Memory-based adaptive partitioning (MAP) of search space for the enhancement of convergence in Pareto-based multi-objective evolutionary algorithms

A new algorithm, dubbed memory-based adaptive partitioning (MAP) of search space, which is intended to provide a better accuracy/speed ratio in the convergence of multi-objective evolutionary algorithms (MOEAs) is presented in this work. This algorithm works by performing an adaptive-probabilistic refinement of the search space, with no aggregation in objective space. This work investigated the integration of MAP within the state-of-the-art fast and elitist non-dominated sorting genetic algorithm (NSGAII). Considerable improvements in convergence were achieved, in terms of both speed and accuracy. Results are provided for several commonly used constrained and unconstrained benchmark problems, and comparisons are made with standalone NSGAII and hybrid NSGAII-efficient local search (eLS).     

Convergence analysis of a self-adaptive multi-objective evolutionary algorithm based on grids

Evolutionary algorithms have been successfully applied to various multi-objective optimization problems. However, theoretical studies on multi-objective evolutionary algorithms, especially with self-adaption, are relatively scarce. This paper analyzes the convergence properties of a self-adaptive (μ+1)-algorithm. The convergence of the algorithm is defined, and general convergence conditions are studied. Under these conditions, it is proven that the proposed self-adaptive (μ+1)-algorithm converges in probability or almost surely to the Pareto-optimal front.     

Convergence of multi-objective evolutionary algorithms to a uniformly distributed representation of the Pareto front

In evolutionary multi-objective optimization (EMO), the convergence to the Pareto set of a multi-objective optimization problem (MOP) and the diversity of the final approximation of the Pareto front are two important issues. In the existing definitions and analyses of convergence in multi-objective evolutionary algorithms (MOEAs), convergence with probability is easily obtained because diversity is not considered. However, diversity cannot be guaranteed. By combining the convergence with diversity, this paper presents a new definition for the finite representation of a Pareto set, the B-Pareto set, and a convergence metric for MOEAs. Based on a new archive-updating strategy, the convergence of one such MOEA to the B-Pareto sets of MOPs is proved. Numerical results show that the obtained B-Pareto front is uniformly distributed along the Pareto front when, according to the new definition of convergence, the algorithm is convergent.     

Achieving super-linear performance in parallel multi-objective evolutionary algorithms by means of cooperative coevolution

This article introduces three new multi-objective cooperative coevolutionary variants of three state-of-the-art multi-objective evolutionary algorithms, namely, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Strength Pareto Evolutionary Algorithm 2 (SPEA2) and Multi-objective Cellular Genetic Algorithm (MOCell). In such a coevolutionary architecture, the population is split into several subpopulations or islands, each of them being in charge of optimizing a subset of the global solution by using the original multi-objective algorithm. Evaluation of complete solutions is achieved through cooperation, i.e., all subpopulations share a subset of their current partial solutions. Our purpose is to study how the performance of the cooperative coevolutionary multi-objective approaches can be drastically increased with respect to their corresponding original versions. This is specially interesting for solving complex problems involving a large number of variables, since the problem decomposition performed by the model at the island level allows for much faster executions (the number of variables to handle in every island is divided by the number of islands). We conduct a study on a real-world problem related to grid computing, the bi-objective robust scheduling problem of independent tasks. The goal in this problem is to minimize makespan (i.e., the time when the latest machine finishes its assigned tasks) and to maximize the robustness of the schedule (i.e., its tolerance to unexpected changes on the estimated time to complete the tasks). We propose a parallel, multithreaded implementation of the coevolutionary algorithms and we have analyzed the results obtained in terms of both the quality of the Pareto front approximations yielded by the techniques as well as the resulting speedups when running them on a multicore machine.     

