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Differential Evolution (DE) is one of the most effective approaches in Evolutionary Computation to tackling complex black-box optimization, however, the overall performance of a DE variant is heavily dependent on its mutation strategy and the associated parameter control schemes. According to the “No free Lunch theorem”, every mutation strategy has its own fatal defect, therefore, DE variant with a single mutation strategy can not tackle all optimization problems. Furthermore, DE variant with ensemble of mutation strategies usually needs more parameter control schemes, which inevitably decreases the practicality of it. Here in this paper, a novel Cooperative Strategy based DE (CS-DE) with population diversity enhancement is proposed, and the CS-DE algorithm has the following contributions: First, a cooperative strategy pool containing two similar mutation strategies is advanced in the algorithm, and the two mutation strategies share the same parameter control. Second, a novel grouping strategy is proposed, then the two mutation strategies can be chosen in an adaptive manner by different individuals in generating trial vectors during the evolution. Third, novel adaptation schemes for the three control parameters F , CR and PS as well as a stagnation based re-initialization mechanism are also proposed in our CS-DE algorithm. 58 benchmarks from the CEC2013 and CEC2014 test suites are employed in algorithm validation, and experiment results show the competitiveness of the CS-DE algorithm with several state-of-the-art DE variants.

No Free Lunch Theorem presents a dilemma in the evaluation of emerging evolutionary algorithms in terms of handling various real world problems and their unknown internal structures, since the performances of these algorithms are related to the corresponding benchmarks. Although white and black box schemes have made impressive progress in overcoming this dilemma, such as clear property definition and basis function composition, the evaluation of algorithms on sophisticated suites remains insufficient on account of the limited quantity and diversity of such benchmarks, which can induce bias in a narrow problem domain. Therefore, this study proposes a novel framework for randomly generating diversified benchmark functions to comprehensively evaluate evolutionary algorithms in a black box scenario. The proposed approach adopts a recurrent neural network with various activation functions to produce test problems with important characteristics such as ruggedness and multi-funnels. In addition, the proposed framework can generate virtually limitless chaotic benchmarks by using random weights. The experimental results demonstrate a distinct difference among the performance of the tested optimizers on the proposed problems and the well-known BBOB and CEC problems, which implies the necessity of the proposed benchmarks when facilitating a more comprehensive evaluation.

Owing to no free lunch theorem, meta-heuristic search algorithms, behaviour and performance are different for solving specific class of optimization problems than another. Further, search algorithms are conceptualized of exploration and exploitation aspects. Ameliorated grey wolf optimization algorithm is proposed to solve economic power load dispatch problem that synergizes between exploration and exploitation aspects. Ameliorated grey wolf optimization procedure coordinates the behaviour of grey wolves, random exploratory search, local random search and opposition learning heuristics. Grey wolf optimization algorithm is considered to perform global search and random exploratory search applied to perform a search in the neighbourhood of already visited search locations. To maintain good solutions and diversity among solutions, opposition based learning has been implemented. The practical aspects i.e. value-point loading effect, avoidance of prohibited operating zones and ramp rate limits, generation limits of generators and satisfaction of power demand constraint are undertaken to solve economic power load dispatch problem. Heuristic search is exploited to handle equality constraints. The proposed algorithm is validated on standard benchmark functions and medium to large electric power systems. Results reveal that proposed technique is a potential method to solve economic load dispatch problems as it competes with recent algorithms undertaken for comparison.

This paper addresses a newly introduced variant of traveling salesman problem, viz. k-Interconnected Multi-Depot Multi-Traveling Salesman Problem (k-IMDMTSP). This problem has the potential to address a variety of problems as it is a general problem that can change its characteristics according to the combination of parameter values. In fact, k-IMDMTSP can become an altogether different problem depending on the choice of its parameter values. According to the No Free Lunch Theorem [43], it is not possible to have a general algorithm that can outperform all algorithms across all problems emanating from k-IMDMTSP due to various parameter values. However, an appropriate combination of different algorithms can successfully deal with all such problems emanating from k-IMDMTSP. Here, we have made an attempt in this direction with the help of hyper-heuristics. A hyper-heuristic based artificial bee colony algorithm is proposed for k-IMDMTSP. A new solution encoding scheme is proposed for representing a k-IMDMTSP solution within the proposed approach, and its associated search space is analyzed theoretically. It has been proved that our encoding scheme yields a search space that is considerably smaller in comparison to encoding schemes used previously. Experimental results on standard benchmark instances show that the proposed approach outperforms other state-of-the-art approaches available in literature in terms of both solution quality and running time.

