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In this paper, we first propose a graph neural network encoding method for multiobjective evolutionary algorithm to handle the community detection problem in complex attribute networks. In the graph neural network encoding method, each edge in an attribute network is associated with a continuous variable. Through non-linear transformation, a continuous valued vector (i.e. a concatenation of the continuous variables associated with the edges) is transferred to a discrete valued community grouping solution. Further, two objective functions for single- and multi-attribute network are proposed to evaluate the attribute homogeneity of the nodes in communities, respectively. Based on the new encoding method and the two objectives, a multiobjective evolutionary algorithm (MOEA) based upon NSGA-II, termed as continuous encoding MOEA, is developed for the transformed community detection problem with continuous decision variables. Experimental results on single- and multi-attribute networks with different types show that the developed algorithm performs significantly better than some well-known evolutionary and non-evolutionary based algorithms. The fitness landscape analysis verifies that the transformed community detection problems have smoother landscapes than those of the original problems, which justifies the effectiveness of the proposed graph neural network encoding method.

The tradeoff between exploration and exploitation is critical to the performance of an evolutionary algorithm . Different levels of exploration-exploitation tradeoff are required at different evolutionary stages for achieving a satisfactory performance of an evolutionary algorithm. In this paper, we propose a novel survival analysis method to intelligently guide the maintenance of the exploration-exploitation tradeoff in multiobjective evolutionary algorithms. The survival analysis stems from a deep understanding of the evolutionary search procedure. Through survival analysis, an indicator is derived, which is used to guide the adoption of appropriate recombination operators , based on the assumption that the roles of these operators in terms of their capabilities on exploration-exploitation can be asserted. In the developed algorithm, a differential evolution recombination operator and a new sampling strategy are hybridized. Empirical comparison with five well-known multiobjective evolutionary algorithms on a number of test instances with complex Pareto sets and Pareto fronts indicates the effectiveness and superiority of the developed algorithm in terms of commonly-used performance metrics on these test instances.

In some real-world applications, it has been found that the performance of multiobjective optimization evolutionary algorithms (MOEAs) may deteriorate when boundary solutions in the Pareto front (PF) are more difficult to approximate than others. Such a problem feature, referred to as difficult-to-approximate (DtA) PF boundaries, is seldom considered in existing multiobjective optimization test problems. To fill this gap and facilitate possible systematic studies, we introduce a new test problem generator. The proposed generator enables the design of test problems with controllable difficulties regarding the feature of DtA PF boundaries. Three representative MOEAs, NSGA-II, SMS-EMOA, and MOEA/D-DRA, are performed on a series of test problems created using the proposed generator. Experimental results indicate that all the three algorithms perform poorly on the new test problems. Meanwhile, a modified variant of MOEA/D-DRA, denoted as MOEA/D-DRA-UT, is validated to be more effective in dealing with these problems. Subsequently, it is concluded that the rational allocation of computational resources between different PF parts is crucial for MOEAs to handle the problems with DtA PF boundaries.

Combining machine learning techniques has shown great potentials in evolutionary optimization since the domain knowledge of an optimization problem, if well learned, can be a great help for creating high-quality solutions. However, existing learning-based multiobjective evolutionary algorithms (MOEAs) spend too much computational overhead on learning. To address this problem, we propose a learning-based MOEA where an online learning algorithm is embedded within the evolutionary search procedure. The online learning algorithm takes the stream of sequentially generated solutions along the evolution as its training data. It is noted that the stream of solutions are temporal, dependent, nonstationary, and nonstatic. These data characteristics make existing online learning algorithm not suitable for the evolution data. We hence modify an existing online agglomerative clustering algorithm to accommodate these characteristics. The modified online clustering algorithm is applied to adaptively discover the structure of the Pareto optimal set; and the learned structure is used to guide new solution creation. Experimental results have shown significant improvement over four state-of-the-art MOEAs on a variety of benchmark problems.

