This paper describes a Genetic Algorithms approach to a manpower-scheduling problem arising at a major UK hospital. Although Genetic Algorithms have been successfully used for similar problems in the past, they always had to overcome the limitations of the classical Genetic Algorithms paradigm in handling the conflict between objectives and constraints. The approach taken here is to use an indirect coding based on permutations of the nurses, and a heuristic decoder that builds schedules from these permutations. Computational experiments based on 52 weeks of live data are used to evaluate three different decoders with varying levels of intelligence, and four well-known crossover operators. Results are further enhanced by introducing a hybrid crossover operator and by making use of simple bounds to reduce the size of the solution space. The results reveal that the proposed algorithm is able to find high quality solutions and is both faster and more flexible than a recently published Tabu Search approach.

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. Many problems in industry are a form of openshop scheduling problem (OSSP). We describe a hybrid approach to this problem which combines a Genetic Algorithm (GA) with simple heuristic schedule building rules. Excellent performance is found on some benchmark OSS problems, including improvements on previous best-known results. We describe how our approach can be simply amended to deal with the more complex style of open shop scheduling problems which occur in industry, and discuss issues relating to further improvement of performance and integration of the approach into industrial job shop environments. 1 INTRODUCTION The Open-Shop Scheduling Problem (OSSP) is a complex and common industrial problem [6]. OSSPs arise in an environment where there is a collection of operations to perform on one or more machines. Efficient production and manufacturing demands effective methods to optimise various aspects of a schedule, usually focussing on the total time taken to process all of the oper...

This paper presents a new type of genetic algorithm for the set covering problem. It differs from previous evolutionary approaches first because it is an indirect algorithm, i.e. the actual solutions are found by an external decoder function. The genetic algorithm itself provides this decoder with permutations of the solution variables and other parameters. Second, it will be shown that results can be further improved by adding another indirect optimisation layer. The decoder will not directly seek out low cost solutions but instead aims for good exploitable solutions. These are then post optimised by another hill-climbing algorithm. Although seemingly more complicated, we will show that this three-stage approach has advantages in terms of solution quality, speed and adaptability to new types of problems over more direct approaches. Extensive computational results are presented and compared to the latest evolutionary and other heuristic approaches to the same data instances.

Evolutionary algorithms (EAs) have been applied to many optimization problems successfully in recent years. The genetic algorithm (GAs) and evolutionary programming (EP) are two different types of EAs. GAs use crossover as the primary search operator and mutation as a background operator, while EP uses mutation as the primary search operator and does not employ any crossover. This paper proposes a novel EP algorithm for cutting stock problems with and without contiguity. Two new mutation operators are proposed. Experimental studies have been carried out to examine the effectiveness of the EP algorithm. They show that EP can provide a simple yet more effective alternative to GAs in solving cutting stock problems with and without contiguity. The solutions found by EP are significantly better (in most cases) than or comparable to those found by GAs. Scope and purpose The one-dimensional cuttingstock problem (CSP) is one of the classical combinatorial optimization problems. While most previous work only considered minimizing trim loss, this paper considers CSPs with two objectives. One is the minimization of trim loss (i.e., wastage). The other is the minimization of the number of stocks with wastage, or the number of partially finished items (pattern sequencing or contiguity

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimisation problems. Exact solution methods can only be used for very small instances, so for real-world problems we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimisation (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can outperform some existing solution methods, whereas the hybrid approach can compete with the best known solution methods. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO.

A number of optimisation problems involve the optimal grouping of a finite set of items into a number of categories subject to one or more constraints. Such problems raise interesting issues in mapping solutions in genetic algorithms. These problems range from the knapsack problem to bin packing and cutting stock problems. This paper describes research involving cutting stock problems. Results show that the mapping that is used affects the solution in terms of both quality of the solution found and time taken to find solutions, and that different mappings are suitable for different variants of the problem. 1. Introduction Genetic algorithms(GAs) have been applied to a number of ordering problems, ranging from the Travelling Salesperson Problem (Goldberg 1985) to Job-shop Scheduling (Davis 1985). Typically these problems have been mapped by representing the solutions as ordered lists of alleles, each allele representing an item. Falkenauer (1991) has defined a sub-set of these problem...

Evolutionary Algorithms, evolution based optimization algorithms, are often applied to combinatorial problems. An important issue in such problems is handling the constraints. This is also one of the most challenging areas within Evolutionary Computation. Several approaches for handling constraints exist, each with their own advantages and disadvantages. Which approach is suitable depends on the given problem. In this thesis, two constrained problems are investigated. For the bin packing problem, a number of constraint handling approaches is implemented, tested and compared. Furthermore, attention is payed to a hybrid approach, i.e., the combination of an evolutionary algorithm and a local optimizer, and asexual evolutionary algorithms. For the satisfiability problem a new idea is tested: a floating point representation together with a continuous graded penalty function. A comparison is made with an evolutionary algorithm with adaptive penalty function. Evolutionary algorithms for both...

Efficient multi-processor scheduling is essentially the problem of allocating a set of computational jobs to a set of processors to minimise the overall execution time. There are many variations of this problem, most of which are NP-hard, so we must rely on heuristics to solve real world problem instances. This dissertation describes several novel approaches using the ant colony optimisation (ACO) meta-heuristic and local search techniques, including tabu search, to two important versions of the problem: the static scheduling of independent jobs onto homogeneous and heterogeneous processors.

Iterative methods and genetic algorithms have been used separately to minimise the loss function of many representative-based clustering formulations. Neither of them alone seems to be significantly better. Moreover, the trade-off of effort vs quality slightly favours gradient descent. We present a unifying view for the three most popular loss functions: least sum of squares, its fuzzy version and the log likelihood function. We identify commonalties in gradient descent algorithms for the three loss functions and the evaluation of the loss function itself. We can then construct hybrids (genetic algorithms with a mutation operation that performs few gradient descent steps) for all three clustering approaches. We demonstrate that these hybrids are much efficient and effective (significantly render better performance as normalised by the number of function evaluations). Keywords. Evolutionary computation, knowledge discovery in databases, statistical approaches, clustering...