Unrelated Problems Research Articles

Optimizing energy efficiency in unrelated parallel machine scheduling problem through reinforcement learning

The industrial sector plays a significant role in global energy consumption and greenhouse gas emissions. To reduce this environmental impact, it's crucial to implement energy-efficient manufacturing systems that utilize sustainable materials and optimize energy usage. This can lead to benefits such as reduced carbon footprints and cost savings.In recent years, metaheuristic approaches have been focused on minimizing energy consumption within the Unrelated Parallel Machine Scheduling Problem (UPMSP). Traditional methods often overlook complex factors like release dates, due dates, and job setup times. This research introduces a novel algorithm that integrates reinforcement learning (RL) with a genetic algorithm (GA) to address this gap.The proposed RLGA algorithm, rooted in the dynamic field of evolutionary reinforcement learning, breaks down policies into smaller components to isolate essential parameters for problem-solving. Through comprehensive analysis, hyperparameters that influence optimal results are identified, facilitating automated hyperparameter selection and optimization. The expert system takes into account problem characteristics such as machine or job saturation, job overlap, and the maximum values of target variables, allowing instances to be grouped into clusters. These clusters are solved using a genetic algorithm with varying combinations of mutation and crossover hyperparameters. The most suitable approach for each cluster is determined by analyzing the results, and this configuration of hyperparameters is applied iteratively to optimize the solution search.The effectiveness of RLGA is evaluated across benchmark instances with different complexities, machine sets, jobs, and constraints. Comprehensive comparisons against existing methods highlight the superior performance and efficiency of RLGA in optimizing energy use and solution quality. Experimental results show that RLGA outperforms well-known solvers like CPO, CPLEX, OR-tools, and Gecode, making it a promising approach for optimizing energy-efficient manufacturing systems.

Detecting And Predicting Price Jumps With Consecutive Signature Distance

In order to estimate the hidden states of dynamical systems, Jump Models cluster financial observations along time series and impose a cost on jumping from one cluster to another. While these models can detect abrupt changes in the underlying time series, they suffer from two major drawbacks when it comes to detecting price jumps: (1) they cannot detect two (or more) consecutive jumps; (2) they cannot dissociate high volatility from jumps. To remedy these drawbacks, Bloch and Liao consider two seemingly unrelated problems: (1) Detecting and predicting price jumps by identifying whether a new observation results in a price jump relative to previous observations; (2) Anomaly detection of segments of a time series, that is, fixed size segments of a time series are treated as a normal corpus, and search for outliers. It is observed that while these problems are clearly different, the former can be reformulated in terms of the latter and they can therefore associate jump indicators to data-driven metrics for anomaly detection. Bloch and Liao propose a three-step process: (1) jump detection: the variance norm is combined with path signatures to come up with a data-driven jump indicator; (2) training: Bloch and Liao use this Variance Norm Jump Indicator as an input feature for Jump Models; (3) prediction: the authors use new incoming data to predict its hidden state. This approach aims at enhancing the model�s accuracy and predictive capabilities by leveraging the strengths of variance norm on detecting data points after the jump as outliers from previous distribution. Bloch and Liao conducted an extensive analysis on simulated data, examining the structure, benefits and limitations of the approach, and found that they could retrieve the true hidden states with high accuracy without using future information.

Algorithm for solving multi-objective hybrid flow shop scheduling problem

Aiming at the multi-objective unrelated parallel machine hybrid flow shop scheduling problem, a multi-objective mathematical model is established with the goal of minimizing the maximum completion time, total machine energy consumption and machine processing cost. An improved multi-objective evolution algorithm based on decomposition (IMOEAD) is proposed. The uniform design table is used to generate the initial weight vector to improve the population diversity. Normal distribution crossover and adaptive Gaussian mutation are used to improve the global and local search capabilities of the algorithm. Individuals are selected in the neighborhood of the weight vector to generate new solutions. The non-dominated rank and crowding distance are used to update the external archive. The inverse generation distance, generation distance and number of non-dominated solutions are used as performance indicators. Through a large number of case simulations, the algorithm is compared with the non-dominated sorting genetic algorithm II and the multi-objective evolution algorithm based on decomposition. The results verify the effectiveness of the algorithm.

Can the male germline offer insight into mammalian brain size expansion?