In evolutionary optimization, the preselection is an efficient operator to improve the search efficiency, which aims to filter unpromising candidate solutions before fitness evaluation. Most existing preselection operators rely on fitness values, surrogate models, or classification models. Basically, the classification based preselection regards the preselection as a classification procedure, i.e., differentiating promising and unpromising candidate solutions. However, the difference between promising and unpromising classes becomes fuzzy as the running process goes on, as all the left solutions are likely to be promising ones. Facing this challenge, this paper proposes a fuzzy classification based preselection (FCPS) scheme, which utilizes the membership function to measure the quality of candidate solutions. The proposed FCPS scheme is applied to two state-of-the-art evolutionary algorithms on a test suite. The experimental results show the potential of FCPS on improving algorithm performance.

Complicated geometric shapes of Pareto fronts can cause difficulties for multiobjective evolutionary algorithms. To deal with these difficulties, efficient diversity strategies must be highly addressed in order to obtain a set of representative Pareto solutions. In decomposition-based multiobjective evolutionary algorithms, this is often done by optimizing multiple single objective subproblems defined by a set of weight vectors. For complicated Pareto fronts with extreme convexity, disconnection or degeneracy, however, it is nontrivial to set these weight vector properly. To overcome this shortcoming, we propose a new decomposition-based multiobjective evolutionary algorithm based on a hybrid weighting strategy, which optimizes both random subproblems and fixed subproblems. To maintain diversity of nondominated solutions stored in external population, a new archiving strategy based on adaptive Epsilon dominance is also suggested in our proposed algorithm. Our experimental results have showed that our proposed algorithm is superior to several other state-of-the-art multiobjective evolutionary algorithms on a set of benchmark multiobjective test problems with different challenging difficulties regarding the geometric shapes of Pareto fronts.

In this paper, we propose an adaptive multi-objective evolutionary algorithm for multi-objective optimization problems (MOPs). In the algorithm, a clustering approach is employed to learn the Pareto optimal set's manifold structure adaptively, in accordance with the regularity property of MOPs, along the evolution. An advanced sampling strategy is developed for the generation of promising offspring from the learned structure. To generate trial solution, each non-dominated solution at present generation is Gaussian-perturbed using the variance-covariance matrix within its cluster. The other new features include 1) an adaptive hybridization of the developed sampling strategy with a differential evolution (DE) operator which aims to combine local and global information; 2) a reusing scheme which is to reduce the computational cost on modeling (clustering); and 3) an adaptive strength Pareto based approach which is to adaptively determine the contribution of the developed sampling strategy and the DE operator for balancing exploration and exploitation. The developed algorithm was empirically compared with four well-known MOEAs on a number of test instances with complex Pareto optimal set structure and complicated Pareto fronts. Experimental results suggest that it outperforms the compared algorithms on these test instances in terms of two commonly-used measure metrics. The effectiveness of the developed sampling strategy, the reusing scheme, the hybrid strategy, and the adaptive strategy was also empirically validated.

Differential evolution is one of the most prestigious population-based stochastic optimization algorithm for black-box problems. The performance of a differential evolution algorithm depends highly on its mutation and crossover strategy and associated control parameters. However, the determination process for the most suitable parameter setting is troublesome and time consuming. Adaptive control parameter methods that can adapt to problem landscape and optimization environment are more preferable than fixed parameter settings. This article proposes a novel adaptive parameter control approach based on learning from the optimization experiences over a set of problems. In the approach, the parameter control is modeled as a finite-horizon Markov decision process. A reinforcement learning algorithm, named policy gradient, is applied to learn an agent (i.e., parameter controller) that can provide the control parameters of a proposed differential evolution adaptively during the search procedure. The differential evolution algorithm based on the learned agent is compared against nine well-known evolutionary algorithms on the CEC’13 and CEC’17 test suites. Experimental results show that the proposed algorithm performs competitively against these compared algorithms on the test suites.