The No Free Lunch Theorem establishes that for any algorithm, any elevated performance over one class of problems is offset by performance over another class. Empirically, this is true for Granularity Control algorithms, particularly in Fork-Join style concurrent programs. Cut-off Algorithms make the decision to either continue forking work (parallelising) or instead computing the remaining execution branches sequentially. These algorithms affect how well a program dynamically adjusts to the parallelism available in the machine. To put things into context, choosing the wrong algorithm can make a program go from 30 s of execution to over a day. Cut-off Algorithms such as Max-Tasks, Max-Level, SurplusTasks and variants do not provide the same performance improvements over the same classes of Fork-Join programs. Thus, programmers have to decide which Cut-off Algorithms to use on different classes of problems. Finding the right Cut-off Algorithm is a time-consuming task, as, most of times, it requires trial-and-error execution of several configurations before determining the right solution. To the best of our knowledge, there is no definitive solution for making this decision automatically. Being able to do so would largely enhance the performance of parallel programs generated by optimising compilers and/or executed by parallelising frameworks. In this work, we address the problem of automatically selecting the right Cut-off Algorithm for highly parallel programs. We evaluate the performance of nowadays most relevant Cut-off Algorithms over different programs. We identify possible correlations between program characteristics and performance improvements observed with different cut-off strategies. Finally, we derive a set classification rules for selection of Cut-off Algorithms that can be integrated into compilers and frameworks that perform automatic parallelisation of programs.

Feature selection has become an indispensable preprocessing step in data mining problems as high amount of data become prevalent with the advances in technology. The objective of feature selection is twofold: reducing data amount and improving learning performance. In this study, we leverage the multi-core nature of a regular PC to build a robust framework for feature selection. This framework executes the feature selection algorithm on four processors, in parallel. As per the No Free Lunch Theorem, we facilitate 40 different execution settings for the processors by employing two multiobjective selection algorithms, four initial population generation methods, and five machine learning techniques. Besides, we introduce six setting selection schemes to decide the most fruitful setting for each processor. We carry out extensive experiments on 11 UCI benchmark datasets and analyze the results with statistical tests. Finally, we compare our proposed method with state-of-the-art studies and record remarkable improvement in terms of maximum accuracy.

Several reasons such as no free lunch theorem indicates that any learning algorithm in combination with a specific feature selection (FS) technique may give more accurate estimation than other learning algorithms. Therefore, there is not a universal approach that outperforms other algorithms. Moreover, due to the large number of FS techniques, some recommended solutions such as using synthetic dataset or combining different FS techniques are very tedious and time consuming. In this study to tackle the issue of more accurate estimation of NPPs parameters, the performance of the major supervised learning algorithms in combination with the different FS techniques which are appropriate for parameters estimation is considered. The target parameters/transients of the Bushehr nuclear power plant (BNPP) are examined as the case study. By comparing three major supervised learning algorithms (i.e. the MLP-BR, the MLP-LM, and the SVM) in combination with six principal FS techniques (i.e. the NCA, the F-test, the Kendall’s tau, the Pearson, the Spearman, and the Relief) for estimation of three important parameters of NPP (i.e. FMT, CMT, and the DNBR), the BR learning algorithm gives the more accurate results. Therefore, the results show that if the number of FS techniques is m and the number of learning algorithms is n, the search space for more accurate estimation of the NPPs important parameters can be reduced from n × m to 1 × m.

An existing estimation distribution algorithm (EDA) with univariate marginal Gaussian model was improved by designing and incorporating an extreme elitism selection method. This selection method highlighted the effect of a few top best solutions in the evolution and advanced EDA to form a primary evolution direction and obtain a fast convergence rate. Simultaneously, this selection can also keep the population diversity to make EDA avoid premature convergence. Then the modified EDA was tested by means of benchmark low-dimensional and high-dimensional optimization problems to illustrate the gains in using this extreme elitism selection. Besides, no-free-lunch theorem was implemented in the analysis of the effect of this new selection on EDAs.

Well placement optimization is one of the major challenging factors in the field development process of oil and gas industry. The objective function of well placement optimization is considered as high dimensional, discontinuous and multi-model. Over the last decade, both gradient-based and gradient-free optimization methods have been implemented to tackle this problem. Nature-inspired gradient-free optimization algorithms like particle swarm optimization, genetic algorithm, covariance matrix adaptation evolution strategy and differential evolution have been utilized in this area. These optimization techniques are implemented as stand-alone or as hybrid form to maximize the economic factors. In this paper, several nature-inspired metaheuristic optimization techniques and their application to maximize the economic factors are reviewed. Newly developed optimization algorithms are very efficient and favorable when compared to other established optimization algorithms and in all cases, it has been noticed that hybridization of two or more algorithms works better than stand-alone algorithms. Furthermore, none of the single optimization techniques can be established as being universally superior which aligns with no free lunch theorem. For future endeavor, combining optimization methods and exploiting multiple optimization processes for faster convergence and developing efficient proxy model is expected.