一种基于CUDA的并行多目标进化算法

传统的多目标进化算法多是基于Pareto最优概念的类随机搜索算法,求解速度较慢,特别是当问题维度变高,需要群体规模较大时,上述问题更加凸显。这一问题已经获得越来越多研究人员以及从业人员的关注。实验仿真中可以发现,构造非支配集和保持群体多样性这两部分工作占用了算法99%以上的执行时间。解决上述问题的一个有效方法就是对这一部分算法进行并行化改造。本文提出了一种基于CUDA平台的并行化解决方案,采用小生境技术实现共享适应度来维持候选解集的多样性,将多目标进化算法的实现全部置于GPU端,区别于以往研究中非支配排序的部分工作以及群体多样性保持的全部工作仍在CPU上执行。通过对ZDT系列函数的仿真结果,可以看出本文算法性能远远优于NSGA-Ⅱ和NPGA。最后通过求解油品调和过程这一有约束多目标优化问题,可以看出在解决化工应用中的有约束多目标优化问题时,该算法依然表现出优异的加速效果。     

A multi-objective evolutionary algorithm for examination timetabling

This paper considers the scheduling of exams for a set of university courses. The solution to this exam timetabling problem involves the optimization of complete timetables such that there are as few occurrences of students having to take exams in consecutive periods as possible but at the same time minimizing the timetable length and satisfying hard constraints such as seating capacity and no overlapping exams. To solve such a multi-objective combinatorial optimization problem, this paper presents a multi-objective evolutionary algorithm that uses a variable-length chromosome representation and incorporates a micro-genetic algorithm and a hill-climber for local exploitation and a goal-based Pareto ranking scheme for assigning the relative strength of solutions. It also imports several features from the research on the graph coloring problem. The proposed algorithm is shown to be a more general exam timetabling problem solver in that it does not require any prior information of the timetable length to be effective. It is also tested against a few influential and recent optimization techniques and is found to be superior on four out of seven publicly available datasets.     

Discovering gene association networks by multi-objective evolutionary quantitative association rules

In the last decade, the interest in microarray technology has exponentially increased due to its ability to monitor the expression of thousands of genes simultaneously. The reconstruction of gene association networks from gene expression profiles is a relevant task and several statistical techniques have been proposed to build them. The problem lies in the process to discover which genes are more relevant and to identify the direct regulatory relationships among them. We developed a multi-objective evolutionary algorithm for mining quantitative association rules to deal with this problem. We applied our methodology named GarNet to a well-known microarray data of yeast cell cycle. The performance analysis of GarNet was organized in three steps similarly to the study performed by Gallo et al. GarNet outperformed the benchmark methods in most cases in terms of quality metrics of the networks, such as accuracy and precision, which were measured using YeastNet database as true network. Furthermore, the results were consistent with previous biological knowledge.     

Context adaptation of fuzzy systems through a multi-objective evolutionary approach based on a novel interpretability index

Context adaptation (CA) based on evolutionary algorithms is certainly a promising approach to the development of fuzzy rule-based systems (FRBSs). In CA, a context-free model is instantiated to a context-adapted FRBS so as to increase accuracy. A typical requirement in CA is that the context-adapted system maintains the same interpretability as the context-free model, a challenging constraint given that accuracy and interpretability are often conflicting objectives. Furthermore, interpretability is difficult to quantify because of its very nature of being a qualitative concept. In this paper, we first introduce a novel index based on fuzzy ordering relations in order to provide a measure of interpretability. Then, we use the proposed index and the mean square error as goals of a multi-objective evolutionary algorithm aimed at generating a set of Pareto-optimum context-adapted Mamdani-type FRBSs with different trade-offs between accuracy and interpretability. CA is obtained through the use of specifically designed operators that adjust the universe of the input and output variables, and modify the core, the support and the shape of fuzzy sets characterizing the partitions of these universes. Finally, we show results obtained by using our approach on synthetic and real data sets.     

