Tugba Saraç

A genetic algorithm for the quadratic multiple knapsack problem

The Quadratic Multiple Knapsack Problem (QMKP) is a generalization of the quadratic knapsack problem, which is one of the well-known combinatorial optimization problems, from a single knapsack to k knapsacks with (possibly) different capacities. The objective is to assign each item to at most one of the knapsacks such that none of the capacity constraints are violated and the total profit of the items put into the knapsacks is maximized. In this paper, a genetic algorithm is proposed to solve QMKP. Specialized crossover operator is developed to maintain the feasibility of the chromosomes and two distinct mutation operators with different improvement techniques from the non-evolutionary heuristic are presented. The performance of the developed GA is evaluated and the obtained results are compared to the previous study in the literature.

A genetic algorithm with proper parameters for manufacturing cell formation problems

One fundamental problem in cellular manufacturing is the formation of product families and machine cells. Many solution methods have been developed for the cell formation problem. Since efficient grouping is the prerequisite of a successful Cellular Manufacturing installation the research in this area will likely be continued. In this paper, we consider the problem of cell formation in cellular manufacturing systems with the objective of maximizing the grouping efficacy. We propose a Genetic Algorithm (GA) to obtain machine-cells and part-families. Developed GA has three different selection and crossover operators. The proper operators and parameters of the GA were determined by design of experiments. A set of 15 test problems with various sizes drawn from the literature is used to test the performance of the proposed algorithm. The corresponding results are compared to several well-known algorithms published. The comparative study shows that the proposed GA improves the grouping efficacy for 40% of the test problems.

A multi-objective programming approach to 1.5-dimensional assortment problem

In this paper we study a 1.5-dimensional cutting stock and assortment problem which includes determination of the number of different widths of roll stocks to be maintained as inventory and determination of how these roll stocks should be cut by choosing the optimal cutting pattern combinations. We propose a new multi-objective mixed integer linear programming (MILP) model in the form of simultaneously minimization two contradicting objectives related to the trim loss cost and the combined inventory cost in order to fulfill a given set of cutting orders. An equivalent nonlinear version and a particular case related to the situation when a producer is interested in choosing only a few number of types among all possible roll sizes, have also been considered. A new method called the conic scalarization is proposed for scalarizing non-convex multi-objective problems and several experimental tests are reported in order to demonstrate the validity of the developed modeling and solving approaches.

A genetic algorithm extended modified sub-gradient algorithm for cell formation problem with alternative routings

This paper addresses the cell formation problem with alternative part routes. The problem is considered in the aspect of the natural constraints of real-life production systems such as cell size, separation and co-location constraints. Co-location constraints were added to the proposed model in order to deal with the necessity of grouping certain machines in the same cell for technical reasons, and separation constraints were included to prevent placing certain machines in close vicinity. The objective is to minimise the weighted sum of the voids and the exceptional elements. A hybrid algorithm is proposed to solve this problem. The proposed algorithm hybridises the modified sub-gradient (MSG) algorithm with a genetic algorithm. MSG algorithm solves the sharp augmented Lagrangian dual problems, where zero duality gap property is guaranteed for a wide class of optimisation problems without convexity assumption. Generally, the dual problem is solved by using GAMS solvers in the literature. In this study, a genetic algorithm has been used for solving the dual problem at the first time. The experimental results show the advantage of combining the MSG algorithm and the genetic algorithm. Although the MSG algorithm, whose dual problem is solved by GAMS solver, and the genetic algorithm cannot find feasible solutions, hybrid algorithm generates feasible solutions for all of the test problems.

Generalized quadratic multiple knapsack problem and two solution approaches

The Quadratic Knapsack Problem (QKP) is one of the well-known combinatorial optimization problems. If more than one knapsack exists, then the problem is called a Quadratic Multiple Knapsack Problem (QMKP). Recently, knapsack problems with setups have been considered in the literature. In these studies, when an item is assigned to a knapsack, its setup cost for the class also has to be accounted for in the knapsack. In this study, the QMKP with setups is generalized taking into account the setup constraint, assignment conditions and the knapsack preferences of the items. The developed model is called Generalized Quadratic Multiple Knapsack Problem (G-QMKP). Since the G-QMKP is an NP-hard problem, two different meta-heuristic solution approaches are offered for solving the G-QMKP. The first is a genetic algorithm (GA), and the second is a hybrid solution approach which combines a feasible value based modified subgradient (F-MSG) algorithm and GA. The performances of the proposed solution approaches are shown by using randomly generated test instances. In addition, a case study is realized in a plastic injection molding manufacturing company. It is shown that the proposed hybrid solution approach can be successfully used for assigning jobs to machines in production with plastic injection, and good solutions can be obtained in a reasonable time for a large scale real-life problem.

Determining the parameters of MSG algorithm for multi period layout problem

Purpose – The facility layout problem aims to assign machines/departments to locations and modeled as a quadratic assignment problem (QAP). Multi period facility layout is a special case of this problem where the sum of material handling and re‐layout costs are minimized. Since the problem is proved to be NP‐hard, several exact and heuristic methods are proposed in the literature. The purpose of this paper is to solve the multi period layout problem by using the modified sub‐gradient (MSG) algorithm for the first time and to determine its parameters.Design/methodology/approach – The MSG algorithm can solve a large‐scale of optimization problems that also includes multi period facility layout. Since the performance of the algorithm depends on parameters, a design of experiment is made to determine the appropriate parameter values.Findings – The proposed method evaluates the parameters of the MSG algorithm and most suitable general algebraic modeling solvers. It is observed that the parameter α value and so...

A Mathematical Model and Heuristic Algorithms for an Unrelated Parallel Machine Scheduling Problem with Sequence-Dependent Setup Times, Machine Eligibility Restrictions and a Common Server

Abstract Parallel machine scheduling problems with common servers have many industrial applications. In this paper, we study a generalized problem of scheduling with a common server, which is the unrelated parallel machine scheduling problem with sequence-dependent setup times and machine eligibility restrictions. The objective function involves the minimization of the total weighted tardiness. A mixed integer linear programming (MILP) model is proposed to solve this complex problem. Due to the NP hardness of the problem, tabu search (TS) and simulated annealing (SA) algorithms are proposed. The initial solutions of the algorithms are obtained by a modified apparent tardiness cost with setups (ATCS) dispatching rule. The proposed algorithms are compared using a randomly generated data set.