Application loader in the RW. Ring platform

When developing decision support systems in agriculture, the task often arises of creating applications that include a large number of different components. These components can have dependencies on each other, so you need to load them in the correct order. This boils down to solving the classic topological sorting problem. However, in addition to the purely algorithmic part, the loader must correctly interact with the environment, which poses a large number of other technology-specific tasks for its developer. These are the tasks of obtaining and storing information about dependencies, ensuring that components are loaded in the user interface thread where necessary, as well as ensuring the most responsive program behavior so that loading an application does not annoy the user, as well as ensuring the extensibility of the decision support system without recompiling. This work is devoted to the description of the solution of these problems in the RW.Ring platform based on the .NET technological stack and intended for the development of such software systems.

A Method to Deduce and Synthesize the Dafny Programs

We propose a systematic method to deduce and synthesize the Dafny programs. First, the specification of problem is described in strict mathematical language. Then, the derivation process uses program specification transformation technology to perform equivalent transformation. Furthermore, Dafny program is synthesized through the obtained recursive relationship and loop invariants. Finally, the functional correctness of Dafny program is automatically verified by Dafny verifier or online tool. Through this method, we deduce and synthesize Dafny programs for many typical problems such as the cube sum problem, the minimum (or maximum) contiguous subarray problems, several searching problems, several sorting problems, and so on. Due to space limitation, we only illustrate the development process of Dafny programs for two typical problems: the minimum contiguous subarray problem and the new local bubble sorting problem. It proves that our method can effectively improve the correctness and reliability of Dafny program developed. What’s more, we demonstrate the potential of the deductive synthesis method by developing a new local bubble Sorting program.

Exact Markov chain-based runtime analysis of a discrete particle swarm optimization algorithm on sorting and OneMax

Meta-heuristics are powerful tools for solving optimization problems whose structural properties are unknown or cannot be exploited algorithmically. We propose such a meta-heuristic for a large class of optimization problems over discrete domains based on the particle swarm optimization (PSO) paradigm. We provide a comprehensive formal analysis of the performance of this algorithm on certain “easy” reference problems in a black-box setting, namely the sorting problem and the problem OneMax. In our analysis we use a Markov model of the proposed algorithm to obtain upper and lower bounds on its expected optimization time. Our bounds are essentially tight with respect to the Markov model. We show that for a suitable choice of algorithm parameters the expected optimization time is comparable to that of known algorithms and, furthermore, for other parameter regimes, the algorithm behaves less greedy and more explorative, which can be desirable in practice in order to escape local optima. Our analysis provides a precise insight on the tradeoff between optimization time and exploration. To obtain our results we introduce the notion of indistinguishability of states of a Markov chain and provide bounds on the solution of a recurrence equation with non-constant coefficients by integration.

Large-Scale Storage/Retrieval Requests Sorting Algorithm for Multi-I/O Depots Automated Storage/Retrieval Systems

This paper addresses the sequence sorting problem of large-scale storage/retrieval (S/R) requests in multiple Input/Output (multi-I/O) depots automated storage/retrieval systems (AS/RS), in which the cargoes can enter/leave the system through multi-I/O depots, the stacker can load only one cargo, and the load travel time of stacker is fixed. The problem is to find an optimal sequence for a certain S/R requests sequence, and it is a special kind of traveling salesman problem. In this paper, a heuristic algorithm based on assignment is proposed. In order to eliminate the subloops emerged in the sorting process, the equivalent merging and minimum cost merging methods of subloops are considered, and the proposed algorithm is modified. Experimental results indicate the effectiveness of the proposed algorithm.

Recursively Divided Pancake Graphs with a Small Network Cost

Graphs are often used as models to solve problems in computer science, mathematics, and biology. A pancake sorting problem is modeled using a pancake graph whose classes include burnt pancake graphs, signed permutation graphs, and restricted pancake graphs. The network cost is degree × diameter. Finding a graph with a small network cost is like finding a good sorting algorithm. We propose a novel recursively divided pancake (RDP) graph that has a smaller network cost than other pancake-like graphs. In the pancake graph Pn, the number of nodes is n!, the degree is n − 1, and the network cost is O(n2). In an RDPn, the number of nodes is n!, the degree is 2log2n − 1, and the network cost is O(n(log2n)3). Because O(n(log2n)3) < O(n2), the RDP is superior to other pancake-like graphs. In this paper, we propose an RDPn and analyze its basic topological properties. Second, we show that the RDPn is recursive and symmetric. Third, a sorting algorithm is proposed, and the degree and diameter are derived. Finally, the network cost is compared between the RDP graph and other classes of pancake graphs.

