Blockchains (BCs) are distributed database systems, popular for their innovative, unsupervised maintenance process. They use a so-called consensus protocol to prevent inference by any third party of absolute trust. Security, privacy, consistency, and energy consumption have been identified as the main issues involved in BC maintenance. According to the recent literature, some of these issues can be formulated as combinatorial optimization (CO) problems, and this fact motivated us to consider incorporating CO approaches into a BC. In this paper, we propose the new combinatorial optimization consensus protocol (COCP) based on the proof-of-useful-work (PoUW) concept that assumes solving instances of real-life CO problems. Due to the complexity of the underlying CO problems, we have developed various types of heuristic methods, which are utilized in the COCP. Most of these methods are problem-dependent stochastic heuristic or metaheuristic methods. As is the case with the majority of consensus protocols, PoUW exhibits the property of asymmetry. It is difficult to find a solution for the considered CO problem; however, once a solution is found, its verification is straightforward. We present here a BC framework combining the two above-mentioned fields of research: BC and CO. This framework consists of improvements aiming towards developing the COCP of the PoUW type. The main advantage of this consensus protocol is the efficient utilization of computing resources (by exploring them for finding solutions of real-life CO problem instances), and the provision of a broad range of incentives for the various BC participants. We enumerate the potential benefits of the COCP with respect to its practical impacts and savings in power consumption, describing in detail an illustrative example based on part of the real-life BC network. In addition, we identify several challenges that should be resolved in order to implement a useful, secure, and efficient PoUW consensus protocol.

With the growing environmental concerns and the rising number of electric vehicles, researchers and companies are paying more and more attention to green logistics. This paper studies the Electric Vehicle Routing Problem with time-dependent speeds and soft time windows. The purpose is to minimize the total distance travelled, while penalizing early or late arrivals at the customers’ locations. For this purpose, we formulated the Mixed Integer Linear Program (MILP) and developed a General Variable Neighborhood Search (GVNS) metaheuristic, an efficient way to tackle this problem. To prove the efficiency of our approach, we tested the GVNS against the Adaptive Large Neighborhood Search (ALNS) algorithm and our MILP model, using a set of available benchmark instances. After an extensive experimental evaluation, we concluded that GVNS can find better quality solutions than other methods considered in this research or the same quality solution in less time.

The green vehicle routing problem (GVRP) is a relatively new topic, which aims to minimize greenhouse gasses (GHG) emissions produced by a fleet of vehicles. Both internal combustion vehicles (ICV) and alternative fuel vehicles (AFV) are considered, dividing GVRP into two separate subclasses: ICV-based GVRP and AFV-based GVRP. In the ICV-based subclass, the environmental aspect comes from the objective function which aims to minimize GHG emissions or fuel usage of ICVs. On the other hand, the environmental aspect of AFV-based GVRP is implicit and comes from using AFVs in transport. Since GVRP is NP-hard, finding the exact solution in a reasonable amount of time is often impossible for larger instances, which is why metaheuristic approaches are predominantly used. The purpose of this study is to detect gaps in the literature and present suggestions for future research in the field. For that purpose, we review recent papers in which GVRP was tackled by some metaheuristic methods and describe algorithm specifics, VRP attributes, and objectives used in them.