Tuning hyper-parameters for evolutionary algorithms is an important issue in computational intelligence. Performance of an evolutionary algorithm depends not only on its operation strategy design, but also on its hyper-parameters. Hyper-parameters can be categorized in two dimensions as structural/numerical and time-invariant/time-variant. Particularly, structural hyper-parameters in existing studies are usually tuned in advance for time-invariant parameters, or with hand-crafted scheduling for time-invariant parameters. In this paper, we make the first attempt to model the tuning of structural hyper-parameters as a reinforcement learning problem, and present to tune the structural hyper-parameter which controls computational resource allocation in the CEC 2018 winner algorithm by Q-learning. Experimental results show favorably against the winner algorithm on the CEC 2018 test functions.

This paper proposes a simple but promising clustering-based multi-objective evolutionary algorithm, termed as CMOEA. At each generation, CMOEA first divides the current population into several subpopulations by Gaussian mixture clustering. To generate offsprings, the search stage, either exploration or exploitation, is determined by the relative difference between the subpopulations’ hypervolumes of two adjacent generations. CMOEA selects the parents from different subpopulations in case of exploration stage, and from the same subpopulation in case of exploitation stage. In the environmental selection phase, the hypervolume indicator is used to update the population. Simulation experiments on nine multi-objective problems show that CMOEA is competitive with five popular multi-objective evolutionary algorithms.

The goal in sparse approximation is to find a sparse representation of a system. This can be done by minimizing a data-fitting term and a sparsity term at the same time. This sparse term imposes penalty for sparsity. In classical iterative thresholding methods, these two terms are often combined into a single function, where a relaxed parameter is used to balance the error and the sparsity. It is acknowledged that the setting of relaxed parameter is sensitive to the performance of iterative thresholding methods. In this paper, we proposed to address this difficulty by finding a set of nondominated solutions with different sparsity levels via multiobjective evolutionary algorithms (MOEAs). A new MOEA/D is developed specifically for sparse optimization, in which a chain-based random local search (CRLS) is employed for optimizing subproblems with various sparsity levels. The performance of the proposed algorithm, denoted by MOEA/D-CRLS, is tested on a set of sixteen noise-free or noisy test problems. Our experimental results suggest that MOEA/D-CRLS is competitive regarding the solution precision on the noise-free test problems, and clearly superior on the noisy test problems against three existing representative sparse optimization methods.

A blocking lot-streaming flow shop (BLSFS) scheduling problem is to schedule a number of jobs on more than one machine, where each job is split into a number of sublots while no intermediate buffers exist between adjacent machines. The BLSFS scheduling problem roots from traditional job shop scheduling problems but with additional constraints. It is more difficult to be solved than traditional job shop scheduling problems, yet very popular in real-world applications, and research on the problem has been in its infancy to date. This paper presents a hybrid multi-objective discrete artificial bee colony (HDABC) algorithm for the BLSFS scheduling problem with two conflicting criteria: the makespan and the earliness time. The main contributions of this paper include: (1) developing an initialization approach using a prior knowledge which can produce a number of promising solutions, (2) proposing two crossover operators by taking advantage of valuable information extracted from all the non-dominated solutions in the current population, and (3) presenting an efficient Pareto local search operator based on the Pareto dominance relation. The proposed algorithm is empirically compared with four state-of-the-art multi-objective evolutionary algorithms on 18 test subsets of the BLSFS scheduling problem. The experimental results show that the proposed algorithm significantly outperforms the compared ones in terms of several widely-used performance metrics.

External archive can be used to improve the performance of a multi-objective evolutionary algorithm. Various archiving approaches have been developed but with some drawbacks. These drawbacks such as computation-inefficiency, retreating and shrinking, have not yet been well addressed. In this paper, we propose an efficient decomposition-based archiving approach (DAA) inspired from the decomposition strategy for dealing with multi-objective optimization. In DAA, the whole objective space is uniformly divided into a number of subspaces according to a set of weight vectors. At each generation, only one non-dominated solution lying in a subspace is chosen to be used for updating the external archive in consideration of its diversity. A normalized distance-based method, incorporated with the Pareto dominance, is proposed to decide which subspace a new solution should fall into, and whether this solution should replace existing one in this subspace or not. Empirical results on a diverse set of benchmark test problems show that DAA is more efficient than a number of state-of-the-art archiving methods in terms of the diversity of the obtained non-dominated solutions; and DAA can accelerate the convergence speed of the evolutionary search for most test problems.

