In this paper we present an adaptive multi-element generalized polynomial chaos (ME-gPC) method, which can achieve hp-convergence in random space. ME-gPC is based on the decomposition of random space and generalized polynomial chaos (gPC). Using proper numerical schemes to maintain the local orthogonality on-the-fly, we perform gPC locally and adaptively. The key idea is to combine the polynomial chaos method of h version and p version. The adaptive ME-gPC shows good performance in dealing with problems related to long-term integration, large perturbation and discontinuities. Benchmarks and applications of ME-gPC are presented.
In the above titled paper (ibid., vol. 12, no. 6, pp. 714-723, Dec. 08), there was an error in the pseudo-code for the incremental hypervolume by slicing objectives (IHSO) that might prevent its easy implementation. The corrected pseudo-code is presented here.
We propose a crossover-based adaptive local search (LS) operation for enhancing the performance of standard differential evolution (DE) algorithm. Incorporating LS heuristics is often very useful in designing an effective evolutionary algorithm for global optimization. However, determining a single LS length that can serve for a wide range of problems is a critical issue. We present a LS technique to solve this problem by adaptively adjusting the length of the search, using a hill-climbing heuristic. The emphasis of this paper is to demonstrate how this LS scheme can improve the performance of DE. Experimenting with a wide range of benchmark functions, we show that the proposed new version of DE, with the adaptive LS, performs better, or at least comparably, to classic DE algorithm. Performance comparisons with other LS heuristics and with some other well-known evolutionary algorithms from literature are also presented.
Methods are developed to numerically analyze an evolutionary algorithm (EA) that applies mutation and selection on a bit-string representation to find the optimum for a bimodal unitation function called a trap function. This research bridges part of the gap between the existing convergence velocity analysis of strictly unimodal functions and global convergence results assuming the limit of infinite time. As a main result of this analysis, a new so-called (1 : λ)-EA is proposed, which generates offspring using individual mutation rates p<sub>i</sub>. While a more traditional EA using only one mutation rate is not able to find the global optimum of the trap function within an acceptable (nonexponential) time, our numerical investigations provide evidence that the new algorithm overcomes these limitations. The analysis tools used for the analysis, based on absorbing Markov chains and the calculation of transition probabilities, are demonstrated to provide an intuitive and useful method for investigating the capabilities of EAs to bridge the gap between a local and a global optimum in bimodal search spaces.
The use of intelligent techniques in the manufacturing field has
been growing the last decades due to the fact that most manufacturing
optimization problems are combinatorial and NP hard. This paper examines
recent developments in the field of evolutionary computation for
manufacturing optimization. Significant papers in various areas are
highlighted, and comparisons of results are given wherever data are
available. A wide range of problems is covered, from job shop and flow
shop scheduling, to process planning and assembly line balancing
This paper presents a new cooperative coevolving particle swarm optimization (CCPSO) algorithm in an attempt to address the issue of scaling up particle swarm optimization (PSO) algorithms in solving large-scale optimization problems (up to 2000 real-valued variables). The proposed CCPSO2 builds on the success of an early CCPSO that employs an effective variable grouping technique random grouping. CCPSO2 adopts a new PSO position update rule that relies on Cauchy and Gaussian distributions to sample new points in the search space, and a scheme to dynamically determine the coevolving subcomponent sizes of the variables. On high-dimensional problems (ranging from 100 to 2000 variables), the performance of CCPSO2 compared favorably against a state-of-the-art evolutionary algorithm sep-CMA-ES, two existing PSO algorithms, and a cooperative coevolving differential evolution algorithm. In particular, CCPSO2 performed significantly better than sep-CMA-ES and two existing PSO algorithms on more complex multimodal problems (which more closely resemble real-world problems), though not as well as the existing algorithms on unimodal functions. Our experimental results and analysis suggest that CCPSO2 is a highly competitive optimization algorithm for solving large-scale and complex multimodal optimization problems.