Recent advances in single-cell transcriptomic data have greatly expanded our understanding of both spermatogenesis and the molecular mechanisms of male infertility. However, this growing wealth of data could also shed light on a seemingly unrelated biological problem: the genetic basis of mammalian brain size expansion throughout evolution. It is now increasingly recognized that the testis and brain share many cellular and molecular similarities including pivotal roles for the RAS/MAPK and PI3K/AKT/mTOR pathways, mutations in which are known to have a pronounced impact on cell proliferation. Most notably, in the stem cell lineages of both organs, new mutations have been shown to increase cellular output over time. These include 'selfish' mutations in spermatogonial stem cells, which disproportionately increase the proportion of mutant sperm, and-to draw a parallel-human-specific mutations in neural stem cells which, by increasing the number of neurons, have been implicated in neocortical expansion. Here we speculate that the origin for many 'expansion'-associated mutations is the male germline and that as such, a deeper understanding of the mechanisms controlling testicular turnover may yield fresh insight into the biology and evolution of the brain.

Entry into A Cardiac Surgery Set Up: The Associated Risks and Difficulties for Inexperienced New Medical Staff

Background: Cardiac Surgery is one of the most sophisticated branches of medical science, which is continually being updated. With very little inclusion in medical course curriculum, medical graduates have limited orientation of this pristine subject. Capacity building is lengthy and cardiac surgery units often contain unrelated junior doctors due to scarcity of cardiac surgeons. New residents may also face similar difficulties. The objectives of this article are to describe the difficulties faces by newly posted doctors and offer some solutions. Methods: This study was conducted in the Department of Cardiac Surgery, Chittagong Medical College & Hospital (CMCH) between January 2020 and December 2022. A confidential self-report system questionnaire was used to interview 30 newcomers in CMCH and other cardiac surgery set ups and their findings are compiled in the article. Results: The interviewed doctors and residents have described individualities of cardiac surgery department and the difficulties they faced while working here. They also offered some solutions of the problems faced by them. Conclusion: Cardiac surgery is a stressful job. The new residents and unrelated doctors face various problems while beginning here. This is more troublesome for the female doctors, but doctors trained in cardiology or other surgical disciplines suffered least. Orientation initiatives by the cardiac surgery department and publishing a complete manual handbook to provide guidelines will be helpful in this regard. Cardiovasc j 2024; 16(2): 81-85

Mixed Variational Inequalities and Nonconvex Analysis

In this expository paper, we provide an account of fundamental aspects of mixed variational inequalities with major emphasis on the computational properties, various generalizations, dynamical systems, nonexpansive mappings, sensitivity analysis and their applications. Mixed variational inequalities can be viewed as novel extensions and generalizations of variational principles. A wide class of unrelated problems, which arise in various branches of pure and applied sciences are being investigated in the unified framework of mixed variational inequalities. It is well known that variational inequalities are equivalent to the fixed point problems. This equivalent fixed point formulation has played not only a crucial part in studying the qualitative behavior of complicated problems, but also provide us numerical techniques for finding the approximate solution of these problems. Our main focus is to suggest some new iterative methods for solving mixed variational inequalities and related optimization problems using resolvent methods, resolvent equations, splitting methods, auxiliary principle technique, self-adaptive method and dynamical systems coupled with finite difference technique. Convergence analysis of these methods is investigated under suitable conditions. Sensitivity analysis of the mixed variational inequalities is studied using the resolvent equations method. Iterative methods for solving some new classes of mixed variational inequalities are proposed and investigated. Our methods of discussing the results are simple ones as compared with other methods and techniques. Results proved in this paper can be viewed as significant and innovative refinement of the known results.

Just-in-time scheduling of unrelated parallel machines with family setups and soft time window constraints

ABSTRACT This study addresses an unrelated parallel machine scheduling problem with family setups and soft time windows, which includes considerations for machine eligibility. The objective is to minimize the total weighted tardiness and earliness, and to maximize the number of Just-in-Time jobs. Four different metaheuristic algorithms are compared to determine which type – single-point (simulated annealing), population-based evolutionary (artificial immune system, genetic algorithm), or swarm intelligence algorithms (ant colony optimization) – is more effective in solving this problem. Two strategies, namely penalty and repair, are proposed to handle precedence constraints. Experimental results demonstrate that ant colony optimization with local search which employs the repair strategy, as a swarm intelligence-based algorithm outperforms its rivals in terms of objective function values and robustness. The performance of this algorithm has shown an improvement in objective function values ranging from 2.12% to 8.52% on average, with a relative percentage deviation of 10.35.