Decomposition-based multi-objective evolutionary algorithm has been acknowledged as a promising paradigm for multi-objective optimization problems. Nevertheless, its performance deteriorates seriously when the number of objectives increases. To improve its performance, generating high-quality solution is vital. Acknowledging the success of hybridizing different recombination operators, a selection strategy to choose from a set of differential evolution (DE) operators is adopted in this paper. The selection strategy could combine the advantages of these DE operators. Yet, the performance of DE operators depends highly on their control parameters, which should be tuned adaptively along the search process to fully explore their search abilities. An adaptive parameter tuning strategy is hereby proposed by estimating a Cauchy and a normal distribution from history information for the control parameters, respectively. Experimental comparison using DTLZ1-DTLZ4, with the number of objectives ranging from three to ten, is carried out between six state-of-the-art algorithms and the developed algorithm. Empirical results justify the outperformance of the developed algorithm against the compared algorithms in terms of some commonly-used performance metrics.

Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D) is one of the dominant algorithmic frameworks for multi-objective optimization in the area of evolutionary computation. The performance of multi-objective algorithms based on MOEA/D framework highly depends on how a diverse set of single objective subproblems are generated. Among all decomposition methods, the Penalty-based Boundary Intersection (PBI) method has received particular research interest in MOEA/D due to its ability for controlling the diversity of population for many-objective optimization. However, optimizing multiple PBI subproblems defined via a set of uniformly-distributed weight vectors may not be able to produce a good approximation of Pareto-optimal front when objectives have different scales. To overcome this weakness, we suggest a new strategy for adjusting weight vectors of PBI-based subproblems in this paper. Our experimental results have shown that the performance of MOEA/D-PBI with adjusted weight vectors is competitive to NSGA-III in diversity when dealing with the scaled version of some benchmark multi-objective test problems.

In this paper, we propose a multi-cycled sequential memetic computing structure for constrained optimisation. The structure is composed of multiple evolutionary cycles. At each cycle, an evolutionary algorithm is considered as an operator, and connects with a local optimiser. This structure enables the learning of useful knowledge from previous cycles and the transfer of the knowledge to facilitate search in latter cycles. Specifically, we propose to apply an estimation of distribution algorithm (EDA) to explore the search space until convergence at each cycle. A local optimiser, called DONLP2, is then applied to improve the best solution found by the EDA. New cycle starts after the local improvement if the computation budget has not been exceeded. In the developed EDA, an adaptive fully-factorized multivariate probability model is proposed. A learning mechanism, implemented as the guided mutation operator, is adopted to learn useful knowledge from previous cycles. The developed algorithm was experimentally studied on the benchmark problems in the CEC 2006 and 2010 competition. Experimental studies have shown that the developed probability model exhibits excellent exploration capability and the learning mechanism can significantly improve the search efficiency under certain conditions. The comparison against some well-known algorithms showed the superiority of the developed algorithm in terms of the consumed fitness evaluations and the solution quality.

Balancing exploration and exploitation is fundamental to the performance of an evolutionary algorithm. In this paper, we propose a survival analysis method to address this issue. Results of the analysis is used to adaptively choose appropriate new solution creation operators which prefer either exploration or exploitation. In the developed algorithm, a differential evolution recombination operator is used for the exploration purpose, while a new clustering-based operator is proposed for exploitation. Empirical comparison with four well-known multi-objective evolutionary algorithms on test instances with complex Pareto sets and Pareto fronts indicates the effectiveness and outperformance of the developed algorithms on these test instances in terms of commonly-used metrics.

In this paper, we propose a reference-inspired multiobjective evolutionary algorithm for many-objective optimisation. The main idea is (1) to summarise information inspired by a set of randomly generated reference points in the objective space to strengthen the selection pressure towards the Pareto front; and (2) to decompose the objective space into subregions for diversity management and offspring recombination. We showed that the mutual relationship between the objective vectors and the reference points provides not only a fine selection pressure, but also a balanced convergence-diversity information. The decomposition of the objective space into subregions is able to preserve the Pareto front’s diversity. A restricted stable match strategy is proposed to choose appropriate parent solutions from solution sets constructed at the subregions for high-quality offspring generation. Controlled experiments conducted on a commonly-used benchmark test suite have shown the effectiveness and competitiveness of the proposed algorithm in comparison with several state-of-the-art many-objective evolutionary algorithms.