A Novel Multi-Criteria Decision Sorting Approach based on Chebyshev's Theorem for Supplier Classification Problem

One of the interesting features of Multi-Criteria Decision Making/ Multiple Attribute Decision Making (MCDM/ MADM) is that a number of techniques that can be used to solve the same problem. In general, three common categories of decision problems are choice problem, ranking problem, and sorting problem. While, the issue of choice and ranking problems is more emphasized in MCDM/ MADM, but the literature weakly consider sorting problems. Several solutions for the above problem are suggested (i.e., Flow sort, AHP-Sort, ELECTRE Tri, etc.). Theoretically, there is no reason to be limited to these techniques. Hence, in this paper we propose a novel multi-criteria sorting method that is based on Chebyshev’s theorem. More specifically, different from other studies on MCDM sorting problems, which put more emphasis on the extension of new models, this work attempts to present a general framework using the Chebyshev’s inequality, to transform the results of conventional MCDM models from ranking format to sort mode. Finally, the proposed approach is compared with three existed models. Compared results show that the proposed method is efficient and the results are stable.

A Novel Multi-Criteria Sorting Model Based on AHP-Entropy Grey Clustering for Dealing with Uncertain Incoming Core Quality in Remanufacturing Systems

Remanufacturing is a key pillar of a circular economy and helps in recovering used products by extending their life cycle via remanufacturing them into new products. A vital aspect in a remanufacturing system is the quality assessment of incoming worn-out products (cores) prior to remanufacturing to ensure that non-conforming cores are discarded at an early stage in order to avoid unnecessary processing. Therefore, quality sorting plays an important role in core acquisition for remanufacturing systems when attempting to mitigate uncertain incoming core quality as an immediate solution. The main problem is that it is difficult to acquire the important information required to decide on the sorting of incoming cores, such as the core quality. The data are also commonly limited, not always available, or inaccurate. Grey systems are powerful methods in decision making when handling uncertainty with small data. In this paper, we consider the usefulness of grey systems for handling uncertain quality information for sorting incoming cores in a remanufacturing system. For this reason, we propose a multi-criteria quality sorting model based on an analytical hierarchy process (AHP)-entropy model that is coupled with grey clustering using possibility functions. The quality criteria for sorting the incoming cores are considered according to the technological, physical, and usage conditions. To demonstrate the practical contribution of this research, a case study of the quality sorting problem with a heavy-duty equipment remanufacturer is presented. The proposed model consistently classifies the quality of used hydraulic cylinders into two grey classes.

A path formula for the sock sorting problem

Допустим, что в сушильном барабане находятся $n$ различных пар носков. По окончании сушки носки выкладываются на стол один за другим. Если очередной вынутый носок оказывается из той же пары, что и один из лежащих на столе, то пара убирается, если нет, то носок остается на столе до тех пор, пока из сушки не появится носок из его пары. Каждый раз, когда один из $2n$ носков выкладывается на стол, мы записываем число носков, остающихся на столе. В работе получена явная формула для вероятности события, состоящего в том, что полученная последовательность совпадает с заданной последовательностью длины $2n$.

An Empirical Investigation of Transfer Effects for Reinforcement Learning

Previous studies have shown that training a reinforcement model for the sorting problem takes very long time, even for small sets of data. To study whether transfer learning could improve the training process of reinforcement learning, we employ Q-learning as the base of the reinforcement learning algorithm, apply the sorting problem as a case study, and assess the performance from two aspects, the time expense and the brain capacity. We compare the total number of training steps between nontransfer and transfer methods to study the efficiencies and evaluate their differences in brain capacity (i.e., the percentage of the updated Q-values in the Q-table). According to our experimental results, the difference in the total number of training steps will become smaller when the size of the numbers to be sorted increases. Our results also show that the brain capacities of transfer and nontransfer reinforcement learning will be similar when they both reach a similar training level.