Swarm intelligent algorithms focus on imitating the collective intelligence of a group of simple agents that can work together as a unit. Such algorithms have particularly significant impact in the fields like optimization and artificial intelligence (AI). This research article focus on a recently proposed swarm-based metaheuristic called the Artificial Bee Colony (ABC) algorithm and suggests modification to the algorithmic framework in order to enhance its performance. The proposed ABC variant shall be referred to as Migratory Multi-swarm Artificial Bee Colony (MiMSABC) algorithm. Different perturbation schemes of ABC function differently in varying landscapes. Hence to maintain the basic essence of all these schemes, MiMSABC deploys a multiple swarm populations that are characterized by different and unique perturbation strategies. The concept of reinitializing foragers around a depleted food source using a limiting parameter, as often used conventionally in ABC algorithms, has been avoided. Instead a performance based set of criteria has been introduced to thoroughly detect subpopulations that have shown limited progress to eke out the global optimum. Once failure is detected in a subpopulation provisions have been made so that constituent foragers can migrate to a better performing subpopulation, maintaining, however, a minimum number of members for successful functioning of a subpopulation. To evaluate the performance of the algorithm, we have conducted comparative study involving 8 algorithms for testing the problems on 25 benchmark functions set proposed in the Special Session on IEEE Congress on Evolutionary Competition 2005. Thorough a detailed analysis we have highlighted the statistical superiority of our proposed MiMSABC approach over a set of population based metaheuristics.

The weighted circle packing problem is a kind of important combination optimization problem and has the NP-hard property. Inspired by the No Free Lunch Theorem, a knowledge-based heuristic particle swarm optimization approach with the adjustment strategy (KHPSOA) is developed for this problem. The knowledge (e.g., the relation between its weight matrix and better solution) is obtained from this problem itself and existing layout scheme diagrams and applied to form more effective ordering and positioning rules of the proposed heuristic method. A better layout scheme of larger circles is obtained through the heuristic method. The optimal solution of this problem is obtained by inserting a few residual smaller circles into the gaps of the better layout scheme and further optimizing it through the proposed particle swarm optimization with the adjustment strategy. The numerical experiments show that KHPSOA is superior to the existing algorithms in the performances.

Economic dispatch (ED) is an important task in power system operation. It is able to decrease the operating cost, save energy resources, and reduce environmental load. In this paper, a multi-strategy ensemble biogeography-based optimization (MsEBBO) based method for ED problems is proposed. BBO is a population-based meta-heuristic algorithm inspired by the science of biogeography and mainly consists of three components: migration model, migration operator, and mutation operator. It has good local exploitation ability but lacks satisfactory global exploration ability. To keep a proper balance between exploration and exploitation, MsEBBO has three extensions to BBO’s three components according to the no free lunch theorem. First, a nonlinear migration model based on sinusoidal curve is employed. Second, a backup migration operator through adopting a backup strategy to combine perturb operator and blended operator is presented. This operator can make the entire population fully exchange or share information and thus further strengthen the exploitation ability. Finally, both differential mutation and Levy local search are embedded as mutation operator for MsEBBO using a similar backup strategy. Gaining from this mutation operator, MsEBBO can be accelerated to escape from local optima and perform efficient search within global range. Additionally, an effective repair technique is proposed to handle different constraints of ED problems. The performance of MsEBBO is tested on four ED problems with diverse complexities. Experimental results and comparisons with other recently reported ED solution methods confirm that MsEBBO is capable of yielding a good balance between exploration and exploitation, and obtaining competitive solution quality. Moreover, the sensitivity of MsEBBO to variations in population size is investigated as well.

The No-Free-Lunch theorem states that there does not exist a genuine general-purpose optimizer because all algorithms have the identical performance on average over all functions. However, such a result does not imply that search heuristics or optimization algorithms are futile if we are more cautious with the applicability of these methods and the search space. In this paper, within the No-Free-Lunch framework, we firstly introduce the discrete Lipschitz class by transferring the Lipschitz functions, i.e., functions with bounded slope, as a measure to fulfill the notion of continuity in discrete functions. We then investigate the properties of the discrete Lipschitz class, generalize an algorithm called subthreshold-seeker for optimization, and show that the generalized subthreshold-seeker outperforms random search on this class. Finally, we propose a tractable sampling-test scheme to empirically demonstrate the superiority of the generalized subthreshold-seeker under practical configurations. This study concludes that there exist algorithms outperforming random search on the discrete Lipschitz class in both theoretical and practical aspects and indicates that the effectiveness of search heuristics may not be universal but still general in some broad sense.

