Dynamic Objectives Aggregation in Multi-objective Evolutionary Optimization

Several approaches for solving multi-objective optimization problems entail a form of scalarization of the objectives. This paper proposes a study of different dynamic objectives aggregation methods in the context of evolutionary algorithms. These methods are mainly based on both weighted sum aggregations and curvature variations. A comparison analysis is presented on the basis of a campaign of computational experiments on a set of benchmark problems from the literature.Multi-objective optimization, Evolutionary algorithms, Aggregate objective functions

Local search based evolutionary multi-objective optimization algorithm for constrained and unconstrained problems

Evolutionary multi-objective optimization algorithms are commonly used to obtain a set of non-dominated solutions for over a decade. Recently, a lot of emphasis have been laid on hybridizing evolutionary algorithms with MCDM and mathematical programming algorithms to yield a computationally efficient and convergent procedure. In this paper, we test an augmented local search based EMO procedure rigorously on a test suite of constrained and unconstrained multi-objective optimization problems. The success of our approach on most of the test problems not only provides confidence but also stresses the importance of hybrid evolutionary algorithms in solving multi-objective optimization problems

Hybridization of multi-objective deterministic particle swarm with derivative-free local searches

The paper presents a multi-objective derivative-free and deterministic global/local hybrid algorithm for the efficient and effective solution of simulation-based design optimization (SBDO) problems. The objective is to show how the hybridization of two multi-objective derivative-free global and local algorithms achieves better performance than the separate use of the two algorithms in solving specific SBDO problems for hull-form design. The proposed method belongs to the class of memetic algorithms, where the global exploration capability of multi-objective deterministic particle swarm optimization is enriched by exploiting the local search accuracy of a derivative-free multi-objective line-search method. To the authors best knowledge, studies are still limited on memetic, multi-objective, deterministic, derivative-free, and evolutionary algorithms for an effective and efficient solution of SBDO for hull-form design. The proposed formulation manages global and local searches based on the hypervolume metric. The hybridization scheme uses two parameters to control the local search activation and the number of function calls used by the local algorithm. The most promising values of these parameters were identified using forty analytical tests representative of the SBDO problem of interest. The resulting hybrid algorithm was finally applied to two SBDO problems for hull-form design. For both analytical tests and SBDO problems, the hybrid method achieves better performance than its global and local counterparts

Process Knowledge-guided Autonomous Evolutionary Optimization for Constrained Multiobjective Problems

Various real-world problems can be attributed to constrained multi-objective optimization problems. Although there are various solution methods, it is still very challenging to automatically select efficient solving strategies for constrained multi-objective optimization problems. Given this, a process knowledge-guided constrained multi-objective autonomous evolutionary optimization method is proposed. Firstly, the effects of different solving strategies on population states are evaluated in the early evolutionary stage. Then, the mapping model of population states and solving strategies is established. Finally, the model recommends subsequent solving strategies based on the current population state. This method can be embedded into existing evolutionary algorithms, which can improve their performances to different degrees. The proposed method is applied to 41 benchmarks and 30 dispatch optimization problems of the integrated coal mine energy system. Experimental results verify the effectiveness and superiority of the proposed method in solving constrained multi-objective optimization problems.The National Key R&D Program of China, the National Natural Science Foundation of China, Shandong Provincial Natural Science Foundation, Fundamental Research Funds for the Central Universities and the Open Research Project of The Hubei Key Laboratory of Intelligent Geo-Information Processing.http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4235hj2023Electrical, Electronic and Computer Engineerin

Phylogenetic inference's algorithms

Phylogenetic inference consist in the search of an evolutionary tree to explain the best way possible genealogical relationships of a set of species. Phylogenetic analysis has a large number of applications in areas such as biology, ecology, paleontology, etc. There are several criterias which has been defined in order to infer phylogenies, among which are the maximum parsimony and maximum likelihood. The first one tries to find the phylogenetic tree that minimizes the number of evolutionary steps needed to describe the evolutionary history among species, while the second tries to find the tree that has the highest probability of produce the observed data according to an evolutionary model. The search of a phylogenetic tree can be formulated as a multi-objective optimization problem, which aims to find trees which satisfy simultaneously (and as much as possible) both criteria of parsimony and likelihood. Due to the fact that these criteria are different there won't be a single optimal solution (a single tree), but a set of compromise solutions. The solutions of this set are called "Pareto Optimal". To find this solutions, evolutionary algorithms are being used with success nowadays.This algorithms are a family of techniques, which aren’t exact, inspired by the process of natural selection. They usually find great quality solutions in order to resolve convoluted optimization problems. The way this algorithms works is based on the handling of a set of trial solutions (trees in the phylogeny case) using operators, some of them exchanges information between solutions, simulating DNA crossing, and others apply aleatory modifications, simulating a mutation. The result of this algorithms is an approximation to the set of the “Pareto Optimal” which can be shown in a graph with in order that the expert in the problem (the biologist when we talk about inference) can choose the solution of the commitment which produces the higher interest. In the case of optimization multi-objective applied to phylogenetic inference, there is open source software tool, called MO-Phylogenetics, which is designed for the purpose of resolving inference problems with classic evolutionary algorithms and last generation algorithms. REFERENCES [1] C.A. Coello Coello, G.B. Lamont, D.A. van Veldhuizen. Evolutionary algorithms for solving multi-objective problems. Spring. Agosto 2007 [2] C. Zambrano-Vega, A.J. Nebro, J.F Aldana-Montes. MO-Phylogenetics: a phylogenetic inference software tool with multi-objective evolutionary metaheuristics. Methods in Ecology and Evolution. En prensa. Febrero 2016

