A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> 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. <s> BIB001 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> 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 (/spl mu/, /spl lambda/) 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 performance significantly. <s> BIB002 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> This paper presents a multi-populated differential evolution algorithm to solve real-parameter constrained optimization problems. The notion of the “ near feasibility threshold” is employed in the proposed algorithm to penalize the infeasible solutions. The algorithm was tested using benchmark instances in Congress on Evolutionary Computation 2006. For these benchmark problems, the problem definition file, codes and evaluation criteria are available in http://www.ntu.edu.sg/home/EPNSugan. The performance of the multi-populated differential evolution algorithm is evaluated with the best known or optimal solutions provided in the literature. The experimental results with detailed statistics required for this session show that the proposed multi-populated differential algorithm was able to solve 22 out of 24 benchmark instances to either optimality or best known solutions in the literature. In addition, 6 out of 24 best known solutions are ultimately improved by the proposed multi-populated differential evolution algorithm. <s> BIB003 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> Solving constrained optimization problems (COPs) via evolutionary algorithms (EAs) has attracted much attention. In this article, an orthogonal design based constrained optimization evolutionary algorithm (ODCOEA) to tackle COPs is proposed. In principle, ODCOEA belongs to a class of steady state evolutionary algorithms. In the evolutionary process, several individuals are chosen from the population as parents and orthogonal design is applied to pairs of parents to produce a set of representative offspring. Then, after combining the offspring generated by different pairs of parents, non-dominated individuals are chosen. Subsequently, from the parent’s perspective, it is decided whether a non-dominated individual replaces a selected parent. Finally, ODCOEA incorporates an improved BGA mutation operator to facilitate the diversity of the population. The proposed ODCOEA is effectively applied to 12 benchmark test functions. The computational experiments show that ODCOEA not only quickly converges to optimal ... <s> BIB004 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> In this paper we present a boundary search based ACO algorithm for solving nonlinear constrained optimization problems. The aim of this work is twofold. Firstly, we present a modified search engine which implements a boundary search approach based on a recently proposed ACO metaheuristic for continues problems. Secondly, we propose the incorporation of the stochastic ranking technique to deal with feasible and infeasible solutions during the search which focuses on the boundary region. In our experimental study we compare the overall performance of the proposed ACO algorithm by including two different complementary constraint-handling techniques: a penalty function and stochastic ranking. In addition, we include in our comparison of results the stochastic ranking algorithm, which was originally implemented using an evolution strategy as its search engine. <s> BIB005 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> One of the most important issues in developing an evolutionary optimization algorithm is the proper handling of any constraints on the problem. One must balance the objective function against the degree of constraint violation in such a way that neither is dominant. Common approaches to strike this balance include implementing a penalty function and the more recent stochastic ranking method, but these methods require an extra tuning parameter which must be chosen by the user. The present paper demonstrates that a proper balance can be achieved using an addition of ranking method. Through the ranking of the individuals with respect to the objective function and constraint violation independently, we convert these two properties into numerical values of the same order of magnitude. This removes the requirement of a user-specified penalty coefficient or any other tuning parameters. Direct addition of the ranking terms is then performed to integrate all information into a single decision variable. This approach is incorporated into a (@m,@l) evolution strategy and tested on thirteen benchmark problems, one engineering design problem, and five difficult problems with a high dimensionality or many constraints. The performance of the proposed strategy is similar to that of the stochastic ranking method when dealing with inequality constraints, but it has a much simpler ranking procedure and does not require any tuning parameters. A percentage-based tolerance value adjustment scheme is also proposed to enable feasible search when dealing with equality constraints. <s> BIB006 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> This paper presents a novel evolutionary algorithm (EA) for constrained optimization problems, i.e., the hybrid constrained optimization EA (HCOEA). This algorithm effectively combines multiobjective optimization with global and local search models. In performing the global search, a niching genetic algorithm based on tournament selection is proposed. Also, HCOEA has adopted a parallel local search operator that implements a clustering partition of the population and multiparent crossover to generate the offspring population. Then, nondominated individuals in the offspring population