Pavel A. Borisovsky

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.

Genetic algorithm for balancing reconfigurable machining lines

We consider the problem of designing a reconfigurable machining line. Such a line is composed of a sequence of workstations performing specific sets of operations. Each workstation is comprised of several identical CNC machines (machining centers). The line is required to satisfy the given precedence order, inclusion, exclusion and accessibility constraints on the given set of operations. Inclusion and exclusion are zoning constraints which oblige or forbid certain operations to be performed on the same workstation. The accessibility constraints imply that each operation has a set of possible part positions under which it can be performed. All the operations performed on the same workstation must have a common part position. Workstation times are computed taking into account processing and setup times for operations and must not exceed a given bound. The number of CNC machines at one workstation is limited, and the total number of machines must be minimized. A genetic algorithm is proposed. This algorithm is based on the permutation representation of solutions. A heuristic decoder is suggested to construct a solution from a permutation, so that the output solution is feasible w.r.t. precedence, accessibility, cycle time, and exclusion constraints. The other constraints are treated with a penalty approach. For a local improvement of solutions, a mixed integer programming model is suggested for an optimal design of workstations if the order of operations is fixed. An experimental evaluation of the proposed GA on large scale test instances is performed.

Algorithms and implementation of a set partitioning approach for modular machining line design

A transfer line design problem is considered. Transfer lines are sequences of workstations equipped with processing modules called blocks each of which performs specific operations. These lines are used for mass production of one type of product and thus execute repetitively a given set of operations. The machine parts move along the stations in the same direction. An identical cost is associated with each station and differing costs are associated with the blocks. The problem is to determine the number of stations, select a set of blocks and assign selected blocks to the stations so that operations of the selected blocks constitute the original set of operations and the total cost is minimized. A distinct feature of the problem is that operations at the same station are performed in parallel. Plus, there are inclusion, exclusion and precedence relations that restrict the assignment of the blocks and operations to the same station as well as the processing order of the operations on the transfer line. We implement a novel set partitioning formulation of this design problem with pre-processing procedures and heuristics. The presented approach has the best performance among the existing methods in terms of solution time and quality.

Balancing reconfigurable machining lines via a set partitioning model

We consider the problem of constructing an optimal machining line as a sequence of workstations performing specific sets of operations. The line is required to satisfy the given precedence order on operations, inclusion, exclusion and accessibility constraints. The cycle times of workstations are computed taking into account the processing and sequence dependent set-up times of operations and must not exceed the given bound. For solving the problem, we propose a reduction of this machining line design problem to a set partitioning type problem. This approach implies generating all possible workstations and, for each workstation, solving a scheduling problem in order to find the sequence of operations which minimises the total set-up time. To do this, a dynamic programming algorithm is developed. Several preprocessing procedures are suggested to reduce the number of workstations. A set of exact algorithms are proposed to solve the obtained set partitioning type problem: a constraint generation, a branch and cut, and a parallel branch and cut algorithms. Our experimental investigation demonstrated that the proposed method achieves a significant improvement in CPU times over those required by a previous study that is based on a different model formulation, and also, that the proposed method is able to solve large-sized problem instances.

Modelling transfer line design problem via a set partitioning problem

The design of a transfer line is considered. This line is used for a repetitive execution of a given set of operations to produce identical items. The line is composed of a sequence of workstations equipped with processing modules (blocks). Each block performs specific operations. The machined items move along the workstations in the same direction. There is the same cost associated with each workstation and different costs associated with diverse blocks. The problem is to determine the number of workstations, select a set of blocks and assign the selected blocks to the workstations so that, for each item, each operation is performed exactly once with total line cost to be minimized. The specificity of the problem is that all operations of the same workstation are performed in parallel. There are inclusion, exclusion, and precedence relations that restrict the assignment of blocks and operations to the same workstation and constrain the processing order of the operations on the transfer line. We suggest a reduction of this transfer line design problem to a simple set partitioning problem. This reduction is based on the concept of a locally feasible workstation.

Trading Hubs Construction for Electricity Markets

In this chapter, we consider a problem of constructing trading hubs in the structure of the electricity wholesale markets. The nodes of a trading hub are used to calculate a reference price that can be employed by the market participants for different types of hedging. The need for such a reference price is due to considerable variability of energy prices at different nodes of the electricity grid at different periods of time. The hubs construction is viewed as a mathematical programming problem here. We discuss its connections with clustering problems, consider the heuristic algorithms of solution and indicate some complexity issues. The performance of algorithms is illustrated on the real-life data.

Experimental comparison of two evolutionary algorithms for the independent set problem

This work presents an experimental comparison of the steady-state genetic algorithm to the (1+1)-evolutionary algorithm applied to the maximum vertex independent set problem. The penalty approach is used for both algorithms and tuning of the penalty function is considered in the first part of the paper. In the second part we give some reasons why one could expect the competitive performance of the (1+1)-EA. The results of computational experiment are presented.

GENETIC ALGORITHMS FOR SUPPLY MANAGEMENT PROBLEM WITH LOWER-BOUNDED DEMANDS

Abstract 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 providers to a set of consumers minimizing the total transportation cost, given lower and upper bounds on shipment sizes, lower-bounded consumption and linear delivery costs. The first variant of GA uses the standard binary representation of solutions, the second one is based on the permutation representation and a greedy decoder. The experiments show the behaviour of the algorithms on different problem classes and indicate their competitiveness to the CPLEX solver.

Trading hubs construction in electricity markets using evolutionary algorithms

The trading hubs construction problem for electricity markets under locational marginal prices is considered. Given historical prices for all nodes of the electricity grid and for all market participants over a sufficiently long period of time, the problem is to choose a required number of node clusters (hubs) and to assign market participants to hubs so as to minimize the deviation of hub prices from the prices of participants under certain constraints.In view of problem complexity, two evolutionary algorithms are proposed: a genetic algorithm and a hybrid local search heuristic. It is proved that the proposed genetic algorithm converges to optimum almost surely. The algorithms are tested and compared on the real-life data. The structure of the fitness landscapes is analyzed using multiple restarts of the local search and the behavior of the evolutionary algorithms is explained on the basis of this analysis.

Balancing reconfigurable machining lines by means of set partitioning model

We consider the problem of construction of an optimal reconfigurable machining line as a sequence of workstations performing specific sets of operations. The line is required to satisfy the given precedence order on operations, inclusion, exclusion and accessibility constraints. The cycle times of workstations are computed taking into account the processing and setup times of operations and must not exceed the given bound. For solving the problem, we propose a reduction of this machining line design problem to a set partitioning type problem. This approach implies generating all possible workstations and finding optimal sequence of operations in each workstation. To do this, a dynamic programming algorithm is developed. Several preprocessing procedures are suggested for reducing the number of workstations. For solving the obtained set partitioning type problem, a constraint generation algorithm based on mixed integer programming model is proposed.