Athanasios Migdalas

Serial-batching scheduling with time-dependent setup time and effects of deterioration and learning on a single-machine

This paper deals with serial-batching scheduling problems with the effects of deterioration and learning, where time-dependent setup time is also considered. In the proposed scheduling models, all jobs are first partitioned into serial batches, and then all batches are processed on a single serial-batching machine. The actual job processing time is a function of its starting time and position. In addition, a setup time is required when a new batch is processed, and the setup time of the batches is time-dependent, i.e., it is a linear function of its starting time. Structural properties are derived for the problems of minimizing the makespan, the number of tardy jobs, and the maximum earliness. Then, three optimization algorithms are developed to solve them, respectively.

Single-machine serial-batching scheduling with a machine availability constraint, position-dependent processing time, and time-dependent set-up time

This article considers the single-machine serial-batching scheduling problem with a machine availability constraint, position-dependent processing time, and time-dependent set-up time. The objective of this problem is to make the decision of batching jobs and sequencing batches to minimize the makespan. To solve the problem, three cases of machine non-availability periods are considered, and the structural properties of the optimal solution are derived for each case. Based on these structural properties, an optimization algorithm is developed and an example is proposed to illustrate this algorithm.

Locating facilities in a competitive environment

The research work dealing with the bi-level formulation of location problems is limited only to the competition among the locators, that is, it is supposed that either both the locator and the allocator are the same or the customer knows the optimality criterion of the locator and agrees passively with it. Customers’ preferences as well as externalities (such as road congestion, facility congestion, emissions etc) caused by the location decisions are either ignored or controlled by incorporating constraints in order to ensure the achievement of a predetermined target. However, this approach treats customers as irresolute beings. Thus, if, for example, the customers travel to the facilities to obtain the offered service, then there is no compulsion or intensive for them to attend the designated facility. This means that, once the facilities are open, what the locator wishes the customers to do may not coincide with their own wish and behavior. We suppose that the customers are involved in a Nash game in order to ensure what they conceive as the best level of services for themselves. In order to take into consideration the effects of such competition in the facilities location decisions we propose a bi-level programming approach to the problem.

Scheduling jobs on a single serial-batching machine with dynamic job arrivals and multiple job types

This paper investigates a scheduling model with certain co-existing features of serial-batching, dynamic job arrival, multi-types of job, and setup time. In this proposed model, the jobs of all types are first partitioned into serial batches, which are then processed on a single serial-batching machine with an independent constant setup time for each new batch. In order to solve this scheduling problem, we divide it into two phases based on job arrival times, and we also derive and prove certain constructive properties for these two phases. Relying on these properties, we develop a two-phase hybrid algorithm (TPHA). In addition, a valid lower bound of the problem is also derived. This is used to validate the quality of the proposed algorithm. Computational experiments, both with small- and large-scale problems, are performed in order to evaluate the performance of TPHA. The computational results indicate that TPHA outperforms seven other heuristic algorithms. For all test problems of different job sizes, the average gap percentage between the makespan, obtained using TPHA, and the lower bound does not exceed 5.41 %.

A generic column generation principle : derivation and convergence analysis

AbstractGiven a non-empty, compact and convex set, and an a priori defined condition which each element either satisfies or not, we want to find an element belonging to the former category. This is a fundamental problem of mathematical programming which encompasses nonlinear programs, variational inequalities, and saddle-point problems. We present a conceptual column generation scheme, which alternates between solving a restriction of the original problem and a column generation phase which is used to augment the restricted problems. We establish the general applicability of the conceptual method, as well as to the three problem classes mentioned. We also establish a version of the conceptual method in which the restricted and column generation problems are allowed to be solved approximately, and of a version allowing for the dropping of columns. We show that some solution methods (e.g., Dantzig–Wolfe decomposition and simplicial decomposition) are special instances, and present new convergent column generation methods in nonlinear programming, such as a sequential linear programming type method. Along the way, we also relate our quite general scheme in nonlinear programming presented in this paper with several other classic, and more recent, iterative methods in nonlinear optimization.