are used to replace the dominated individuals in the parent population. Meanwhile, the best infeasible individual replacement scheme is devised for the purpose of rapidly guiding the population toward the feasible region of the search space. During the evolutionary process, the global search model effectively promotes high population diversity, and the local search model remarkably accelerates the convergence speed. HCOEA is tested on 13 well-known benchmark functions, and the experimental results suggest that it is more robust and efficient than other state-of-the-art algorithms from the literature in terms of the selected performance metrics, such as the best, median, mean, and worst objective function values and the standard deviations <s> BIB007 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> How much attention should be paid to the promising infeasible solutions during the evolution process is investigated in this paper. Stochastic ranking has been demonstrated as an effective technique for constrained optimization. In stochastic ranking, the comparison probability will affect the position of feasible solution after ranking, and the quality of the final solutions. In this paper, the dynamic stochastic selection (DSS) is put forward within the framework of multimember differential evolution. Firstly, a simple version named DSS-MDE is given, where the comparison probability decreases linearly. The algorithm DSS-MDE has been compared with two state-of-the-art evolution strategies and three competitive differential evolution algorithms for constrained optimization on 13 common benchmark functions. DSS-MDE is also evaluated on four well-studied engineering design examples, and the experimental results are significantly better than current available results. Secondly, other dynamic settings of the comparison probability for DSS-MDE are also designed and tested. From the experimental results, DSS-MDE is effective for constrained optimization. Finally, DSS-MDE with a square root adjusted comparison probability is evaluated on the 22 benchmark functions in CEC'06, and the experimental results on most functions are competitive. <s> BIB008 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> The present paper proposes a double-multiplicative penalty strategy for constrained optimization by means of genetic algorithms (GAs). The aim of this research is to provide a simple and efficient way of handling constrained optimization problems in the GA framework without the need for tuning the values of penalty factors for any given optimization problem. After a short review on the most popular and effective exterior penalty formulations, the proposed penalty strategy is presented and tested on five different benchmark problems. The obtained results are compared with the best solutions provided in the literature, showing the effectiveness of the proposed approach. <s> BIB009 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> This paper presents an improved particle swarm optimization algorithm with feasibility- based rules (FRIPSO) to solve mixed-variable constrained optimization problems. Different kinds of variables are dealt in different ways in FRIPSO algorithm. Constraint handling is based on simple feasibility-based rules without the use of a penalty function which is frequently cumbersome to parameterize, nor need it to guarantee the particles be in the feasible region at all time which turn out to cost much time sometimes. In order to improve the convergence speed of FRIPSO with the iteration growing and to find global optimum, the standard PSO is used to find a better position for the best history position of the swarm on the condition that the discrete value are same with those of Gbest in each iteration. Two practical benchmark mixed-variable optimization problems are tested by our FRIPSO algorithm to demonstrate the effectiveness and robustness of the proposed approach. <s> BIB010 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> In this paper, we propose a methodology to improve the performance of the standard Differential Evolution (DE) in constraint optimization applications, in terms of accelerating its search speed, and improving the success rate. One critical mechanism embedded in the approach is applying Stochastic Ranking (SR) to rank the whole population of individuals with both objective value and constraint violation to be compared. The ranked population is then in a better shape to provide useful information e.g. direction to guide the search process. The strength of utilizing the directional information can be further controlled by a parameter - population partitioning factor, which is adjusted according to the evolution stage and generations. Because the adaptive adjustment of the parameter is predefined and does not need user input, the resulting algorithm is free of definition of this extra parameter and easier to implement. The performance of the proposed approach, which we call SRaDE (Stochastic Ranking based Adaptive Differential Evolution) is investigated and compared with standard DE. The experimental results show that SRDE significantly outperforms, or at least is comparable with standard DE in all the tested benchmark functions. We also conducted an experiment to compare SRaDE with SRDE - a variant of Stochastic Ranking based Differential Evolution without adaptive adjustment of the population partitioning factor. Experimental results show that SRaDE can also achieve improved performance over SRDE. <s> BIB011 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> Evolutionary Algorithms are amongst the best known methods of solving difficult constraint optimization problems, for which traditional methods are not