A Survey on Home Energy Management <s> 3) EARLY CONSTRAINT-HANDLING TECHNIQUES <s> This paper presents an application of genetic algorithms (GAs) to nonlinear constrained optimization. GAs are general purpose optimization algorithms which apply the rules of natural genetics to explore a given search space. When GAs are applied to nonlinear constrained problems, constraint handling becomes an important issue. The proposed search algorithm is realized by GAs which utilize a penalty function in the objective function to account for violation. This extension is based on systematic multi-stage assignments of weights in the penalty method as opposed to single-stage assignments in sequential unconstrained minimization. The experimental results are satisfactory and agree well with those of the gradient type methods. <s> BIB001 </s> A Survey on Home Energy Management <s> 3) EARLY CONSTRAINT-HANDLING TECHNIQUES <s> During the last two years several methods have been proposed for handling nonlinear constraints by genetic algorithms for numerical optimization problems; most of them were based on penalty functions. However, the performance of these methods is highly problem-dependent; moreover, many methods require additional tuning of several parameters. We present a new optimization system (Genocop III), which is based on concepts of co-evolution and repair algorithms. We present the results of the system on a few selected test problems and discuss some directions for further research. <s> BIB002 </s> A Survey on Home Energy Management <s> 3) EARLY CONSTRAINT-HANDLING TECHNIQUES <s> Abstract The quadratic assignment problem (QAP) is a well-known combinatorial optimization problem with a wide variety of practical applications. Although many heuristics and semi-enumerative procedures for QAP have been proposed, no dominant algorithm has emerged. In this paper, we describe a genetic algorithm (GA) approach to QAP. Genetic algorithms are a class of randomized parallel search heuristics which emulate biological natural selection on a population of feasible solutions. We present computational results which show that this GA approach finds solutions competitive with those of the best previously-known heuristics, and argue that genetic algorithms provide a particularly robust method for QAP and its more complex extensions. <s> BIB003 </s> A Survey on Home Energy Management <s> 3) EARLY CONSTRAINT-HANDLING TECHNIQUES <s> Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems; however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing. ::: ::: In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem; (2) survey several approaches that have emerged in the evolutionary computation community; and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods. <s> BIB004 </s> A Survey on Home Energy Management <s> 3) EARLY CONSTRAINT-HANDLING TECHNIQUES <s> When genetic algorithms are applied to large-scale optimization problems taking only integer-valued solutions, too often the chromosomes generated fail to satisfy the constraint conditions. In such cases, the selection operator is unable to produce high-quality chromosomes, worsening the search efficiency. As a consequence, many times good solutions cannot be obtained. In this paper, in order to cope with such a problem, a new algorithm with improved chromosome selection mechanism is proposed, taking into account the evaluation function including some information about chromosomes not contained in the feasible region of the nonlinear integer programming problem under consideration. The proposed method considers how far each unfeasible chromosome is from the feasible region. The improved algorithm was applied to a large-scale problem of optimal design of system reliability formulated as a nonlinear integer programmng problem and numerical experiments confirmed the effectiveness of the method. <s> BIB005 </s> A Survey on Home Energy Management <s> 3) EARLY CONSTRAINT-HANDLING TECHNIQUES <s> Based on evolutionary computation (EC) concepts, we developed an adaptive evolutionary planner/navigator (EP/N) as a novel approach to path planning and navigation. The EP/N is characterized by generality, flexibility, and adaptability. It unifies off-line planning and online planning/navigation processes in the same evolutionary algorithm which 1) accommodates different optimization criteria and changes in these criteria, 2) incorporates various types of problem-specific domain knowledge, and 3) enables good tradeoffs among near-optimality of paths, high planning efficiency, and effective handling of unknown obstacles. More importantly, the EP/N can self-tune its performance for different task environments and changes in such environments, mostly through adapting probabilities of its operators and adjusting paths constantly, even during a robot's motion toward the goal. <s> BIB006 </s> A Survey on Home Energy Management <s> 3) EARLY CONSTRAINT-HANDLING TECHNIQUES <s> During the last five years, several methods have been proposed for handling nonlinear constraints using evolutionary algorithms (EAs) for numerical optimization problems. Recent survey papers classify these methods into four categories: preservation of feasibility, penalty functions, searching for feasibility, and other hybrids. In this paper we investigate a new approach for solving constrained numerical optimization problems which incorporates a homomorphous mapping between n-dimensional cube and a feasible search space. This