Anton V. Eremeev

A Genetic Algorithm for the Allocation of Buffer Storage Capacities in a Production Line with Unreliable Machines

In this paper, we consider a flow-line manufacturing system organized as a series of workstations separated by finite buffers. The failure and repair times of machines are supposed to be exponentially distributed. The production rate of each machine is deterministic, and different machines may have different production rates. The buffer allocation problem consists in determining the buffer capacities with respect to a given optimality criterion, which depends on the average production rate of the line, the buffer acquisition and installation cost, and the inventory cost. For this problem we propose a genetic algorithm where the tentative solutions are evaluated with an approximate method based on the Markov-model aggregation approach.

HBBA : Hybrid Algorithm for Buffer Allocation in Tandem Production Lines

In this paper, we consider the problem of buffer space allocation for a tandem production line with unreliable machines. This problem has various formulations all aiming to answer the question: how much buffer storage to allocate between the processing stations? Many authors use the knapsack-type formulation of this problem. We investigate the problem with a broader statement. The criterion depends on the average steady-state production rate of the line and the buffer equipment acquisition cost. We evaluate black-box complexity of this problem and propose a hybrid optimization algorithm (HBBA), combining the genetic and branch-and-bound approaches. HBBA is excellent in computational time. HBBA uses a Markov model aggregation technique for goal function evaluation. Nevertheless, HBBA is more general and can be used with other production rate evaluation techniques.

Genetic algorithms for a supply management problem: MIP-recombination vs greedy decoder

Two variants of genetic algorithm (GA) for solving the Supply Management Problem with Lower-Bounded Demands (SMPLD) are proposed and experimentally tested. The SMPLD problem consists in planning the shipments from a set of suppliers to a set of customers minimizing the total cost, given lower and upper bounds on shipment sizes, lower-bounded consumption and linear costs for opened deliveries. The first variant of GA uses the standard binary representation of solutions and a new recombination operator based on the mixed integer programming (MIP) techniques. The second GA is based on the permutation representation and a greedy decoder. Our experiments indicate that the GA with MIP-recombination compares favorably to the other GA and to the MIP-solver CPLEX 9.0 in terms of cost of obtained solutions. The GA based on greedy decoder is shown to be the most robust in finding feasible solutions.

Statistical analysis of local search landscapes

This paper discusses the application of some statistical estimation tools in trying to understand the nature of the combinatorial landscapes induced by local search methods. One interesting property of a landscape is the number of optima that are present. In this paper we show that it is possible to compute a confidence interval on the number of independent local searches needed to find all optima. By extension, this also expresses the confidence that the global optimum has been found. In many cases, this confidence may be too low to be acceptable, but it is also possible to estimate the number of optima that exist. Theoretical analysis and empirical studies are discussed, which show that it may be possible to obtain a fairly accurate picture of this property of a combinatorial landscape. The approach is illustrated by analysis of an instance of the flowshop scheduling problem.

Evolutionary algorithms and dynamic programming

Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation, which enables them to construct solutions in a dynamic programming fashion. We take a general approach and relate the construction of such algorithms to the development of algorithms using dynamic programming techniques. Thereby, we give general guidelines on how to develop evolutionary algorithms that have the additional ability of carrying out dynamic programming steps.

On confidence intervals for the number of local optima

The number of local optima is an important indicator of optimization problem difficulty for local search algorithms. Here we will discuss some methods of finding the confidence intervals for this parameter in problems where the large cardinality of the search space does not allow exhaustive investigation of solutions. First results are reported that were obtained by using these methods for NK landscapes, and for the low autocorrelation binary sequence and vertex cover problems.

Non-parametric Estimation of Properties of Combinatorial Landscapes

Earlier papers [1,2] introduced some statistical estimation methods for measuring certain properties of landscapes induced by heuristic search methods: in particular, the number of optima. In this paper we extendthis approach to non-parametric methods which allow us to relax a critical assumption of the earlier approach.Two techniques are described--the jackknife and the bootstrap--based on statistical ideas of resampling, and the results of some empirical studies are presented and analysed.

MIP-based GRASP and Genetic Algorithm for Balancing Transfer Lines

Abstract In this chapter, we consider a problem of balancing transfer lines with multi-spindle machines. The problem has a number of distinct features in comparison with the well-studied assembly line balancing problem, such as parameterized operation times, non-strict precedence constraints, and parallel operations execution. We propose a mixed-integer programming (MIP)-based greedy randomized adaptive search procedure (GRASP) and a genetic algorithm (GA) for this problem using a MIP formulation. Both algorithms are implemented in GAMS using the CPLEX MIP solver and compared to problem-specific heuristics on randomly generated instances of different types. The results of computational experiments indicate that on large-scale problem instances the proposed methods have an advantage over the methods from literature for finding high quality solutions. The MIP-based recombination operator that arranges the elements of parent solutions in the best possible way is shown to be useful in the GA.

Multi-product lot sizing and scheduling on unrelated parallel machines

This article studies a problem of optimal scheduling and lot sizing a number of products on m unrelated parallel machines to satisfy given demands. A sequence-dependent setup time is required between lots of different products. The products are assumed to be all continuously divisible or all discrete. The criterion is to minimize the time at which all the demands are satisfied, C max, or the maximum lateness of the product completion times from the given due dates, L max. The problem is motivated by the real-life scheduling applications in multi-product plants. The properties of optimal solutions, NP-hardness proofs, enumeration, and dynamic programming algorithms for various special cases of the problem are presented. A greedy-type heuristic is proposed and experimentally tested. The major contributions are an NP-hardness proof, pseudo-polynomial algorithms linear in m for the case, in which the number of products is a given constant and the heuristic. The results can be adapted for solving a production line design problem.

Complexity of Buffer Capacity Allocation Problems for Production Lines with Unreliable Machines

Buffer capacity allocation problems for flow-line manufacturing systems with unreliable machines are studied. These problems arise in a wide range of manufacturing systems and concern determining buffer capacities with respect to a given optimality criterion which can depend on the average production rate of the line, buffer cost, inventory cost, etc. Here, this problem is proven to be NP-hard for a tandem production line and oracle representation of the revenue and cost functions, and NP-hard for a series-parallel line and stepwise revenue function.