Bus terminal assignment with the objective of maximizing public transportation service is known as bus terminal location problem (BTLP). We formulate the BTLP, a problem of concern in transportation industry, as a p-uncapacitated facility location problem (p-UFLP) with distance constraint. The p-UFLP being NP-hard (Krarup and Pruzan, 1990), we propose evolutionary algorithms for its solution. According to the No Free Lunch theorem and the good efficiency of the distinctive preserve recombination (DPX) operator, we design a new recombination operator for solving a BTLP by new evolutionary and memetic algorithms namely, genetic local search algorithms (GLS). We also define the potential objective function (POF) for the nodes and design a new mutation operator based on POF. To make the memetic algorithm faster, we estimate the variation of the objective function based on POF in the local search as part of an operator in memetic algorithms. Finally, we explore numerically the performance of nine proposed algorithms on over a thousand randomly generated problems and select the best two algorithms for further testing. The comparative studies show that our new hybrid algorithm composing the evolutionary algorithm with the GLS outperforms the multistart simulated annealing algorithm.

Mutation operators such as Gaussian, Levy and Cauchy have been used with evolutionary programming (EP). According to the no free lunch theorem, it is impossible for EP with a single mutation operator to outperform always. For example, Classical EP (CEP) with Gaussian mutation is better at searching in a local neighborhood while the Fast EP (FEP) with the Cauchy mutation performs better over a larger neighborhood. Motivated by these observations, we propose an ensemble approach where each mutation operator has its associated population and every population benefits from every function call. This approach enables us to benefit from different mutation operators with different parameter values whenever they are effective during different stages of the search process. In addition, the recently proposed Adaptive EP (AEP) using Gaussian (ACEP) and Cauchy (AFEP) mutations is also evaluated. In the AEP, the strategy parameter values are adapted based on the search performance in the previous few generations. The performance of ensemble is compared with a mixed mutation strategy, which integrates several mutation operators into a single algorithm as well as against the AEP with a single mutation operator. Improved performance of the ensemble over the single mutation-based algorithms and mixed mutation algorithm is verified using statistical tests.

This paper introduces a new method for learning algorithm evaluation and selection, with empirical results based on classification. The empirical study has been conducted among 8 algorithms/classifiers with 100 different classification problems. We evaluate the algorithms' performance in terms of a variety of accuracy and complexity measures. Consistent with the No Free Lunch theorem, we do not expect to identify the single algorithm that performs best on all datasets. Rather, we aim to determine the characteristics of datasets that lend themselves to superior modelling by certain learning algorithms. Our empirical results are used to generate rules, using the rule-based learning algorithm C5.0, to describe which types of algorithms are suited to solving which types of classification problems. Most of the rules are generated with a high confidence rating.

Optimization (adaptation) of agents interacting with dynamic persistent environments (DPEs) poses a separate class of problems from those of static optimization. Such environments must be incorporated into models of interactive computation.By the No Free Lunch Theorem (NFLT), no general-purpose function-optimization algorithm can exist that is superior to random search. But interactive adaptation in environments with persistent state falls outside the scope of the NFLT, and useful general-purpose interactive optimization protocols for DPEs exist, as we show.Persistence of state supports indirect interaction. Based on the observation that mutual causation is inherent to interactive computation, and on the key role of persistent state in multiagent systems, we establish that indirect interaction is essential to multiagent systems (MASs).This work will be useful to researchers in coordination, evolutionary computation, and design of multiagent and adaptive systems.

The No Free Lunch (NFL) theorem due to Wolpert and Macready (IEEE Trans. Evol. Comput. 1(1) (1997) 67) has led to controversial discussions on the usefulness of randomized search heuristics, in particular, evolutionary algorithms. Here a short and simple proof of the NFL theorem is given to show its elementary character. Moreover, the proof method leads to a generalization of the NFL theorem. Afterwards, realistic complexity theoretical-based scenarios for black box optimization are presented and it is argued why NFL theorems are not possible in such situations. However, an Almost No Free Lunch (ANFL) theorem shows that for each function which can be optimized efficiently by a search heuristic there can be constructed many related functions where the same heuristic is bad. As a consequence, search heuristics use some idea how to look for good points and can be successful only for functions “giving the right hints”. The consequences of these theoretical considerations for some well-known classes of functions are discussed.