approach constitutes an example of the fifth decoder-based category of constraint handling techniques. We demonstrate the power of this new approach on several test cases and discuss its further potential. <s> BIB007 </s> A Survey on Home Energy Management <s> 3) EARLY CONSTRAINT-HANDLING TECHNIQUES <s> This paper provides a comprehensive survey of the most popular constraint-handling techniques currently used with evolutionary algorithms. We review approaches that go from simple variations of a penalty function, to others, more sophisticated, that are biologically inspired on emulations of the immune system, culture or ant colonies. Besides describing briefly each of these approaches (or groups of techniques), we provide some criticism regarding their highlights and drawbacks. A small comparative study is also conducted, in order to assess the performance of several penalty-based approaches with respect to a dominance-based technique proposed by the author, and with respect to some mathematical programming approaches. Finally, we provide some guidelines regarding how to select the most appropriate constraint-handling technique for a certain application, and we conclude with some of the most promising paths of future research in this area. <s> BIB008 </s> A Survey on Home Energy Management <s> 3) EARLY CONSTRAINT-HANDLING TECHNIQUES <s> In this paper, we propose a generic, two-phase framework for solving constrained optimization problems using genetic algorithms. In the first phase of the algorithm, the objective function is completely disregarded and the constrained optimization problem is treated as a constraint satisfaction problem. The genetic search is directed toward minimizing the constraint violation of the solutions and eventually finding a feasible solution. A linear rank-based approach is used to assign fitness values to the individuals. The solution with the least constraint violation is archived as the elite solution in the population. In the second phase, the simultaneous optimization of the objective function and the satisfaction of the constraints are treated as a biobjective optimization problem. We elaborate on how the constrained optimization problem requires a balance of exploration and exploitation under different problem scenarios and come to the conclusion that a nondominated ranking between the individuals will help the algorithm explore further, while the elitist scheme will facilitate in exploitation. We analyze the proposed algorithm under different problem scenarios using Test Case Generator-2 and demonstrate the proposed algorithm's capability to perform well independent of various problem characteristics. In addition, the proposed algorithm performs competitively with the state-of-the-art constraint optimization algorithms on 11 test cases which were widely studied benchmark functions in literature. <s> BIB009
All CHTs present similar shortcomings, namely in terms of generalisation capacity, parameter fine-tuning and premature convergence. They can be grouped into the following subcategories  , BIB008 : (a) Penalty functions -constraints are replaced with an additional term on the adopted criteria function f (x), which penalises the evaluation of a given solution, according to its degree of constraint violation. This term is usually represented by means of a penalty function, φ(x), being a solution evaluated as eval(x) = f (x) + φ(x). Penalty functions of different types have been considered, namely: (i) static penalties BIB008 , BIB001 which define fixed-value penalisations, (ii) dynamic penalties BIB004 - BIB005 computed based on information from the evolutionary process, namely infeasibility degree, generation number or best fitness in the population BIB008 , and (iii) less popular alternatives derived based on coevolution  and segregated GA  principles. Penalty functions are extensively adopted, mostly due to their simplicity, ease of implementation and integration with existing optimisation-based scheduling strategies, but they require proper tuning, in particular in terms of optimal penalty values. As such, it has been suggested adopting the minimum penalty rule BIB008 , according to which penalisation should be kept just above the limit below which infeasible solutions become optimal. The most tricky aspect of the penalty function approach is how to find appropriate penalty parameters in order to guide the search towards a constrained optimum. (b) Special operators -in evolutionary and genetic algorithms, crossover and mutation operators are used to maintain population genetic diversity. As infeasible individuals may be generated, tweaks have been proposed to preserve the feasibility of candidate solutions  -  . Some examples include GENO-COP  , GENOCOP III BIB002 , decoders BIB007 ,  and repair algorithms BIB003 - BIB006 , just to name out a few. (c) Separation of objectives and constraints -treating objectives and constraints separately, unlike penalty functions. Examples include co-evolutionary techniques  ,  , optimising objectives and constraints in two distinct populations, and multi-objective optimisation  - BIB009 . Feasibility rules  consist of a set of rules that govern comparisons between individuals, assuming an explicit preference for feasible solutions over infeasible alternatives  -  . A drawback of this methodology is a poor exploration of infeasible regions, which can lead to a premature convergence to a solution, resulting in a suboptimal solution.