Illustration of fairness in evolutionary multi-objective optimization

It is widely assumed that evolutionary algorithms for multi-objective optimization problems should use certain mechanisms to achieve a good spread over the Pareto front. In this paper, we examine such mechanisms from a theoretical point of view and analyze simple algorithms incorporating the concept of fairness. This mechanism tries to balance the number of offspring of all individuals in the current population. We rigorously analyze the runtime behavior of different fairness mechanisms and present illustrative examples to point out situations, where the right mechanism can speed up the optimization process significantly. We also indicate drawbacks for the use of fairness by presenting instances, where the optimization process is slowed down drastically.     

Enabling energy-efficient and lossy-aware data compression in wireless sensor networks by multi-objective evolutionary optimization

Nodes of wireless sensor networks (WSNs) are typically powered by batteries with a limited capacity. Thus, energy is a primary constraint in the design and deployment of WSNs. Since radio communication is in general the main cause of power consumption, the different techniques proposed in the literature to improve energy efficiency have mainly focused on limiting transmission/reception of data, for instance, by adopting data compression and/or aggregation. The limited resources available in a sensor node demand, however, the development of specifically designed algorithms. To this aim, we propose an approach to perform lossy compression on single node based on a differential pulse code modulation scheme with quantization of the differences between consecutive samples. Since different combinations of the quantization process parameters determine different trade-offs between compression performance and information loss, we exploit a multi-objective evolutionary algorithm to generate a set of combinations of these parameters corresponding to different optimal trade-offs. The user can therefore choose the combination with the most suitable trade-off for the specific application. We tested our lossy compression approach on three datasets collected by real WSNs. We show that our approach can achieve significant compression ratios despite negligible reconstruction errors. Further, we discuss how our approach outperforms LTC, a lossy compression algorithm purposely designed to be embedded in sensor nodes, in terms of compression rate and complexity.     

Multi-objective evolutionary algorithms based on the summation of normalized objectives and diversified selection

Most multi-objective evolutionary algorithms (MOEAs) use the concept of dominance in the search process to select the top solutions as parents in an elitist manner. However, as MOEAs are probabilistic search methods, some useful information may be wasted, if the dominated solutions are completely disregarded. In addition, the diversity may be lost during the early stages of the search process leading to a locally optimal or partial Pareto-front. Beside this, the non-domination sorting process is complex and time consuming. To overcome these problems, this paper proposes multi-objective evolutionary algorithms based on Summation of normalized objective values and diversified selection (SNOV-DS). The performance of this algorithm is tested on a set of benchmark problems using both multi-objective evolutionary programming (MOEP) and multi-objective differential evolution (MODE). With the proposed method, the performance metric has improved significantly and the speed of the parent selection process has also increased when compared with the non-domination sorting. In addition, the proposed algorithm also outperforms ten other algorithms.     

小生态进化技术综述

进化计算存在的遗传漂移现象使种群均匀地收敛于单一的优良解,导致早熟收敛或可选优良解的丢失,小生态技术是一种形成和维持稳定子种群、抑制遗传漂移的并行进化技术。系统地综述了小生态技术研究的主要成果,归纳了存在的问题,指出了进一步的研究方向。     

Seeding the initial population of multi-objective evolutionary algorithms: A computational study

Most experimental studies initialize the population of evolutionary algorithms with random genotypes. In practice, however, optimizers are typically seeded with good candidate solutions either previously known or created according to some problem-specific method. This seeding has been studied extensively for single-objective problems. For multi-objective problems, however, very little literature is available on the approaches to seeding and their individual benefits and disadvantages. In this article, we are trying to narrow this gap via a comprehensive computational study on common real-valued test functions. We investigate the effect of two seeding techniques for five algorithms on 48 optimization problems with 2, 3, 4, 6, and 8 objectives. We observe that some functions (e.g., DTLZ4 and the LZ family) benefit significantly from seeding, while others (e.g., WFG) profit less. The advantage of seeding also depends on the examined algorithm.     

