

As one of the most competitive approaches to multi-objective optimization, evolutionary algorithms have been shown to obtain very good results for many realworld multi-objective problems. One of the issues that can affect the performance of these algorithms is the uncertainty in the quality of the solutions which is usually represented with the noise in the objective values. Therefore, handling noisy objectives in evolutionary multi-objective optimization algorithms becomes very important and is gaining more attention in recent years. In this paper we present ?-degree Pareto dominance relation for ordering the solutions in multi-objective optimization when the values of the objective functions are given as intervals. Based on this dominance relation, we propose an adaptation of the non-dominated sorting algorithm for ranking the solutions. This ranking method is then used in a standardmulti-objective evolutionary algorithm and a recently proposed novel multi-objective estimation of distribution algorithm based on joint variable-objective probabilistic modeling, and applied to a set of multi-objective problems with different levels of independent noise. The experimental results show that the use of the proposed method for solution ranking allows to approximate Pareto sets which are considerably better than those obtained when using the dominance probability-based ranking method, which is one of the main methods for noise handling in multi-objective optimization

Rotationally invariant techniques for handling parameter interactions in evolutionary multi-objective optimization

In traditional optimization approaches the interaction of parameters associated with a problem is not a significant issue, but in the domain of Evolutionary Multi-Objective Optimization (EMOO) traditional genetic algorithm approaches have difficulties in optimizing problems with parameter interactions. Parameter interactions can be introduced when the search space is rotated. Genetic algorithms are referred to as being not rotationally invariant because their behavior changes depending on the orientation of the search space. Many empirical studies in single and multi-objective evolutionary optimization are done with respect to test problems which do not have parameter interactions. Such studies provide a favorably biased indication of genetic algorithm performance. This motivates the first aspect of our work; the improvement of the testing of EMOO algorithms with respect to the aforementioned difficulties that genetic algorithms experience in the presence of parameter interactions. To this end, we examine how EMOO algorithms can be assessed when problems are subject to an arbitrarily uniform degree of parameter interactions. We establish a theoretical basis for parameter interactions and how they can be measured. Furthermore, we ask the question of what difficulties a multi-objective genetic algorithm experiences on optimization problems exhibiting parameter interactions. We also ask how these difficulties can be overcome in order to efficiently find the Pareto-optimal front on such problems. Existing multi-objective test problems in the literature typically introduce parameter interactions by altering the fitness landscape, which is undesirable. We propose a new suite of test problems that exhibit parameter interactions through a rotation of the decision space, without altering the fitness landscape. In addition, we compare the performance of a number of recombination operators on these test problems. The second aspect of this work is concerned with developing an efficient multi-objective optimization algorithm which works well on problems with parameter interactions. We investigate how an evolutionary algorithm can be made more efficient on multi-objective problems with parameter interactions by developing four novel rotationally invariant differential evolution approaches. We also ask whether the proposed approaches are competitive in comparison with a state-of-the-art EMOO algorithm. We propose several differential evolution approaches incorporating directional information from the multi-objective search space in order to accelerate and direct the search. Experimental results indicate that dramatic improvements in efficiency can be achieved by directing the search towards points which are more dominant and more diverse. We also address the important issue of diversity loss in rotationally invariant vector-wise differential evolution. Being able to generate diverse solutions is critically important in order to avoid stagnation. In order to address this issue, one of the directed approaches that we examine incorporates a novel sampling scheme around better individuals in the search space. This variant is able to perform exceptionally well on the test problems with much less computational cost and scales to very high decision space dimensions even in the presence of parameter interactions