applicable. However, there are no inbuilt or organic mechanisms available in Evolutionary Algorithms for handling constraints in optimization problems. These problems are solved by converting or treating them as unconstrained optimization problems. Several constraint handling techniques have been developed and reported in literature, of which, the penalty factor and feasibility rules are the most promising and widely used for such purposes. However, each of these techniques has its own advantages and disadvantages and often require fine tuning of one or more parameters, which in itself becomes an optimization problem. This paper presents a hybrid constraint handling technique for a two population adaptive coevolutionary algorithm, which uses a self determining and regulating penalty factor method as well as feasibility rules for handling constraints. Thus, the method overcomes the drawbacks in both the methods and utilizes their strengths to effectively and efficiently handle constraints. The simulation on ten benchmark problems demonstrates the efficacy of the approach. <s> BIB012 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> Over the last few decades, many different variants of Genetic Algorithms (GAs) have been introduced for solving Constrained Optimization Problems (COPs). However, a comparative study of their performances is rare. In this paper, our objective is to analyze different variants of GA and compare their performances by solving the 36 CEC benchmark problems by using, a new scoring scheme introduced in this paper and, a nonparametric test procedure. The insights gain in this study will help researchers and practitioners to decide which variant to use for their problems. <s> BIB013 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> A variant of competitive differential evolution modified for the solution of single objective constrained realparameter optimization is presented in this paper. The modification consists in alternation of minimization of the constrains' violation and minimization of objective function value. The variant was tested on the family of 18 problems developed for the Special Session S000 of CEC2010. Using competitive setting avoids tuning of most control-parameter values because only size of population must be set by the user of the algorithm. The experimental results showed acceptable reliability of the search in most of test problems. <s> BIB014 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> During the last three decades, several constraint handling techniques have been developed to be used with evolutionary algorithms (EAs). According to the no free lunch theorem, it is impossible for a single constraint handling technique to outperform all other techniques on every problem. In other words, depending on several factors such as the ratio between feasible search space and the whole search space, multimodality of the problem, the chosen EA, and global exploration/local exploitation stages of the search process, different constraint handling methods can be effective during different stages of the search process. Motivated by these observations, we propose an ensemble of constraint handling techniques (ECHT) to solve constrained real-parameter optimization problems, where each constraint handling method has its own population. A distinguishing feature of the ECHT is the usage of every function call by each population associated with each constraint handling technique. Being a general concept, the ECHT can be realized with any existing EA. In this paper, we present two instantiations of the ECHT using four constraint handling methods with the evolutionary programming and differential evolution as the EAs. Experimental results show that the performance of ECHT is better than each single constraint handling method used to form the ensemble with the respective EA, and competitive to the state-of-the-art algorithms. <s> BIB015 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> This paper presents an ensemble of differential evolution algorithms employing the variable parameter search and two distinct mutation strategies in the ensemble to solve real-parameter constrained optimization problems. It is well known that the performance of DE is sensitive to the choice of mutation strategies and associated control parameters. For these reasons, the ensemble is achieved in such a way that each individual is assigned to one of the two distinct mutation strategies or a variable parameter search (VPS). The algorithm was tested using benchmark instances in Congress on Evolutionary Computation 2010. For these benchmark problems, the problem definition file, codes and evaluation criteria are available in http://www.ntu.edu.sg/home/EPNSugan. Since the optimal or best known solutions are not available in the literature, the detailed computational results required in line with the special session format are provided for the competition. <s> BIB016 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> Abstract In their original versions, nature-inspired search algorithms such as evolutionary algorithms and those based on swarm intelligence, lack a mechanism to deal with the constraints of a numerical optimization problem. Nowadays, however, there exists a considerable amount of research devoted to design techniques for handling constraints within a nature-inspired algorithm. This paper presents an analysis of the most relevant types of constraint-handling techniques that have been adopted with nature-inspired algorithms. From them, the most popular approaches are analyzed in more detail. For each of them, some representative instantiations are further discussed. In the last part of the paper, some of the future trends in the area, which