The classical algorithms based on regularization usually solve sparse optimization problems under the framework of single objective optimization, which combines the sparse term with the loss term. The majority of these algorithms suffer from the setting of regularization parameter or its estimation. To overcome this weakness, the extension of multiobjective evolutionary algorithm based on decomposition (MOEA/D) has been studied for sparse optimization. The major advantages of MOEA/D lie in two aspects: (1) free setting of regularization parameter and (2) detection of true sparsity. Due to the generational mode of MOEA/D, its efficiency for searching the knee region of the Pareto front is not very satisfactory. In this paper, we proposed a new steady-state MOEA/D with the preference to search the region of Pareto front near the true sparse solution. Within each iteration of our proposed algorithm, a local search step is performed to examine a number of solutions with similar sparsity levels in a neighborhood. Our experimental results have shown that the new MOEA/D clearly performs better than its previous version on reconstructing artificial sparse signals.

Solving dynamic multi-objective optimisation problem means to search adaptively for the Pareto optimal solutions when the environment changes. It is important to find out the changing pattern for the efficiency of the evolutionary search. Learning techniques are thus widely used to explore the dependence structure of the changing for population re-initialisation in the evolutionary search paradigm. The learning techniques are expected to discover some useful knowledge from history information, while the learned knowledge can help improve the search speed through good initialisation when change occurs. In this paper, we propose a new learning strategy based on the incorporation of mutual information, stable matching strategy and Newton's laws of motion. Mutual information is used to identify the relationship between previously found solutions; the stable matching strategy is used to associate previous found solutions bijectively and Newton's Laws of motion is applied to re-initialise the new population. Controlled experiments were carried out systematically on some widely used test problems. Comparison against several state-of-the-art dynamic multi-objective evolutionary algorithms showed comparable performance in favour of the developed algorithm.

In this paper, a two-stage evolutionary algorithm is proposed to solve an NP-complete telecommunication problem-all optical wavelength-division multiplexing (WDM) mesh network survivability under shared-risk-link-group (SRLG) constraints. First of all, a novel greedy heuristic with two control parameters is developed to construct feasible solutions of the telecommunication problem. An estimation of distribution algorithm (EDA) with guided mutation is applied to search for optimum settings of the two control parameters in respective two stages. Given the found best control parameters, an optimal solution of the considered problem can be constructed by the greedy heuristic. Experimental results show that the proposed approach compares favorably against the best-known evolutionary-based algorithm in 26 out of 30 test instances in terms of solution quality within given time limit.

The complete topology design problem of survivable mesh-based transport networks is to address simultaneously design of network topology, working path routing, and spare capacity allocation based on span-restoration. Each constituent problem in the complete design problem could be formulated as an Integer Programming (IP) and is proved to be $\mathcal{NP}$ -hard. Due to a large amount of decision variables and constraints involved in the IP formulation, to solve the problem directly by exact algorithms (e.g. branch-and-bound) would be impractical if not impossible. In this paper, we present a two-level evolutionary approach to address the complete topology design problem. In the low-level, two parameterized greedy heuristics are developed to jointly construct feasible solutions (i.e., closed graph topologies satisfying all the mesh-based network survivable constraints) of the complete problem. Unlike existing "zoom-in"-based heuristics in which subsets of the constraints are considered, the proposed heuristics take all constraints into account. An estimation of distribution algorithm works on the top of the heuristics to tune the control parameters. As a result, optimal solution to the considered problem is more likely to be constructed from the heuristics with the optimal control parameters. The proposed algorithm is evaluated experimentally in comparison with the latest heuristics based on the IP software CPLEX, and the "zoom-in"-based approach on 28 test networks problems. The experimental results demonstrate that the proposed algorithm is more effective in finding high-quality topologies than the IP-based heuristic algorithm in 21 out of 28 test instances with much less computational costs, and performs significantly better than the "zoom-in"-based approach in 19 instances with the same computational costs.