Combinatorial optimization methods for yarn dyeing planning

AbstractManaging yarn dyeing processes is one of the most challenging problems in the textile industry due to its computational complexity. This process combines characteristics of multidimensional knapsack, bin packing, and unrelated parallel machine scheduling problems. Multiple customer orders need to be combined as batches and assigned to different shifts of a limited number of machines. However, several practical factors such as physical attributes of customer orders, dyeing machine eligibility conditions like flotte, color type, chemical recipe, and volume capacity of dye make this problem significantly unique. Furthermore, alongside its economic aspects, minimizing the waste of natural resources during the machine changeover and energy are sustainability concerns of the problem. The contradictory nature of these two makes the planning problem multi-objective, which adds another complexity for planners. Hence, in this paper, we first propose a novel mathematical model for this scientifically highly challenging yet very practical problem from the textile industry. Then we propose Adaptive Large Neighbourhood Search (ALNS) algorithms to solve industrial-size instances of the problem. Our computational results show that the proposed algorithm provides near-optimal solutions in very short computational times. This paper provides significant contributions to flexible manufacturing research, including a mixed-integer programming model for a novel industrial problem, providing an effective and efficient adaptive large neighborhood search algorithm for delivering high-quality solutions quickly, and addressing the inefficiencies of manual scheduling in textile companies; reducing a time-consuming planning task from hours to minutes.

Statistical learning and mathematics knowledge: the case of arithmetic principles

Statistical learning—an unconscious cognitive process used to extract regularities—is well-established as a fundamental mechanism underlying learning. Yet, despite the prominence of patterns in the number system and operations, little is known about the relation between statistical learning and mathematics knowledge. This study examined the associations among statistical learning, executive control, and arithmetic knowledge among first graders (N = 54). The relations varied by operation. For addition, children with greater statistical learning capacity responded more quickly to problems that were part of a principle (i.e., commutativity) pair than to unrelated problems, even after accounting for baseline performance, executive control, and age. For subtraction, results indicated an interaction between children's baseline subtraction performance and their statistical learning on accuracy. These findings provide an impetus for testing new models of mathematics learning that include statistical learning as a potentially important mechanism.

An application of mathematical programming to a real case of the unrelated parallel machine problem

An application of mathematical programming to a real case of the unrelated parallel machine problem

An energy-efficient unrelated parallel machine scheduling problem with learning effect of operators and deterioration of jobs

An energy-efficient unrelated parallel machine scheduling problem with learning effect of operators and deterioration of jobs

Imperialist competitive algorithm for unrelated parallel machine scheduling with sequence-and-machine-dependent setups and compatibility and workload constraints

In this paper, we present an in-depth analysis of the unrelated parallel machine scheduling problem (UPMSP) in the context of washing machine production at Vestel Electronics. Vestel Electronics is a leading producer of washing machines and holds a noteworthy market position in the European consumer electronics industry. The production process at Vestel Electronics is make-to-order (MTO) and requires 20 assembly lines to produce 200 different products. The decision maker must consider several important factors while forming the production schedule, including job-assembly line compatibility, the release times and due dates of the jobs, and a workload balance among the different assembly lines. This study aims to develop an algorithm to minimize the total earliness and tardiness while considering sequence-and-machine-dependent setups, unequal release times, machine-job compatibility restrictions, and workload balance requirements. To address this complex scheduling problem, we propose a novel algorithm, the imperialist competitive algorithm (ICA), which has a strong exploration–exploitation balance while mimicking real-world dynamics. Our numerical results show that the ICA significantly outperforms the current practice in Vestel by 39% and the best-performing algorithms in the literature by 23% and 12%.

Derivations in disjointly complete commutative regular algebras

We show that any nonexpansive derivation on a subalgebra of a dis-jointly complete commutative regular algebra extends up to a derivation on . For an algebra of functions , continuous on a dense open subset of Stone compact X, we establish that the lack of nontrivial derivation is equivalent to σ-distributivity of the Boolean algebra of clopen subsets of X. The field is an arbitrary normed field of charachteristic zero containing a complete non-discrete subfield. Our work is motivated by two seemingly unrelated problems due to Ayupov [2] and Wickstead [32].