have been only scarcely explored, are briefly discussed and then the conclusions of this paper are presented. <s> BIB017 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> Over the last two decades, many sophisticated evolutionary algorithms have been introduced for solving constrained optimization problems. Due to the variability of characteristics in different COPs, no single algorithm performs consistently over a range of problems. In this paper, for a better coverage of the problem characteristics, we introduce an algorithm framework that uses multiple search operators in each generation. The appropriate mix of the search operators, for any given problem, is determined adaptively. The framework is tested by implementing two different algorithms. The performance of the algorithms is judged by solving 60 test instances taken from two constrained optimization benchmark sets from specialized literature. The first algorithm, which is a multi-operator based genetic algorithm (GA), shows a significant improvement over different versions of GA (each with a single one of these operators). The second algorithm, using differential evolution (DE), also confirms the benefit of the multi-operator algorithm by providing better and consistent solutions. The overall results demonstrated that both GA and DE based algorithms show competitive, if not better, performance as compared to the state of the art algorithms. <s> BIB018 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> Abstract: Artificial Bee Colony (ABC) algorithm was firstly proposed for unconstrained optimization problems on where that ABC algorithm showed superior performance. This paper describes a modified ABC algorithm for constrained optimization problems and compares the performance of the modified ABC algorithm against those of state-of-the-art algorithms for a set of constrained test problems. For constraint handling, ABC algorithm uses Deb's rules consisting of three simple heuristic rules and a probabilistic selection scheme for feasible solutions based on their fitness values and infeasible solutions based on their violation values. ABC algorithm is tested on thirteen well-known test problems and the results obtained are compared to those of the state-of-the-art algorithms and discussed. Moreover, a statistical parameter analysis of the modified ABC algorithm is conducted and appropriate values for each control parameter are obtained using analysis of the variance (ANOVA) and analysis of mean (ANOM) statistics. <s> BIB019 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> Artificial immune systems (AISs) are computational intelligence (CI) oriented methods using information based on biological immune systems. In this study, an AIS, which combines the metaphor of clonal selection with idiotypic network theories, is developed. Although they are contradictory approaches, clonal selection and idiotypic network may prove useful in designing a stochastic global optimization tool. The AIS method consists of idiotypic network selection, somatic hypermuation, receptor editing and bone marrow operators. The idiotypic network selection operator determines the number of good solutions. The somatic hypermutation and receptor editing operators comprise the searching mechanisms for the exploration of the solution space. Diversity on the population of solutions is ensured by the bone marrow operator. The performance of the proposed AIS method is tested on a set of global constrained optimization problems (GCO), comprising of four benchmark nonlinear programming problems and four generalized polynomial programming (GPP) problems, where GPP problems are nonconvex optimization problems. The best solution found by the AIS algorithm is compared with the known global optimum. Numerical results show that the proposed method converged to the global optimal solution to each tested CGO problem. Moreover, this study compares the numerical results obtained by the AIS approach with those taken from published CI approaches, such as alternative AIS methods and genetic algorithms. <s> BIB020 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> Differential evolution (DE) is a powerful evolutionary algorithm (EA) for numerical optimization. Combining with the constraint-handling techniques, recently, DE has been successfully used for the constrained optimization problems (COPs). In this paper, we propose the adaptive ranking mutation operator (ARMOR) for DE when solving the COPs. The ARMOR is expected to make DE converge faster and achieve feasible solutions faster. In ARMOR, the solutions are adaptively ranked according to the situation of the current population. More specifically, the population is classified into three situations, i.e., infeasible situation, semi-feasible situation, and feasible situation. In the infeasible situation, the solutions are ranked only based on their constraint violations; in the semi-feasible situation, they are ranked according to the transformed fitness; while in the feasible situation, the objective function value is used to assign ranks to different solutions. In addition, the selection probability of each solution is calculated differently in different situations. The ARMOR is simple, and it can be easily combined with most of constrained DE (CDE) variants. As illustrations, we integrate our approach into three representative CDE variants to evaluate its performance. The 24 benchmark functions presented in CEC 2006 and 18 benchmark functions presented in CEC 2010 are chosen as the test suite. Experimental results verify our expectation that the ARMOR is able to accelerate the original CDE variants in the majority of test cases. Additionally, ARMOR-based CDE is able to provide highly