Juan José Durillo

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.

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.

A multi-objective auto-tuning framework for parallel codes

In this paper we introduce a multi-objective autotuning framework comprising compiler and runtime components. Focusing on individual code regions, our compiler uses a novel search technique to compute a set of optimal solutions, which are encoded into a multi-versioned executable. This enables the runtime system to choose specifically tuned code versions when dynamically adjusting to changing circumstances. We demonstrate our method by tuning loop tiling in cache-sensitive parallel programs, optimizing for both runtime and efficiency. Our static optimizer finds solutions matching or surpassing those determined by exhaustively sampling the search space on a regular grid, while using less than 4% of the computational effort on average. Additionally, we show that parallelism-aware multi-versioning approaches like our own gain a performance improvement of up to 70% over solutions tuned for only one specific number of threads.

A Study of the Multi-objective Next Release Problem

One of the first issues which has to be taken into account by software companies is to determine what should be included in the next release of their products, in such a way that the highest possible number of customers get satisfied while this entails a minimum cost for the company. This problem is known as the Next Release Problem (NRP). Since minimizing the total cost of including new features into a software package and maximizing the total satisfaction of customers are contradictory objectives, the problem has a multi-objective nature. In this work we study the NRP problem from the multi-objective point of view, paying attention to the quality of the obtained solutions, the number of solutions, the range of solutions covered by these fronts, and the number of optimal solutions obtained.Also, we evaluate the performance of two state-of-the-art multi-objective metaheuristics for solving NRP: NSGA-II and MOCell. The obtained results show that MOCell outperforms NSGA-II in terms of the range of solutions covered, while this latter is able of obtaining better solutions than MOCell in large instances. Furthermore, we have observed that the optimal solutions found are composed of a high percentage of low-cost requirements and, also, the requirements that produce most satisfaction on the customers.

A study of master-slave approaches to parallelize NSGA-II

Many of the optimization problems from the real world are multiobjective in nature, and the reference algorithm for multiobjective optimization is NSGA-II. Frequently, these problems present a high complexity, so classical metaheuristic algorithms fail to solve them in a reasonable amount of time; in this context, parallelism is a choice to overcome this fact to some extent. In this paper we study three parallel approaches (a synchronous and two asynchronous strategies) for the NSGA-II algorithm based on the master-worker paradigm. The asynchronous schemes are designed to be used in grid systems, so they can make use of hundreds of machines. We have applied them to solve a real world problem which lies in optimizing a broadcasting protocol using a network simulator. Our experiences reveal that significant time reductions can be achieved with the distributed approaches by using a grid system of more than 300 processors.