A review of procedures to evolve quantum algorithms

There exist quantum algorithms that are more efficient than their classical counterparts; such algorithms were invented by Shor in 1994 and then Grover in 1996. A lack of invention since Grover’s algorithm has been commonly attributed to the non-intuitive nature of quantum algorithms to the classically trained person. Thus, the idea of using computers to automatically generate quantum algorithms based on an evolutionary model emerged. A limitation of this approach is that quantum computers do not yet exist and quantum simulation on a classical machine has an exponential order overhead. Nevertheless, early research into evolving quantum algorithms has shown promise. This paper provides an introduction into quantum and evolutionary algorithms for the computer scientist not familiar with these fields. The exciting field of using evolutionary algorithms to evolve quantum algorithms is then reviewed.

Running time analysis of evolutionary algorithms on a simplified multiobjective knapsack problem

In this paper, the expected running time of two multiobjectiveevolutionary algorithms, SEMO and FEMO, is analyzed for a simpleinstance of the multiobjective 0/1 knapsack problem. The considered problem instance has two profit values per item andcannot be solved by one-bit mutations. In the analysis, we make use of two general upper bound techniques, thedecision space partition method and the graph search method. The paperdemonstrates how these methods, which have previously only beenapplied to algorithms with one-bit mutations, are equally applicablefor mutation operators where each bit is flipped independently with acertain probability.     

A general framework for statistical performance comparison of evolutionary computation algorithms

This paper proposes a statistical methodology for comparing the performance of evolutionary computation algorithms. A twofold sampling scheme for collecting performance data is introduced, and these data are analyzed using bootstrap-based multiple hypothesis testing procedures. The proposed method is sufficiently flexible to allow the researcher to choose how performance is measured, does not rely upon distributional assumptions, and can be extended to analyze many other randomized numeric optimization routines. As a result, this approach offers a convenient, flexible, and reliable technique for comparing algorithms in a wide variety of applications.     

一种混合自适应多目标Memetic算法

Memetic算法是求解多目标优化问题最有效的方法之一,融合了局部搜索和进化计算,具有较高的全局搜索能力．混合自适应多目标Memetic算法（HAMA）用基于模拟退火的加权法进行局部搜索,采用Pareto法实现交叉和变异,通过扰动增强算法的exploration能力,且进化过程可根据改善率自适应调整,以提高搜索效率并改善算法的鲁棒性．算例测试说明HAMA能产生更接近Pareto前沿且多样性更好的近似集．     

求解0-1背包问题的人工免疫抗体修正克隆算法

基于细胞克隆选择学说,系统地阐述了用于人工智能的抗体修正克隆算子,提出了相应的人工免疫抗体修正克隆算法;利用Markov链的有关性质,证明了该算法的收敛性.针对0-1背包问题的试验结果表明,人工免疫抗体修正克隆算法解决组合优化问题是有效的,与相应的进化算法相比,该算法有效克服了早熟问题、保持了抗体的多样性,而且收敛速度快.     

Approximate algorithms for the container loading problem

In this paper we develop several algorithms for solving three–dimensional cutting/packing problems. We begin by proposing an adaptation of the approach proposed in Hifi and Ouafi (1997) for solving two–staged unconstrained two–dimensional cutting problems. We show how the algorithm can be polynomially solved for producing a constant approximation ratio. We then extend this algorithm for developing better approximate algorithms. By using hill–climbing strategies, we construct some heuristics which produce a good trade–off between the computational time and the solution quality. The performance of the proposed algorithms is evaluated on different problem instances of the literature, with different sizes and densities (a total of 144 problem instances).     

A comparative study of different approaches using an outranking relation in a multi-objective evolutionary algorithm

This paper presents a comparative analysis of three versions of an evolutionary algorithm in which the decision maker's preferences are incorporated using an outranking relation and preference parameters associated with the ELECTRE TRI method. The aim is using the preference information supplied by the decision maker to guide the search process to the regions where solutions more in accordance with his/her preferences are located, thus narrowing the scope of the search and reducing the computational effort. An example dealing with a pertinent problem in electrical distribution network is used to compare the different versions of the algorithm and illustrate how meaningful information can be elicited from a decision maker and used in the operational framework of an evolutionary algorithm to provide decision support in real-world problems.