Adaptive Tunning of All Parameters in a Multi-Swarm Particle Swarm Optimization Algorithm: An Application to the Probabilistic Traveling Salesman Problem

One of the main issues in the application of a particle swarm optimization (PSO) algorithm and of every evolutionary optimization algorithm is the finding of the suitable parameters of the algorithm. Usually, a trial and error procedure is used but, also, a number of different procedures have been applied in the past. In this chapter, we use a new adaptive version of a PSO algorithm where random values are assigned in the initialization of the algorithm and, then, during the iterations the parameters are optimized together and simultaneously with the optimization of the objective function of the problem. This idea is used for the solution of the probabilistic traveling salesman problem (PTSP). The algorithm is tested on a number of benchmark instances and it is compared with a number of algorithms from the literature.

Minimizing the Fuel Consumption of a Multiobjective Vehicle Routing Problem Using the Parallel Multi-Start NSGA II Algorithm

In this paper, a new multiobjective formulation of the Vehicle Routing Problem, the Multiobjective Fuel Consumption Vehicle Routing Problem (MFCVRP), using two different objective functions is presented. The first objective function corresponds to the optimization of the total travel time and the second objective function is the minimization of the fuel consumption of the vehicle taking into account the travel distance, the load of the vehicle, and other route parameters. We solve two cases of the Multiobjective Fuel Consumption Vehicle Routing Problem. In the first case the problem is symmetric and in the second case the problem is asymmetric. The problem is solved with the Parallel Multi-Start NSGA II that uses more than one initial population of individuals and a Variable Neighborhood Search algorithm for the improvement of each produced solution. The instances that are used for the solution of the problem are modified instances based on the classic Euclidean Traveling Salesman Problem benchmark instances taken from the TSP library.

An Island Memetic Algorithm for Real World Vehicle Routing Problems

In this paper, a new algorithm is presented which is applied to a real world Vehicle Routing Problem (VRP) of a provision company in the island of Crete in Greece. The company serves 116 customers located in Crete. This real world problem is solved effectively by a hybrid Island Memetic Algorithm (IMA) which employs Greedy Randomized Adaptive Search Procedure (GRASP) and Iterated Local Search (ILS). The proposed algorithm is also compared to five other approaches both on the real world problem and on classic benchmark instances from the literature. Methods such as GRASP, local search and Iterated Local Search (ILS) are employed as subroutines with certain probabilities in the algorithms. Furthermore, it is also demonstrated how premature convergence can be prevented by adopting specific strategy. Computational results show the superiority of the proposed hybrid Island Memetic Algorithm.

An Adaptive Bumble Bees Mating Optimization algorithm

Graphical abstractDisplay Omitted HighlightsAn adaptive version of the Bumble Bees Mating Optimization algorithm is proposed.All the parameters of the algorithm are calculated during the optimization process.The algorithm is applied for the solution of the Multicast Routing Problem.The algorithm is also applied for the solution of the Hierarchical Permutation Flowshop Scheduling Problem and of the Probabilistic Traveling Salesman Problem.In all problems comparisons with other algorithms from the literature are performed. The finding of the suitable parameters of an evolutionary algorithm, as the Bumble Bees Mating Optimization (BBMO) algorithm, is one of the most challenging tasks that a researcher has to deal with. One of the most common used ways to solve the problem is the trial and error procedure. In the recent few years, a number of adaptive versions of every evolutionary and nature inspired algorithm have been presented in order to avoid the use of a predefined set of parameters for all instances of the studied problem. In this paper, an adaptive version of the BBMO algorithm is proposed, where initially random values are given to each one of the parameters and, then, these parameters are adapted during the optimization process. The proposed Adaptive BBMO algorithm is used for the solution of the Multicast Routing Problem (MRP). As we would like to prove that the proposed algorithm is suitable for solving different kinds of combinatorial optimization problems we test the algorithm, also, in the Probabilistic Traveling Salesman Problem (PTSP) and in the Hierarchical Permutation Flowshop Scheduling Problem (HPFSP). Finally, the algorithm is tested in four classic benchmark functions for global optimization problems (Rosenbrock, Sphere, Rastrigin and Griewank) in order to prove the generality of the procedure. A number of benchmark instances for all problems are tested using the proposed algorithm in order to prove its effectiveness.

Convex optimization problems in supply chain planning and their solution by a column generation method based on the Frank Wolfe method

Many problems in supply chain optimization concern the minimization of a differentiable convex objective function subject to a set of linear constraints. The aim of this work is to present a number of such problems and to propose an efficient method for their solution. The proposed method is based on improvements of the well known Frank–Wolfe algorithm. The computational results of the proposed algorithm demonstrate its effectiveness and efficiency.