In this study, the performance of the modified subgradient algorithm (MSG) to solve the 0–1 quadratic knapsack problem (QKP) was examined. The MSG was proposed by Gasimov for solving dual problems constructed with respect to sharp Augmented Lagrangian function. The MSG has some important proven properties. For example, it is convergent, and it guarantees zero duality gap for the problems such that its objective and constraint functions are all Lipschtz. Additionally, the MSG has been successfully used for solving non-convex continuous and some combinatorial problems with equality constraints since it was first proposed. In this study, the MSG was used to solve the QKP which has an inequality constraint. The first step in solving the problem was converting zero-one nonlinear QKP problem into continuous nonlinear problem by adding only one constraint and not adding any new variables. Second, in order to solve the continuous QKP, dual problem with "zero duality gap" was constructed by using the sharp Augmented Lagrangian function. Finally, the MSG was used to solve the dual problem, by considering the equality constraint in the computation of the norm. To compare the performance of the MSG with some other methods, some test instances from the relevant literature were solved both by using the MSG and by using three different MINLP solvers of GAMS software. The results obtained were presented and discussed.

The drone arc routing problem (DARP) is one of the arc routing problems (ARPs) that has been studied by researchers recently. Unlike traditional ARPs, drones can travel directly between any two points in the graph. Due to the flexibility of drones, it is possible to use edges not defined in the graphs when deadheading the edges. This advantage of drones makes this problem more challenging than any other ARP. With this study, the energy capacities of drones are considered in a DARP. Thus, a novel DARP called the drone arc routing problem with deadheading demand (DARP-DD) is addressed in this study. Drone capacities are used both when servicing the edges and when deadheading the edges in the DARP-DD. A special case of the DARP-DD, called the multiple service drone arc routing problem with deadheading demand (MS-DARP-DD), is also discussed, where some critical required edges may need to be served more than once. To solve these challenging problems, a simulated annealing algorithm is used, and the components of the algorithm are designed. Additionally, novel neighbor search operators are developed in this study. The computational results show that the proposed algorithm and its components are effective and useful in solving the DARP-DD and MS-DARP-DD.

One of the most common plastic manufacturing methods is injection molding. In injection molding process, scheduling of plastic injection machines is very difficult because of the complex nature of the problem. For example, similar plastic parts should be produced sequentially to prevent long setup times. On the other hand, to produce a plastic part, its mold should be fixed on an injection machine. Machine eligibility restrictions should be considered because a mold can be usually fixed on a subset of the injection machines. Some plastic parts which have same shapes but different colors are used same mold so these parts can only be scheduled simultaneously if their mold has copies, otherwise resource constraints should be considered. In this study, a multi-objective mathematical model is proposed for parallel machine scheduling problem to minimize makespan, total tardiness, and total waiting time. Since NP-hard nature of problem, this paper presents a two-stage mathematical model and a two-stage solution approach. In the first stage of mathematical model, jobs are assigned to the machines and each machine is scheduled separately in the second stage. The integrated model and two-stage mathematical model are scalarized by using goal programming, compromise programming and Lexicographic Weighted Tchebycheff programming methods. To solve large-scale problems in a short time, a two-stage solution approach is also proposed. In the first stage of this approach, jobs are assigned to machines and scheduled by using proposed simulated annealing algorithm. In the second stage of the approach, starting time, completion time and waiting time of the jobs are calculated by using a mathematical model. The performance of the methods is demonstrated on randomly generated test problems.