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.

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.

This paper presents an extended formulation of the unequal area facilities block layout problem which explicitly considers uncertainty in material handling costs by use of expected value and standard deviations of product forecasts. This formulation is solved using a random keys genetic algorithm (RKGA) to circumvent the need for repair operators after crossover and mutation. Because this problem can be highly constrained depending on the maximum allowable aspect ratios of the facility departments, an adaptive penalty function is used to guide the search to feasible, but not suboptimal, regions. The RKGA is shown to be a robust optimizor which allows a user to make an explicit characterization of the cost and uncertainty trade-offs involved in a particular block layout problem. I. INTRODUCTION TO THE FACILITY LAYOUT PROBLEM Facility Layout Problems are a family of design problems involving the partition of a planar region into departments or work areas of known area, so ...

This paper describes a heuristic optimization approach using genetic algorithms. The method solves general network design problems to optimality, or near-optimality, with respect to reliability. The optimization formulation in this paper relaxes the previous restrictions that appear in the literature. Network design is expanded to include links of differing reliability and to select from multiple choices for each possible link component. This significantly expands the search space, necessitating a heuristic approach, but also is much more reflective of actual communications network design problems. The approach can use either exact or approximate network reliability calculations and its flexibility, effectiveness and efficiency are demonstrated on a series of increasingly constrained all-terminal reliability test problems.

This paper describes a general approach to optimal design of communications networks when considering both economics and reliability. The approach uses a genetic algorithm to identify the best topology of network arcs to collectively meet cost and network reliability considerations. This approach is distinct because it is highly flexible and can readily solve many versions of the network design problem, including formulations not seen in the literature before which are more reflective of actual design scenarios. The method is shown to be effective, computationally efficient and flexible on a suite of diverse test problems. 3 1. Introduction The problem of how to cost effectively design a network so that certain constraints are met and an objective is optimized is relevant in many real world applications such as telecommunications [3, 23, 33], computer networking [2, 13, 37], sewage systems [36], and oil and gas lines [36]. This paper focuses on design of minimum cost reliable ...

. The facility design problem is a common one in manufacturing and service industries and has been studied extensively in the literature. However, restrictions on the scope of the design problem have been imposed by the limitations of the optimization techniques employed. This paper uses an evolutionary approach with a subordinate network optimization algorithm to produce integrated designs that have better translations into physical plant designs. A new distance metric to consider material travel along the perimeter of the departments to and from input/output locations is devised. This perimeter distance metric is used in the objective function to produce facility designs that simultaneously optimize design of department shapes, department placement and location of the department input/output points. 1. Introduction Facility design problems are a family of design problems involving the partitioning of a planar region into departments or work centers of given area, so as to...

This paper presents a formulation of the facilities block layout problem which explicitly considers uncertainty in material handling costs by use of expected values and standard deviations of product forecasts. This formulation is solved using a genetic algorithm meta-heuristic with a flexible bay construct of the departments and total facility area. It is shown that depending on the attitude of the decision-maker towards uncertainty, the optimal layout can change significantly. Furthermore, designs can be optimized directly for robustness over a range of uncertainty that is pre-specified by the user. Keywords - facilities, heuristics, optimisation, genetic algorithms, block layout, production uncertainty 1. Introduction Facility design problems generally involve the partition of a planar region into departments (work centers or cells) along with an aisle structure and a material handling system to link the departments. The primary objective of the design problem is to minimi...

informs ® doi 10.1287/ijoc.1030.0040 © 2004 INFORMS This paper puts forth a general method to optimize constrained problems effectively when using tabu search. An adaptive penalty approach is used that exploits the short-term memory structure of the tabu list along with the long-term memory of the search results. It is shown to be effective on a variety of combinatorial problems with different degrees and numbers of constraints. The approach requires few parameters, is robust to their setting, and encourages search in promising regions of the feasible and infeasible regions before converging to a final feasible solution. The method is tested on three diverse NP-hard problems, facility layout, system reliability optimization, and orienteering, and is compared with two other penalty approaches developed explicitly for tabu search. The proposed memory-based approach shows consistent strong performance. Key words: constraint optimization; facility layout; reliability optimization; orienteering; tabu search

Multi-objective problems are often solved by modifying them into equivalent single objective problems using pre-defined weights or utility functions. Then, a multi-objective problem is solved similar to a single objective problem returning a single solution. These methods can be problematic because assigning appropriate numerical values (i.e., weights) to an objective function can be challenging for many practitioners. On the other hand, methods such as genetic algorithms and tabu search often yield numerous non-dominated Pareto optimal solutions, which makes the selection of one single best solution very difficult. In this paper, a new methodology is presented to solve different versions of multi-objective system redundancy allocation problems. A tabu search meta-heuristic approach is used to initially find the entire Pareto-optimal front, and then a Monte-Carlo simulation provides a decision maker with a pruned and prioritized set of Pareto-optimal solutions based user-defined objective function preferences. The purpose of this study is to create a bridge between Pareto optimality and single solution approaches.

Nurse rostering is a difficult search problem with many constraints. In the literature, a number of approaches have been investigated including penalty function methods to tackle these constraints within genetic algorithm frameworks. In this paper, we investigate an extension of a previously proposed stochastic ranking method, which has demonstrated superior performance to other constraint handling techniques when tested against a set of constrained optimisation benchmark problems. An initial experiment on nurse rostering problems demonstrates that the stochastic ranking method is better in finding feasible solutions but fails to obtain good results with regard to the objective function. To improve the performance of the algorithm, we hybridise it with a recently proposed simulated annealing hyper-heuristic within a local search and genetic algorithm framework. The hybrid algorithm shows significant improvement over both the genetic algorithm with stochastic ranking and the simulated annealing hyper-heuristic alone. The hybrid algorithm also considerably outperforms the methods in the literature which have the previously best known results.