Comparative Analysis of Selection Hyper-Heuristics for Real-World Multi-Objective Optimization Problems

As exact algorithms are unfeasible to solve real optimization problems, due to their computational complexity, meta-heuristics are usually used to solve them. However, choosing a meta-heuristic to solve a particular optimization problem is a non-trivial task, and often requires a time-consuming trial and error process. Hyper-heuristics, which are heuristics to choose heuristics, have been proposed as a means to both simplify and improve algorithm selection or configuration for optimization problems. This paper novel presents a novel cross-domain evaluation for multi-objective optimization: we investigate how four state-of-the-art online hyper-heuristics with different characteristics perform in order to find solutions for eighteen real-world multi-objective optimization problems. These hyper-heuristics were designed in previous studies and tackle the algorithm selection problem from different perspectives: Election-Based, based on Reinforcement Learning and based on a mathematical function. All studied hyper-heuristics control a set of five Multi-Objective Evolutionary Algorithms (MOEAs) as Low-Level (meta-)Heuristics (LLHs) while finding solutions for the optimization problem. To our knowledge, this work is the first to deal conjointly with the following issues: (i) selection of meta-heuristics instead of simple operators (ii) focus on multi-objective optimization problems, (iii) experiments on real world problems and not just function benchmarks. In our experiments, we computed, for each algorithm execution, Hypervolume and IGD+ and compared the results considering the Kruskal–Wallis statistical test. Furthermore, we ranked all the tested algorithms considering three different Friedman Rankings to summarize the cross-domain analysis. Our results showed that hyper-heuristics have a better cross-domain performance than single meta-heuristics, which makes them excellent candidates for solving new multi-objective optimization problems

Multi-Objective Self-Organizing Migrating Algorithm: Sensitivity on Controlling Parameters

In this paper, we investigate the sensitivity of a novel Multi-Objective Self-Organizing Migrating Algorithm (MOSOMA) on setting its control parameters. Usually, efficiency and accuracy of searching for a solution depends on the settings of a used stochastic algorithm, because multi-objective optimization problems are highly non-linear. In the paper, the sensitivity analysis is performed exploiting a large number of benchmark problems having different properties (the number of optimized parameters, the shape of a Pareto front, etc.). The quality of solutions revealed by MOSOMA is evaluated in terms of a generational distance, a spread and a hyper-volume error. Recommendations for proper settings of the algorithm are derived: These recommendations should help a user to set the algorithm for any multi-objective task without prior knowledge about the solved problem

A multi-objective and evolutionary hyper-heuristic applied to the Integration and Test Order Problem

The field of Search-Based Software Engineering (SBSE) has widely utilized Multi-Objective Evolutionary Algorithms (MOEAs) to solve complex software engineering problems. However, the use of such algorithms can be a hard task for the software engineer, mainly due to the significant range of parameter and algorithm choices. To help in this task, the use of Hyper-heuristics is recommended. Hyper-heuristics can select or generate low-level heuristics while optimization algorithms are executed, and thus can be generically applied. Despite their benefits, we find only a few works using hyper-heuristics in the SBSE field. Considering this fact, we describe HITO, a Hyper-heuristic for the Integration and Test Order Problem, to adaptively select search operators while MOEAs are executed using one of the selection methods: Choice Function and Multi-Armed Bandit. The experimental results show that HITO can outperform the traditional MOEAs NSGA-II and MOEA/DD. HITO is also a generic algorithm, since the user does not need to select crossover and mutation operators, nor adjust their parameters

