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, ad we conclude with some of the the most promising paths of future research in this area.

In this dissertation we report on our efforts to develop a parallel genetic algorithm and apply it to the solution of the set partitioning problem--a difficult combinatorial optimization problem used by many airlines as a mathematical model for flight crew scheduling. We developed a distributed steady-state genetic algorithm in conjunction with a specialized local search heuristic for solving the set partitioning problem. The genetic algorithm is based on an island model where multiple independent subpopulations each run a steady-state genetic algorithm on their own subpopulation and occasionally fit strings migrate between the subpopulations. Tests on forty real-world set partitioning problems were carried out on up to 128 nodes of an IBM SP1 parallel computer. We found that performance, as measured by the quality of the solution found and the iteration on which it was found, improved as additional subpopulations were added to the computation. With larger numbers of subpopulations the genetic algorithm was regularly able to find the optimal solution to problems having up to a few thousand integer variables. In two cases, high-quality integer feasible solutions were found for problems with 36,699 and 43,749 integer variables, respectively. A notable limitation we found was the difficulty solving problems with many constraints.

This paper describes the use of a genetic algorithm (GA) to determine solutions to the redundancy allocation problem for a series-parallel system. In this problem formulation, there is a specified number of subsystems and, for each subsystem, there are multiple component choices which can be selected, with replacement, and used in parallel. For those systems designed using off-the-shelf component types, with known cost, reliability and weight, system design and component selection becomes a combinatorial 2

During the last ve years, several methods have been proposed for handling nonlinear constraints by evolutionary algorithms (EAs) for numerical optimization problems. Recent survey papers classify them into four categories (preservation of feasibility, penalty functions, searching for feasibility, and other hybrids).

This paper focuses on the issue of evaluation of constraints handling methods, as the advantages and disadvantages of various methods are not well understood. The general way of dealing with constraints -- whatever the optimization method -- is by penalizing infeasible points. However, there are no guidelines on designing penalty functions. Some suggestions for evolutionary algorithms are given in [37], but they do not generalize. Other techniques that can be used to handle constraints in are more or less problem dependent. For instance, the knowledge about linear constraints can be incorporated into specific operators [24], or a repair operator can be designed that projects infeasible points onto feasible ones [30]

The paper reports on the application of genetic algorithms, probabilistic search algorithms based on the model of organic evolution, to NP-complete combinatorial optimization problems. In particular, the subset sum, maximum cut, and minimum tardy task problems are considered. Except for the fitness function, no problem-specific changes of the genetic algorithm are required in order to achieve results of high quality even for the problem instances of size 100 used in the paper. For constrained problems, such as the subset sum and the minimum tardy task, the constraints are taken into account by incorporating a graded penalty term into the fitness function. Even for large instances of these highly multimodal optimization problems, an iterated application of the genetic algorithm is observed to find the global optimum within a number of runs. As the genetic algorithm samples only a tiny fraction of the search space, these results are quite encouraging.

Numerical optimization problems enjoy a significant popularity in evolutionary computation community; all major evolutionary techniques use such problems for various tests and experiments. However, many of these techniques (as well as other, classical optimization methods) encounter difficulties in solving some real-world problems which include non-trivial constraints. This paper discusses a new development which is based on the observation that very often the global solution lies on the boundary of the feasible region. Thus, for many constrained numerical optimization problems it might be beneficial to limit the search to that boundary, using problem-specific operators. Two test cases illustrate this approach: specific operators are designed from the simple analytical expression of the constraints. Some possible generalizations to larger classes of constraints are discussed as well. 1

Despite the extended applicability of evolutionary algorithms to a wide range of domains, the fact that these algorithms are unconstrained optimization techniques leaves open the issue regarding how to incorporate constraints of any kind (linear, non-linear, equality and inequality) into the fitness function as to search efficiently. The main goal of this paper is to provide a detailed and comprehensive survey of the many constraint handling approaches that have been proposed for evolutionary algorithms, analyzing in each case their advantages and disadvantages, and concluding with some of the most promising paths of research.

The application of genetic algorithms (GA) to constrained optimization problems has been hindered by the inefficiencies of reproduction and mutation when feasibility of generated solutions is impossible to guarantee and feasible solutions are very difficult to find. Although several authors have suggested the use of both static and dynamic penalty functions for genetic search, this paper presents a general adaptive penalty technique which makes use of feedback obtained during the search along with a dynamic distance metric. The effectiveness of this method is illustrated on two diverse combinatorial applications; (1) the unequalarea, shape-constrained facility layout problem and (2) the series-parallel redundancy allocation problem to maximize system reliability given cost and weight constraints. The adaptive penalty function is shown to be robust with regard to random number seed, parameter settings, number and degree of constraints, and problem instance. 1. Introduction ...

Evolutionary computation is emerging as a new engineering computational paradigm, which may significantly change the present structural design practice. For this reason, an extensive study of evolutionary computation in the context of structural design has been conducted in the Information Technology and Engineering School at George Mason University and its results are reported here. First, a general introduction to evolutionary computation is presented and recent developments in this field are briefly described. Next, the field of evolutionary design is introduced and its relevance to structural design is explained. Further, the issue of creativity/novelty is discussed and possible ways of achieving it during a structural design process are suggested. Current research progress in building engineering systems ’ representations, one of the key issues in evolutionary design, is subsequently discussed. Next, recent developments in constraint-handling methods in evolutionary optimization are reported. Further, the rapidly growing field of evolutionary multiobjective optimization is presented and briefly described. An emerging subfield of coevolutionary design is subsequently introduced and its current advancements reported. Next, a comprehensive review of the applications of evolutionary computation in structural design is provided and chronologically classified. Finally, a summary of the current research status and a discussion on the most promising paths of future research are also presented.