Evolving many-objective dispatching rule pairs for unrelated parallel machine scheduling with sequence-dependent setup times

The real-world problem of unrelated parallel machine scheduling problem with sequence-dependent setup times (UPMSPSST) is investigated and focuses on two key aspects: fast solution and many-objective optimization. While dispatching rules (DRs) are effective in meeting demand, the manual design of many-objective DRs (MaODRs) is challenging. An alternative approach, based on the automatic evolution of MaODRs using hyper-heuristics, shows promise. However, limited literature exists on the automatic evolution of MaODRs specifically for UPMSPSST. In this study, a many-objective genetic programming (MaOGP) algorithm is formed by combining many-objective evolutionary algorithms (MaOEAs) with genetic programming (GP) algorithms. This enables the automatic evolution of MaODRs, leveraging the respective advantages of each approach. The exploration results demonstrate that the evolved MaODRs outperform manually designed DRs reported in prior literature. Furthermore, when considering combinations of objectives with different correlations, the MaODRs exhibit outstanding performance across multiple objectives simultaneously, surpassing even the performance of DRs trained separately for individual objectives. These findings highlight the potential of the proposed MaOGP approach in efficiently and effectively solving the UPMSPSST problem, opening avenues for further research and practical applications in related industries.

Assessing the Ability of Genetic Programming for Feature Selection in Constructing Dispatching Rules for Unrelated Machine Environments

The automated design of dispatching rules (DRs) with genetic programming (GP) has become an important research direction in recent years. One of the most important decisions in applying GP to generate DRs is determining the features of the scheduling problem to be used during the evolution process. Unfortunately, there are no clear rules or guidelines for the design or selection of such features, and often the features are simply defined without investigating their influence on the performance of the algorithm. However, the performance of GP can depend significantly on the features provided to it, and a poor or inadequate selection of features for a given problem can result in the algorithm performing poorly. In this study, we examine in detail the features that GP should use when developing DRs for unrelated machine scheduling problems. Different types of features are investigated, and the best combination of these features is determined using two selection methods. The obtained results show that the design and selection of appropriate features are crucial for GP, as they improve the results by about 7% when only the simplest terminal nodes are used without selection. In addition, the results show that it is not possible to outperform more sophisticated manually designed DRs when only the simplest problem features are used as terminal nodes. This shows how important it is to design appropriate composite terminal nodes to produce high-quality DRs.

Unrelated Parallel Machine Scheduling Problem Considering Job Splitting, Inventories, Shortage, and Resource: A Meta-Heuristic Approach

This research aims to study a real-world example of the unrelated parallel machine scheduling problem (UPMSP), considering job-splitting, inventories, shortage, and resource constraints. Since the nature of the studied optimization problem is NP-hard, we applied a metaheuristic algorithm named Grey Wolf Optimizer (GWO). The novelty of this study is fourfold. First, the model tackles the inventory problem along with the shortage amount to avoid the late fee. Second, due to the popularity of minimizing completion time (Makespan), each job is divided into small parts to be operated on various machines. Third, renewable resources are included to ensure the feasibility of the production process. Fourth, a mixed-integer linear programming formulation and the solution methodology are developed. To feed the metaheuristic algorithm with an initial viable solution, a heuristic algorithm is also fabricated. Also, the discrete version of the GWO algorithm for this specific problem is proposed to obtain the results. Our results confirmed that our proposed discrete GWO algorithm could efficiently solve a real case study in a timely manner. Finally, future research threads are suggested for academic and industrial communities.

An Energy-Efficient Unrelated Parallel Machine Scheduling Problem with Batch Processing and Time-of-Use Electricity Prices

The extensive consumption of energy in manufacturing has led to a large amount of greenhouse gas emissions that have caused an enormous effect on the environment. Therefore, investigating how to reduce energy consumption in manufacturing is of great significance to cleaner production. This paper considers an energy-conscious unrelated parallel batch processing machine scheduling problem under time-of-use (TOU) electricity prices. Under TOU, electricity prices vary for different periods of a day. This problem is grouping jobs into batches, assigning the batches to machines and allocating time to the batches so as to minimize the total electricity cost. A mixed-integer linear programming model and two groups of heuristics are proposed to solve this problem. The first group of heuristics first forms batches, assigns the batches to machines and finally allocates time to the batches, while the second group of heuristics first assigns jobs to machines, batches the jobs on each machine and finally allocates time to each batch. The computational results show that the SPT-FBLPT-P1 heuristic in the second group can provide high-quality solutions for large-scaled instances in a short time, in which the jobs are assigned to the machines based on the shortest processing time rule, the jobs on each machine are batched following the full-batch longest processing time algorithm, and the time is allocated to each batch following an integer programming approach. The MDEC-FBLPT-P1 heuristic that uses the minimum difference of the power consumption algorithm to assign the jobs also performed well.