Over the last decade, a variety of evolutionary algorithms (EAs) have been proposed for solving multiobjective optimization problems. Especially more recent multiobjective evolutionary algorithms (MOEAs) have been shown to be efficient and superior to earlier approaches. An important question however is whether we can expect such improvements to converge onto a specific efficient MOEA that behaves best on a large variety of problems. In this paper, we argue that the development of new MOEAs cannot converge onto a single new most efficient MOEA because the performance of MOEAs shows characteristics of multiobjective problems. While we point out the most important aspects for designing competent MOEAs in this paper, we also indicate the inherent multiobjective tradeoff in multiobjective optimization between proximity and diversity preservation. We discuss the impact of this tradeoff on the concepts and design of exploration and exploitation operators. We also present a general framework for competent MOEAs and show how current state-of-the-art MOEAs can be obtained by making choices within this framework. Furthermore, we show an example of how we can separate nondomination selection pressure from diversity preservation selection pressure and discuss the impact of changing the ratio between these components.
Based on evolutionary computation (EC) concepts, we developed an
adaptive evolutionary planner/navigator (EP/N) as a novel approach to
path planning and navigation. The EP/N is characterized by generality,
flexibility, and adaptability. It unifies off-line planning and online
planning/navigation processes in the same evolutionary algorithm which
1) accommodates different optimization criteria and changes in these
criteria, 2) incorporates various types of problem-specific domain
knowledge, and 3) enables good tradeoffs among near-optimality of paths,
high planning efficiency, and effective handling of unknown obstacles.
More importantly, the EP/N can self-tune its performance for different
task environments and changes in such environments, mostly through
adapting probabilities of its operators and adjusting paths constantly,
even during a robot's motion toward the goal
A simple optimization procedure for constraint based problems which works without an objective function is described. The absence of an objective function makes the problem formulation particularly simple. The new method lends itself to parallel computation and is well suited for tasks where a family of solutions is required, trade-off situations have to be dealt with or the design center has to be found. ________________________________________ 1) International Computer Science Institute, 1947 Center Street, Berkeley, CA 94704-1198, Suite 600, Fax: 510-643-7684. E-mail: firstname.lastname@example.org. On leave from Siemens AG, ZFE T SN 2, OttoHahn -Ring 6, D-81739 Muenchen, Germany. Fax: 01149-636-44577, Email: email@example.com. 2 1. Introduction The design of a technical system is usually associated with the process of properly choosing some system parameters such that the technical system meets its specifications. The parameter choosing process can also be regarded as an o...
Penalty functions are often used in constrained optimization.
However, it is very difficult to strike the right balance between
objective and penalty functions. This paper introduces a novel approach
to balance objective and penalty functions stochastically, i.e.,
stochastic ranking, and presents a new view on penalty function methods
in terms of the dominance of penalty and objective functions. Some of
the pitfalls of naive penalty methods are discussed in these terms. The
new ranking method is tested using a (μ, λ) evolution strategy
on 13 benchmark problems. Our results show that suitable ranking alone
(i.e., selection), without the introduction of complicated and
specialized variation operators, is capable of improving the search
The potential and effectiveness of the newly developed Pareto-based multiobjective evolutionary algorithms (MOEA) for solving a real-world power system multiobjective nonlinear optimization problem are comprehensively discussed and evaluated in this paper. Specifically, nondominated sorting genetic algorithm, niched Pareto genetic algorithm, and strength Pareto evolutionary algorithm (SPEA) have been developed and successfully applied to an environmental/economic electric power dispatch problem. A new procedure for quality measure is proposed in this paper in order to evaluate different techniques. A feasibility check procedure has been developed and superimposed on MOEA to restrict the search to the feasible region of the problem space. A hierarchical clustering algorithm is also imposed to provide the power system operator with a representative and manageable Pareto-optimal set. Moreover, an approach based on fuzzy set theory is developed to extract one of the Pareto-optimal solutions as the best compromise one. These multiobjective evolutionary algorithms have been individually examined and applied to the standard IEEE 30-bus six-generator test system. Several optimization runs have been carried out on different cases of problem complexity. The results of MOEA have been compared to those reported in the literature. The results confirm the potential and effectiveness of MOEA compared to the traditional multiobjective optimization techniques. In addition, the results demonstrate the superiority of the SPEA as a promising multiobjective evolutionary algorithm to solve different power system multiobjective optimization problems.