A Bayesian approach to constrained single- and multi-objective optimization

This article addresses the problem of derivative-free (single- or multi-objective) optimization subject to multiple inequality constraints. Both the objective and constraint functions are assumed to be smooth, non-linear and expensive to evaluate. As a consequence, the number of evaluations that can be used to carry out the optimization is very limited, as in complex industrial design optimization problems. The method we propose to overcome this difficulty has its roots in both the Bayesian and the multi-objective optimization literatures. More specifically, an extended domination rule is used to handle objectives and constraints in a unified way, and a corresponding expected hyper-volume improvement sampling criterion is proposed. This new criterion is naturally adapted to the search of a feasible point when none is available, and reduces to existing Bayesian sampling criteria---the classical Expected Improvement (EI) criterion and some of its constrained/multi-objective extensions---as soon as at least one feasible point is available. The calculation and optimization of the criterion are performed using Sequential Monte Carlo techniques. In particular, an algorithm similar to the subset simulation method, which is well known in the field of structural reliability, is used to estimate the criterion. The method, which we call BMOO (for Bayesian Multi-Objective Optimization), is compared to state-of-the-art algorithms for single- and multi-objective constrained optimization

Multi-objective cultural algorithms

Evolutionary algorithms, including the Cultural Algorithms and other bio-inspired approaches are frequently used to solve problems that are not tractable for traditional approaches. Previously, research in the field of evolutionary optimization has focused on single-objective problems. On the contrary, most real-world problems involve more than one objective where these objectives may conflict with each other. The newest implementation of the Cultural Algorithms to solve multi-objective optimization is named MOCAT. It is not the first time that the Cultural Algorithms have been used to solve multi-objective problems. Nonetheless, it is the first time that the Cultural Algorithms systematically merge techniques that have been popular in other evolutionary algorithms, such as non-domination sorting and spacing metrics, among other features. The goal of the thesis is to test whether MOCAT can efficiently handle multi-objective optimization. In addition to that, we want to observe how the knowledge sources and agent topologies within a Cultural Algorithm interact with each other during the problem solving process. The MOCA system was evaluated against the ZDT test set proposed by Zitzler (2000). Some basic results that were produced are as follows: 1. The MOCAT system was very effective in the generation of an appropriate configuration for solving problems with different combinations of these features. Even for a given problem, as information was added to the knowledge sources, adjustments in the topologies could be made effectively. 2. As the complexity of the problems increased in terms of the number of problem features, the MOCAT system\u27s relative performance increased. 3. A problem with just a single problem feature, such as ZDT1 and ZDT5, was often effectively solved by just using one metric guide the solution process. However, if there were multiple problems, combining the two metrics together produced a synergy that outperformed each single metric based system. 4. This synergy resulted from the fact that they rewarded spread production in different ways. The spread metric focused on global distribution while the hyper-volume tended to support local optimization. 5. The configuration of the top performing MOCAT system varied markedly from one problem to the next. Our experiments proved the potential of applying the Cultural Algorithms on multi-objective problems and open a gate to observing internal behaviors of various knowledge sources and social fabrics

Incremental evolution strategy for function optimization

This paper presents a novel evolutionary approach for function optimization Incremental Evolution Strategy (IES). Two strategies are proposed. One is to evolve the input variables incrementally. The whole evolution consists of several phases and one more variable is focused in each phase. The number of phases is equal to the number of variables in maximum. Each phase is composed of two stages: in the single-variable evolution (SVE) stage, evolution is taken on one independent variable in a series of cutting planes; in the multi-variable evolving (MVE) stage, the initial population is formed by integrating the populations obtained by the SVE and the MVE in the last phase. And the evolution is taken on the incremented variable set. The other strategy is a hybrid of particle swarm optimization (PSO) and evolution strategy (ES). PSO is applied to adjust the cutting planes/hyper-planes (in SVEs/MVEs) while (1+1)-ES is applied to searching optima in the cutting planes/hyper-planes. The results of experiments show that the performance of IES is generally better than that of three other evolutionary algorithms, improved normal GA, PSO and SADE_CERAF, in the sense that IES finds solutions closer to the true optima and with more optimal objective values

