Antonio J. Nebro

jMetal: A Java framework for multi-objective optimization

This paper describes jMetal, an object-oriented Java-based framework aimed at the development, experimentation, and study of metaheuristics for solving multi-objective optimization problems. jMetal includes a number of classic and modern state-of-the-art optimizers, a wide set of benchmark problems, and a set of well-known quality indicators to assess the performance of the algorithms. The framework also provides support to carry out full experimental studies, which can be configured and executed by using jMetals graphical interface. Other features include the automatic generation of statistical information of the obtained results, and taking advantage of the current availability of multi-core processors to speed-up the running time of the experiments. In this work, we include two case studies to illustrate the use of jMetal in both solving a problem with a metaheuristic and designing and performing an experimental study.

SMPSO: A new PSO-based metaheuristic for multi-objective optimization

In this work, we present a new multi-objective particle swarm optimization algorithm (PSO) characterized by the use of a strategy to limit the velocity of the particles. The proposed approach, called Speed-constrained Multi-objective PSO (SMPSO) allows to produce new effective particle positions in those cases in which the velocity becomes too high. Other features of SMPSO include the use of polynomial mutation as a turbulence factor and an external archive to store the non-dominated solutions found during the search. Our proposed approach is compared with respect to five multi-objective metaheuristics representative of the state-of-the-art in the area. For the comparison, two different criteria are adopted: the quality of the resulting approximation sets and the convergence speed to the Pareto front. The experiments carried out indicate that SMPSO obtains remarkable results in terms of both, accuracy and speed.

AbYSS: Adapting Scatter Search to Multiobjective Optimization

We propose the use of a new algorithm to solve multiobjective optimization problems. Our proposal adapts the well-known scatter search template for single-objective optimization to the multiobjective domain. The result is a hybrid metaheuristic algorithm called Archive-Based hYbrid Scatter Search (AbYSS), which follows the scatter search structure but uses mutation and crossover operators from evolutionary algorithms. AbYSS incorporates typical concepts from the multiobjective field, such as Pareto dominance, density estimation, and an external archive to store the nondominated solutions. We evaluate AbYSS with a standard benchmark including both unconstrained and constrained problems, and it is compared with two state-of-the-art multiobjective optimizers, NSGA-II and SPEA2. The results obtained indicate that, according to the benchmark and parameter settings used, AbYSS outperforms the other two algorithms as regards the diversity of the solutions, and it obtains very competitive results according to the convergence to the true Pareto fronts and the hypervolume metric.

The jMetal framework for multi-objective optimization: Design and architecture

jMetal is a Java-based framework for multi-objective optimization using metaheuristics. It is a flexible, extensible, and easy-to-use software package that has been used in a wide range of applications. In this paper, we describe the design issues underlying jMetal, focusing mainly on its internal architecture, with the aim of offering a comprehensive view of its main features to interested researchers. Among the covered topics, we detail the basic components facilitating the implementation of multi-objective metaheuristics (solution representations, operators, problems, density estimators, archives), the included quality indicators to assess the performance of the algorithms, and jMetals support to carry out full experimental studies.

Multi-Objective Particle Swarm Optimizers: An Experimental Comparison

Particle Swarm Optimization (PSO) has received increasing attention in the optimization research community since its first appearance in the mid-1990s. Regarding multi-objective optimization, a considerable number of algorithms based on Multi-Objective Particle Swarm Optimizers (MOPSOs) can be found in the specialized literature. Unfortunately, no experimental comparisons have been made in order to clarify which MOPSO version shows the best performance. In this paper, we use a benchmark composed of three well-known problem families (ZDT, DTLZ, and WFG) with the aim of analyzing the search capabilities of six representative state-of-the-art MOPSOs, namely, NSPSO, SigmaMOPSO, OMOPSO, AMOPSO, MOPSOpd, and CLMOPSO. We additionally propose a new MOPSO algorithm, called SMPSO, characterized by including a velocity constraint mechanism, obtaining promising results where the rest perform inadequately.