competitive results compared with other state-of-the-art EAs. <s> BIB021 </s> A Survey on Home Energy Management <s> 4) CURRENT CONSTRAINT-HANDLING TECHNIQUES <s> A new rank-based CHT is presented for the solution of engineering optimization problems.Builds multiple separate queues based on objective function and violation of each constraint.Overcomes difficulties for constraints with different orders of magnitude and different units.Easy to implement; without user-defined parameters; may be associated with any evolutionary algorithm.Benchmark studies compare its performance with other well-known CHTs.Results demonstrate its increased accuracy and robustness. This work presents a constraint handling technique (CHT) for the solution of real-world engineering optimization problems by evolutionary algorithms. Referred to as the Multiple Constraint Ranking (MCR), it extends the rank-based approach from many CHTs, by building multiple separate queues based on the values of the objective function and the violation of each constraint. This way, it overcomes difficulties found by other techniques when faced with complex problems characterized by several constraints with different orders of magnitude and/or different units.The MCR follows an uncoupled approach where the CHT is not embedded into the optimization algorithm. Extensive studies are performed to assess its accuracy and robustness, compared to six other up-to-date CHTs, all implemented into the same canonical Genetic Algorithm to allow a neutral and unbiased evaluation. The numerical experiments comprise benchmark functions from the IEEE-CEC competitions on constrained optimization, and also classical structural engineering problems. The performance of the CHTs is compared using efficiency measures in terms of nonparametric statistical tests. The results indicate that the MCR is remarkably more accurate and robust for the subset of problems presenting different-magnitude constraints, while remaining very competitive and one of the top-performers for all other benchmark problems comprising the case studies. <s> BIB022
The so-called current CHTs consist mostly in modifications to existing techniques, split into the following main approaches BIB017 : (a) Feasibility rules -widely employed in heuristic and metaheuristic methodologies considered in the context of GA BIB018 , BIB013 , DE  - BIB014 , PSO BIB010 -  and artificial bee colony (ABC)  , BIB019 . (b) Stochastic ranking (SR) -this technique was originally proposed to address the shortcomings of penalty functions, resulting from poor tuning BIB002 . SR has been widely applied together with evolutionary strategies BIB002 , DE BIB008 , BIB011 and ant colony optimisation BIB005 ,  . It is based on the definition of a penalty function, which quantifies the degree of constraint violation of a candidate solution, implementing an adaptive ranking of candidate solutions, taking into account the underlying objective and penalty function values. Pairs of feasible solutions are compared based on the objective function, whereas for pairs with one or both infeasible solutions a user-defined probability P f determines whether comparisons are carried out using the objective or penalty functions. Other ranking-based techniques can be found in the literature, namely adaptive ranking mutation operator BIB021 and multiple ranking BIB006 , BIB022 . The popularity of these techniques is mainly due to simplicity and ease of integration with population-based heuristic and metaheuristic algorithms. This parameter has a strong influence on the selective pressure of feasible solutions BIB017 . Larger values allow deeper infeasible regions to be explored, while smaller values increase selective pressure, which results in fewer feasible solutions. Hence, a careful tuning of this parameter is required, being a constant value is commonly adopted, although a dynamic conditioning version of can also be found in the literature (see e.g.  ). (d) Penalty functions -despite their shortcomings, they still remain a popular CHT, in particular those embedding adaptive features BIB017 . New penalty functions have explored co-evolution and multi-population concepts, such as in  , BIB003 , BIB012 . Heuristic and metaheuristic algorithms, such as DE  , BIB012 , GA BIB009 , PSO  and artificial immune systems BIB020 take advantage of this approach. (e) Special operators -despite the active research interest, the inherent problem-dependency of specialised operators hinders a proper categorisation of published works. Furthermore, as specialised operators are developed for nature-inspired heuristic algorithms, their adoption and incorporation with other techniques can be quite challenging BIB017 . (f) Multi-Objective Optimisation -in recent years, highly competitive constraint-handling techniques based on MOPs were developed BIB017 , implemented within frameworks such as evolutionary  , BIB004 and pareto dominance  , BIB007 , just to name out a few. (g) CHT Ensembles -motivated by the no-free-lunch theorem BIB001 , multiple CHTs can simultaneously be applied to the same problem, exploring individual strengths and mitigating shortcomings. CHT ensembles result in a high computational burden, which have hampered their extensive use. Some examples include ensembles of feasibility rules, penalty functions, -constrained and SR BIB015 - BIB016 . Constraint metamodelling  is another group of techniques focusing on the development of metamodels for constrained optimisation problems. They can be particularly useful in black-box scenarios, where constraint boundaries are not explicitly provided. Metamodels can be used in feasibility checking and prediction, constraint estimation and repair of infeasible mutations  .