A Tutorial on Evolutionary Multi-Objective Optimization (EMO)

Many real-world search and optimization problems are naturally posed as non-linear programming problems having multiple objectives. Due to lack of suitable solution techniques, such problems are artificially converted into a single-objective problem and solved. The difficulty arises because such problems give rise to a set of Pareto-optimal solutions, instead of a single optimum solution. It then becomes important to find not just one Pareto-optimal solution but as many of them as possible. Classical methods are not quite efficient in solving these problems because they require repetitive applications to find multiple Pareto-optimal solutions and in some occasions repetitive applications do not guarantee finding distinct Pareto-optimal solutions. The population approach of evolutionary algorithms (EAs) allows an efficient way to find multiple Pareto-optimal solutions simultaneously in a single simulation run. In this tutorial, we discussed the following aspects related to EMO: 1. The basic differences in principle of EMO with classical methods. 2. A gentle introduction to evolutionary algorithms with simple examples. A simple method of handling constraints was also discussed. 3. The concept of domination and methods of finding non-dominated solutions in a population of solutions were discussed. 4. A brief history of the development of EMO is highlighted. 5. A number of main EMO methods (NSGA-II, SPEA and PAES) were discussed. 6. The advantage of EMO methodologies was discussed by presenting a number of case studies. They clearly showed the advantage of finding a number of Pareto-optimal solutions simultaneously. 7. Three advantages of using an EMO methodology were stressed: (i) For a better decision making (in terms of choosing a compromised solution) in the presence of multiple solutions (ii) For finding important relationships among decision variables (useful in design optimization). Some case studies from engineering demonstrated the importance of such studies. (iii) For solving other optimization problems efficiently. For example, in solving genetic programming problems, the so-called `bloating problem of increased program size can be solved by using a second objective of minimizing the size of the programs. 8. A number of salient research topics were highlighted. Some of them are as follows: (i) Development of scalable test problems (ii) Development of computationally fast EMO methods (iii) Performance metrics for evaluating EMO methods (iv) Interactive EMO methodologies (v) Robust multi-objective optimization procedures (vi) Finding knee or other important solutions including partial Pareto-optimal set (vii) Multi-objective scheduling and other optimization problems. It was clear from the discussions that evolutionary search methods offers an alternate means of solving multi-objective optimization problems compared to classical approaches. This is why multi-objective optimization using EAs is getting a growing attention in the recent years. The motivated readers may explore current research issues and other important studies from various texts (Coello et al, 2003; Deb, 2001), conference proceedings (EMO-01 and EMO-03 Proceedings) and numerous research papers (http://www.lania.mx/~ccoello/EMOO/). References: ---------- C. A. C. Coello, D. A. VanVeldhuizen, and G. Lamont. Evolutionary Algorithms for Solving Multi-Objective Problems. Boston, MA: Kluwer Academic Publishers, 2002. K.Deb. Multi-objective optimization using evolutionary algorithms. Chichester, UK: Wiley, 2001. C. Fonseca, P. Fleming, E. Zitzler, K. Deb, and L. Thiele, editors. Proceedings of the Second Evolutionary Multi-Criterion Optimization (EMO-03) Conference (Lecture Notes in Computer Science (LNCS) 2632). Heidelberg: Springer, 2003. E. Zitzler, K. Deb, L. Thiele, C. A. C. Coello, and D. Corne, editors. Proceedings of the First Evolutionary Multi-Criterion Optimization (EMO-01) Conference (Lecture Notes in Computer Science (LNCS) 1993). Heidelberg: Springer, 2001

Impact analysis of crossovers in a multi-objective evolutionary algorithm

Multi-objective optimization has become mainstream because several real-world problems are naturally posed as a Multi-objective optimization problems (MOPs) in all fields of engineering and science. Usually MOPs consist of more than two conflicting objective functions and that demand trade-off solutions. Multi-objective evolutionary algorithms (MOEAs) are extremely useful and well-suited for solving MOPs due to population based nature. MOEAs evolve its population of solutions in a natural way and searched for compromise solutions in single simulation run unlike traditional methods. These algorithms make use of various intrinsic search operators in efficient manners. In this paper, we experimentally study the impact of different multiple crossovers in multi-objective evolutionary algorithm based on decomposition (MOEA/D) framework and evaluate its performance over test instances of 2009 IEEE congress on evolutionary computation (CEC?09) developed for MOEAs competition. Based on our carried out experiment, we observe that used variation operators are considered to main source to improve the algorithmic performance of MOEA/D for dealing with CEC?09 complicated test problems

DECMO2: a robust hybrid and adaptive multi-objective evolutionary algorithm.

We describe a hybrid and adaptive coevolutionary optimization method that can efficiently solve a wide range of multi-objective optimization problems (MOOPs) as it successfully combines positive traits from three main classes of multi-objective evolutionary algorithms (MOEAs): classical approaches that use Pareto-based selection for survival criteria, approaches that rely on differential evolution, and decomposition-based strategies. A key part of our hybrid evolutionary approach lies in the proposed fitness sharing mechanism that is able to smoothly transfer information between the coevolved subpopulations without negatively impacting the specific evolutionary process behavior that characterizes each subpopulation. The proposed MOEA also features an adaptive allocation of fitness evaluations between the coevolved populations to increase robustness and favor the evolutionary search strategy that proves more successful for solving the MOOP at hand. Apart from the new evolutionary algorithm, this paper also contains the description of a new hypervolume and racing-based methodology aimed at providing practitioners from the field of multi-objective optimization with a simple means of analyzing/reporting the general comparative run-time performance of multi-objective optimization algorithms over large problem sets