Heterogeneous computing and parallel genetic algorithms

This paper analyzes some technical and practical issues concerning the heterogeneous execution of parallel genetic algorithms (PGAs). In order to cope with a plethora of different operating systems, security restrictions, and other problems associated to multi-platform execution, we use Java to implement a distributed PGA model. The distributed PGA runs at the same time on different machines linked by different kinds of communication networks. This algorithm benefits from the computational resources offered by modern LANs and by Internet, therefore allowing researchers to solve more difficult problems by using a large set of available machines. We analyze the way in which such heterogeneous systems affect the genetic search for two problems. Our conclusion is that super-linear performance can be achieved not only in homogeneous but also in heterogeneous clusters of machines. In addition, we study some special features of the running platforms for PGAs, and basically find out that heterogeneous computing can be as efficient or even more efficient than homogeneous computing for parallel heuristics.

A cellular multi-objective genetic algorithm for optimal broadcasting strategy in metropolitan MANETs

Mobile Ad Hoc Networks (MANETs) are composed of a set of communicating devices which are able to spontaneously interconnect without any pre-existing infrastructure. In such kind of networks, broadcasting becomes an operation of capital importance for the own existence and operation of the network. Optimizing a broadcasting strategy in MANETs is a multi-objective problem targeting three goals: reaching as many devices as possible, minimizing the network utilization, and reducing the duration time of the broadcasting process. In this paper, we study the fine-tuning of broadcasting strategies by using a cellular multi-objective genetic algorithm (cMOGA) which computes a Pareto front of solutions to empower a human designer with the ability of choosing the preferred configuration for the network. We define two formulations of the problem, one with three objectives and another one with two objectives plus a constraint. For our tests, a benchmark of three realistic environments for metropolitan MANETs has been defined. Our experiments using a complex and realistic MANET simulator reveal that cMOGA is a promising approach to solve the optimum broadcasting problem.

A Study of Multiobjective Metaheuristics When Solving Parameter Scalable Problems

To evaluate the search capabilities of a multiobjective algorithm, the usual approach is to choose a benchmark of known problems, to perform a fixed number of function evaluations, and to apply a set of quality indicators. However, while real problems could have hundreds or even thousands of decision variables, current benchmarks are normally adopted with relatively few decision variables (normally from 10 to 30). Furthermore, performing a constant number of evaluations does not provide information about the effort required by an algorithm to get a satisfactory set of solutions; this information would also be of interest in real scenarios, where evaluating the functions defining the problem can be computationally expensive. In this paper, we study the effect of parameter scalability in a number of state-of-the-art multiobjective metaheuristics. We adopt a benchmark of parameter-wise scalable problems (the Zitzler-Deb-Thiele test suite) and analyze the behavior of eight multiobjective metaheuristics on these test problems when using a number of decision variables that range from 8 up to 2048. By using the hypervolume indicator as a stopping condition, we also analyze the computational effort required by each algorithm in order to reach the Pareto front. We conclude that the two analyzed algorithms based on particle swarm optimization and differential evolution yield the best overall results.

Design issues in a multiobjective cellular genetic algorithm

In this paper we study a number of issues related to the design of a cellular genetic algorithm (cGA) for multiobjective optimization. We take as an starting point an algorithm following the canonical cGA model, i.e., each individual interacts with those ones belonging to its neighborhood, so that a new individual is obtained using the typical selection, crossover, and mutation operators within this neighborhood. An external archive is used to store the non-dominated solutions found during the evolution process. With this basic model in mind, there are many different design issues that can be faced. Among them, we focus here on the synchronous/asynchronous feature of the cGA, the feedback of the search experience contained in the archive into the algorithm, and two different replacement strategies. We evaluate the resulting algorithms using a benchmark of problems and compare the best of them against two state-of-the-art genetic algorithms for multiobjective optimization. The obtained results indicate that the cGA model is a promising approach to solve this kind of problem.

Why Is Optimization Difficult

This chapter aims to address some of the fundamental issues that are often encountered in optimization problems, making them difficult to solve. These issues include premature convergence, ruggedness, causality, deceptiveness, neutrality, epistasis, robustness, overfitting, oversimplification, multi-objectivity, dynamic fitness, the No Free Lunch Theorem, etc. We explain why these issues make optimization problems hard to solve and present some possible countermeasures for dealing with them. By doing this, we hope to help both practitioners and fellow researchers to create more efficient optimization applications and novel algorithms.