This paper summaries our recent work on combining estimation of distribution algorithms (EDA) and other techniques for solving hard search and optimization problems: a) guided mutation, an offspring generator in which the ideas from EDAs and genetic algorithms are combined together, we have shown that an evolutionary algorithm with guided mutation outperforms the best GA for the maximum clique problem, b) evolutionary algorithms refining a heuristic, we advocate a strategy for solving a hard optimization problem with complicated data structure, and c) combination of two different local search techniques and EDA for numerical global optimization problems, its basic idea is that not all the new generated points are needed to be improved by an expensive local search.

An evolutionary algorithm (EA) can be used to tune the control parameters of a construction heuristic to an optimization problem and generate a nearly optimal solution. This approach is in the spirit of indirect encoding EAs. Its performance relies on both the heuristic and the EA. This paper proposes a three-phase parameterized construction heuristic for the shared-path protection problem in wavelength division multiplexing networks with shared-risk link group constraints and applies an EA for optimizing the control parameters of the proposed heuristics. The experimental results show that the proposed approach is effective on all the tested network instances. It was also demonstrated that an EA with guided mutation performs better than a conventional genetic algorithm for tuning the control parameters, which indicates that a combination of global statistical information extracted from the previous search and location information of the best solutions found so far could improve the performance of an algorithm.

Estimation of distribution algorithms sample new solutions (offspring) from a probability model which characterizes the distribution of promising solutions in the search space at each generation. The location information of solutions found so far (i.e., the actual positions of these solutions in the search space) is not directly used for generating offspring in most existing estimation of distribution algorithms. This paper introduces a new operator, called guided mutation. Guided mutation generates offspring through combination of global statistical information and the location information of solutions found so far. An evolutionary algorithm with guided mutation (EA/G) for the maximum clique problem is proposed in this paper. Besides guided mutation, EA/G adopts a strategy for searching different search areas in different search phases. Marchiori's heuristic is applied to each new solution to produce a maximal clique in EA/G. Experimental results show that EA/G outperforms the heuristic genetic algorithm of Marchiori (the best evolutionary algorithm reported so far) and a MIMIC algorithm on DIMACS benchmark graphs.

Differential evolution (DE) was very successful in solving the global continuous optimization problem. It mainly uses the distance and direction information from the current population to guide its further search. Estimation of distribution algorithm (EDA) samples new solutions from a probability model which characterizes the distribution of promising solutions. This paper proposes a combination of DE and EDA (DE/EDA) for the global continuous optimization problem. DE/EDA combines global information extracted by EDA with differential information obtained by DE to create promising solutions. DE/EDA has been compared with the best version of the DE algorithm and an EDA on several commonly utilized test problems. Experimental results demonstrate that DE/EDA outperforms the DE algorithm and the EDA. The effect of the parameters of DE/EDA to its performance is investigated experimentally.

Recently, MOEA/D (multi-objective evolutionary algorithm based on decomposition) has achieved great success in the field of evolutionary multi-objective optimization and has attracted a lot of attention. It decomposes a multi-objective optimization problem (MOP) into a set of scalar subproblems using uniformly distributed aggregation weight vectors and provides an excellent general algorithmic framework of evolutionary multi-objective optimization. Generally, the uniformity of weight vectors in MOEA/D can ensure the diversity of the Pareto optimal solutions, however, it cannot work as well when the target MOP has a complex Pareto front (PF; i.e., discontinuous PF or PF with sharp peak or low tail). To remedy this, we propose an improved MOEA/D with adaptive weight vector adjustment (MOEA/D-AWA). According to the analysis of the geometric relationship between the weight vectors and the optimal solutions under the Chebyshev decomposition scheme, a new weight vector initialization method and an adaptive weight vector adjustment strategy are introduced in MOEA/D-AWA. The weights are adjusted periodically so that the weights of subproblems can be redistributed adaptively to obtain better uniformity of solutions. Meanwhile, computing efforts devoted to subproblems with duplicate optimal solution can be saved. Moreover, an external elite population is introduced to help adding new subproblems into real sparse regions rather than pseudo sparse regions of the complex PF, that is, discontinuous regions of the PF. MOEA/D-AWA has been compared with four state of the art MOEAs, namely the original MOEA/D, Adaptive-MOEA/D, [Formula: see text]-MOEA/D, and NSGA-II on 10 widely used test problems, two newly constructed complex problems, and two many-objective problems. Experimental results indicate that MOEA/D-AWA outperforms the benchmark algorithms in terms of the IGD metric, particularly when the PF of the MOP is complex.