Multiple-objective metaheuristics, e.g., multiple-objective
evolutionary algorithms, constitute one of the most active fields of
multiple-objective optimization. Since 1985, a significant number of
different methods have been proposed. However, only few comparative
studies of the methods were performed on large-scale problems. We
continue two comparative experiments on the multiple-objective 0/1
knapsack problem reported in the literature. We compare the performance
of two multiple-objective genetic local search (MOGLS) algorithms to the
best performers in the previous experiments using the same test
instances. The results of our experiment indicate that our MOGLS
algorithm generates better approximations to the nondominated set in the
same number of functions evaluations than the other algorithms
This paper introduces the ant colony system (ACS), a distributed
algorithm that is applied to the traveling salesman problem (TSP). In
the ACS, a set of cooperating agents called ants cooperate to find good
solutions to TSPs. Ants cooperate using an indirect form of
communication mediated by a pheromone they deposit on the edges of the
TSP graph while building solutions. We study the ACS by running
experiments to understand its operation. The results show that the ACS
outperforms other nature-inspired algorithms such as simulated annealing
and evolutionary computation, and we conclude comparing ACS-3-opt, a
version of the ACS augmented with a local search procedure, to some of
the best performing algorithms for symmetric and asymmetric TSPs
The particle swarm is an algorithm for finding optimal regions of
complex search spaces through the interaction of individuals in a
population of particles. This paper analyzes a particle's trajectory as
it moves in discrete time (the algebraic view), then progresses to the
view of it in continuous time (the analytical view). A five-dimensional
depiction is developed, which describes the system completely. These
analyses lead to a generalized model of the algorithm, containing a set
of coefficients to control the system's convergence tendencies. Some
results of the particle swarm optimizer, implementing modifications
derived from the analysis, suggest methods for altering the original
algorithm in ways that eliminate problems and increase the ability of
the particle swarm to find optima of some well-studied test functions
A framework is developed to explore the connection between
effective optimization algorithms and the problems they are solving. A
number of “no free lunch” (NFL) theorems are presented which
establish that for any algorithm, any elevated performance over one
class of problems is offset by performance over another class. These
theorems result in a geometric interpretation of what it means for an
algorithm to be well suited to an optimization problem. Applications of
the NFL theorems to information-theoretic aspects of optimization and
benchmark measures of performance are also presented. Other issues
addressed include time-varying optimization problems and a priori
“head-to-head” minimax distinctions between optimization
algorithms, distinctions that result despite the NFL theorems' enforcing
of a type of uniformity over all algorithms
The premise behind all evolutionary methods is ldquosurvival of the fittest,rdquo and consequently, individuals require a quantitative fitness measure. This paper proposes a novel strategy for evaluating individual's relative strengths and weaknesses, as well as representing these in the form of a binary string fitness characterization (BSFC); in addition, as customary, an overall fitness value is assigned to each individual. Utilizing the BSFC, we demonstrate both novel population evaluation measures and a pairwise mating strategy, comparative partner selection (CPS), with the aim of evolving a population that promotes effective solutions by reducing population-wide weaknesses. This strategy is tested with six standard genetic programming benchmarking problems.
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.
One of the major obstacles to achieving robots capable of operating in real-world environments is enabling them to cope with a continuous stream of unanticipated situations. In previous work, it was demonstrated that a robot can autonomously generate self-models, and use those self-models to diagnose unanticipated morphological change such as damage. In this paper, it is shown that multiple physical quadrupedal robots with similar morphologies can share self-models in order to accelerate modeling. Further, it is demonstrated that quadrupedal robots which maintain separate self-modeling algorithms but swap self-models perform better than quadrupedal robots that rely on a shared self-modeling algorithm. This finding points the way toward more robust robot teams: a robot can diagnose and recover from unanticipated situations faster by drawing on the previous experiences of the other robots.
This paper presents a search method that combines elements from evolutionary and local search paradigms by the systematic use of crossover operations, generally used as structured exchange of genes between a series of solutions in genetic algorithms. Crossover operations here are particularly utilized as a systematic means to generate several possible solutions from two superior solutions. To test the effectiveness of the method, it has been applied to the resource-constrained project scheduling problem. The computational experiments show that the application of the method to this problem is promising.