Self-Adaptive Surrogate-Assisted Covariance Matrix Adaptation Evolution Strategy

This paper presents a novel mechanism to adapt surrogate-assisted population-based algorithms. This mechanism is applied to ACM-ES, a recently proposed surrogate-assisted variant of CMA-ES. The resulting algorithm, saACM-ES, adjusts online the lifelength of the current surrogate model (the number of CMA-ES generations before learning a new surrogate) and the surrogate hyper-parameters. Both heuristics significantly improve the quality of the surrogate model, yielding a significant speed-up of saACM-ES compared to the ACM-ES and CMA-ES baselines. The empirical validation of saACM-ES on the BBOB-2012 noiseless testbed demonstrates the efficiency and the scalability w.r.t the problem dimension and the population size of the proposed approach, that reaches new best results on some of the benchmark problems.Comment: Genetic and Evolutionary Computation Conference (GECCO 2012) (2012

A Parallel General Purpose Multi-Objective Optimization Framework, with Application to Beam Dynamics

Particle accelerators are invaluable tools for research in the basic and applied sciences, in fields such as materials science, chemistry, the biosciences, particle physics, nuclear physics and medicine. The design, commissioning, and operation of accelerator facilities is a non-trivial task, due to the large number of control parameters and the complex interplay of several conflicting design goals. We propose to tackle this problem by means of multi-objective optimization algorithms which also facilitate a parallel deployment. In order to compute solutions in a meaningful time frame a fast and scalable software framework is required. In this paper, we present the implementation of such a general-purpose framework for simulation-based multi-objective optimization methods that allows the automatic investigation of optimal sets of machine parameters. The implementation is based on a master/slave paradigm, employing several masters that govern a set of slaves executing simulations and performing optimization tasks. Using evolutionary algorithms as the optimizer and OPAL as the forward solver, validation experiments and results of multi-objective optimization problems in the domain of beam dynamics are presented. The high charge beam line at the Argonne Wakefield Accelerator Facility was used as the beam dynamics model. The 3D beam size, transverse momentum, and energy spread were optimized

A similarity-based cooperative co-evolutionary algorithm for dynamic interval multi-objective optimization problems

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Dynamic interval multi-objective optimization problems (DI-MOPs) are very common in real-world applications. However, there are few evolutionary algorithms that are suitable for tackling DI-MOPs up to date. A framework of dynamic interval multi-objective cooperative co-evolutionary optimization based on the interval similarity is presented in this paper to handle DI-MOPs. In the framework, a strategy for decomposing decision variables is first proposed, through which all the decision variables are divided into two groups according to the interval similarity between each decision variable and interval parameters. Following that, two sub-populations are utilized to cooperatively optimize decision variables in the two groups. Furthermore, two response strategies, rgb0.00,0.00,0.00i.e., a strategy based on the change intensity and a random mutation strategy, are employed to rapidly track the changing Pareto front of the optimization problem. The proposed algorithm is applied to eight benchmark optimization instances rgb0.00,0.00,0.00as well as a multi-period portfolio selection problem and compared with five state-of-the-art evolutionary algorithms. The experimental results reveal that the proposed algorithm is very competitive on most optimization instances

Evidence of coevolution in multi-objective evolutionary algorithms

This paper demonstrates that simple yet important characteristics of coevolution can occur in evolutionary algorithms when only a few conditions are met. We find that interaction-based fitness measurements such as fitness (linear) ranking allow for a form of coevolutionary dynamics that is observed when 1) changes are made in what solutions are able to interact during the ranking process and 2) evolution takes place in a multi-objective environment. This research contributes to the study of simulated evolution in a at least two ways. First, it establishes a broader relationship between coevolution and multi-objective optimization than has been previously considered in the literature. Second, it demonstrates that the preconditions for coevolutionary behavior are weaker than previously thought. In particular, our model indicates that direct cooperation or competition between species is not required for coevolution to take place. Moreover, our experiments provide evidence that environmental perturbations can drive coevolutionary processes; a conclusion that mirrors arguments put forth in dual phase evolution theory. In the discussion, we briefly consider how our results may shed light onto this and other recent theories of evolution