In this paper, we propose a multi-restart memetic algorithm framework for box constrained global continuous optimisation. In this framework, an evolutionary algorithm (EA) and a local optimizer are employed as separated building blocks. The EA is used to explore the search space for very promising solutions (e.g., solutions in the attraction basin of the global optimum) through its exploration capability and previous EA search history, and local search is used to improve these promising solutions to local optima. An estimation of distribution algorithm (EDA) combined with a derivative free local optimizer, called NEWUOA (M. Powell, Developments of NEWUOA for minimization without derivatives. Journal of Numerical Analysis, 28:649–664, 2008 ), is developed based on this framework and empirically compared with several well-known EAs on a set of 40 commonly used test functions. The main components of the specific algorithm include: (1) an adaptive multivariate probability model, (2) a multiple sampling strategy, (3) decoupling of the hybridisation strategy, and (4) a restart mechanism. The adaptive multivariate probability model and multiple sampling strategy are designed to enhance the exploration capability. The restart mechanism attempts to make the search escape from local optima, resorting to previous search history. Comparison results show that the algorithm is comparable with the best known EAs, including the winner of the 2005 IEEE Congress on Evolutionary Computation (CEC2005), and significantly better than the others in terms of both the solution quality and computational cost.

This paper gives a comprehensive review of the application of meta-heuristics to optimization problems in systems biology, mainly focussing on the parameter estimation problem (also called the inverse problem or model calibration). It is intended for either the system biologist who wishes to learn more about the various optimization techniques available and/or the meta-heuristic optimizer who is interested in applying such techniques to problems in systems biology. First, the parameter estimation problems emerging from different areas of systems biology are described from the point of view of machine learning. Brief descriptions of various meta-heuristics developed for these problems follow, along with outlines of their advantages and disadvantages. Several important issues in applying meta-heuristics to the systems biology modelling problem are addressed, including the reliability and identifiability of model parameters, optimal design of experiments, and so on. Finally, we highlight some possible future research directions in this field.

In this paper, a hierarchical evolutionary approach is proposed for an NP-complete telecommunication problem– all optical WDM mesh network survivability under shared-rish-link-group (SRLG) constraints. A parameterized greedy heuristic is proposed at first to construct solutions of the telecommunication problem. A specific estimation of distribution algorithm (EDA) searches for optimal parameters of the greedy heuristic, and thereafter to construct the optimal solution. Experimental results show that the proposed approach performs significantly better than the best-known evolutionary-based algorithm in 25 out of 30 test instances in terms of solution quality and CPU times.

This paper introduces a new hybrid evolutionary algorithm (EA) for continuous global optimization problems, called estimation of distribution algorithm with local search (EDA/L). Like other EAs, EDA/L maintains and improves a population of solutions in the feasible region. Initial candidate solutions are generated by uniform design, these solutions evenly scatter over the feasible solution region. To generate a new population, a marginal histogram model is built based on the global statistical information extracted from the current population and then new solutions are sampled from the model thus built. The incomplete simplex method applies to every new solution generated by uniform design or sampled from the histogram model. Unconstrained optimization by diagonal quadratic approximation applies to several selected resultant solutions of the incomplete simplex method at each generation. We study the effectiveness of main components of EDA/L. The experimental results demonstrate that EDA/L is better than four other recent EAs in terms of the solution quality and the computational cost.