Minimum+1 ( s, t )-cuts and Dual-edge Sensitivity Oracle

Let G be a directed multi-graph on n vertices and m edges with a designated source vertex s and a designated sink vertex t . We study the ( s,t )-cuts of capacity minimum+1 and as an important application of them, we give a solution to the dual-edge sensitivity for ( s,t )-mincuts—reporting an ( s,t )-mincut upon failure or insertion of any pair of edges. Picard and Queyranne [Mathematical Programming Studies, 13(1): 8–16 (1980)] showed that there exists a directed acyclic graph (DAG) that compactly stores all minimum ( s,t )-cuts of G . This structure also acts as an oracle for the single-edge sensitivity of minimum ( s,t )-cut. For undirected multi-graphs, Dinitz and Nutov [STOC, 509–518 (1995)] showed that there exists an 𝒪( n ) size 2-level Cactus model that stores all global cuts of capacity minimum+1. However, for minimum+1 ( s,t )-cuts, no such compact structure exists till date. We present the following structural and algorithmic results on minimum+1 ( s,t )-cuts. (1) Structure: There is an 𝒪( m ) size 2-level DAG structure that stores all minimum+1 (s,t) -cuts of G such that each minimum+1 ( s,t )-cut appears as 3-transversal cut—it intersects any path in this structure at most thrice. We also show that there is an 𝒪( mn ) size structure for storing and characterizing all minimum+1 (s,t) -cuts in terms of 1-transversal cuts. (2) Data structure: There exists an 𝒪( n 2 ) size data structure that, given a pair of vertices {u,v} that are not separated by an ( s,t )-mincut, can determine in 𝒪(1) time if there exists a minimum+1 ( s,t )-cut, say ( A,B ), such that s,u ∊ A and v,t∊ B ; the corresponding cut can be reported in 𝒪(| B |) time. (3) Sensitivity oracle: There exists an 𝒪( n 2 ) size data structure that solves the dual-edge sensitivity problem for (s,t) -mincuts. It takes 𝒪(1) time to report the capacity of a resulting (s,t) -mincut (A,B) and 𝒪(| B |) time to report the cut. (4) Lower bounds: For the data structure problems addressed in results (2) and (3) above, we also provide a matching conditional lower bound. We establish a close relationship among three seemingly unrelated problems—all-pairs directed reachability problem, the dual-edge sensitivity problem for ( s,t )-mincuts, and the problem of reporting the capacity of ({ x,y }, { u,v })-mincut for any four vertices x,y,u,v in G . Assuming the Directed Reachability Hypothesis by Patrascu [SIAM J. Computing, 827–847 (2011)] and Goldstein et al. [WADS, 421–436 (2017)], this leads to \(\tilde{\Omega }(n^2)\) lower bounds on the space for the latter two problems.

Review of Assessment Instruments to Measure Students’ System Thinking Skills

System thinking is one of the most important skills of the 21st century. System thinking helps students organize their thoughts in a meaningful way and make connections between seemingly unrelated problems. This study aims to determine the application of assessment instruments on system thinking skills based on literature review. This research uses the Systematic Literature Review (SLR) method. The SLR method is used to identify, review, evaluate, and interpret all available research with the topic area of phenomena of interest, with certain relevant research questions totaling 11 articles. The results of the literature review study that researchers analyzed and concluded that a good and relevant assessment instrument can help evaluate system thinking skills objectively and comprehensively, the application of the assessment instrument has an impact on students, especially on the ability to think systemically and critically.

A tabu search algorithm for the unrelated parallel machine scheduling problem with varied carbon emission constraints in different time intervals

The carbon emissions generated during the rapid development of the manufacturing industry have caused severe environmental pollution. Research on parallel machine scheduling problems considering carbon emission constraints has started to emerge in recent years to promote sustainable development and achieve low carbon emissions in production. In this paper, we consider an unrelated parallel machine scheduling problem with various carbon emission constraints in different time intervals. A mixed integer linear programming model with the objective of minimising the makespan is formulated to describe the problem accurately. Since the high complexity of our problem, we propose an efficient tabu search algorithm with a dedicated linked list structure to address this problem. Firstly, we generate four initial sequences according to the proposed heuristic rules and apply a greedy insertion decoding method to obtain the scheduling scheme. Then, we employ the 2-swap neighbourhood search strategy to exploit the promising solution space. The proposed model and algorithm are tested on extensive instances generated randomly. Computational results validate the correctness of the model and the effectiveness of the tabu search algorithm.