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.

The wide range of Blockchain (BC) applications and BC’s ubiquity come from the fact that BC, as a collection of records linked to each other, is strongly resistant to alteration, protected using cryptography, and maintained autonomously. All these benefits come with a cost, which in BC is expressed by a very high use of energy needed to execute consensus protocols. Traditionally, consensus protocols based on Proof-of-Work (PoW) ensure fairness, but are not very useful. The paradigm proposed in the recent literature, known as Proof-of-Useful-Work (PoUW), assumes the completion of additional useful work for the same amount of resources (energy) used. However, the majority of the proposed PoUW approaches do not adequately consider fairness in balancing and controlling the difficulty of the work miners need to perform. A minority of the studies that do address fairness in miners’ work utilize PoW as a tool to ensure it. Therefore, a general framework to provide a structure for understanding the difficulty of useful work and how it can be used to fine-tune the complexity of miners’ effort in PoUW-based consensus protocols is proposed in this paper. The main characteristic of the proposed framework is that controlling the difficulty and fairness of miners’ work in PoUW-based consensus protocols is achieved exclusively through the useful work. The modules of the framework are discussed, and many research challenges and opportunities are articulated. The benefits of the proposed approach are illustrated taking as an example two optimization algorithms for a variant of the scheduling problem. In addition, the steps that should be taken to make this general framework applicable to any PoUW-based consensus protocols are identified.

In the era of open data and open science, it is important that, before announcing their new results, authors consider all previous studies and ensure that they have competitive material worth publishing. To save time, it is popular to replace the exhaustive search of online databases with the utilization of generative Artificial Intelligence (AI). However, especially for problems in niche domains, generative AI results may not be precise enough and sometimes can even be misleading. A typical example is $P\left|\right|C_{max}$, an important scheduling problem studied mainly in a wider context of parallel machine scheduling. As there is an uncovered symmetry between $P\left|\right|C_{max}$ and other similar optimization problems, it is not easy for generative AI tools to include all relevant results into search. Therefore, to provide the necessary background data to support researchers and generative AI learning, we critically discuss comparisons between algorithms for $P\left|\right|C_{max}$ that have been presented in the literature. Thus, we summarize and categorize the “state-of-the-art” methods, benchmark test instances, and compare methodologies, all over a long time period. We aim to establish a framework for fair performance evaluation of algorithms for $P\left|\right|C_{max}$, and according to the presented systematic literature review, we uncovered that it does not exist. We believe that this framework could be of wider importance, as the identified principles apply to a plethora of combinatorial optimization problems.