Solution Approach For Problem Research Articles

Building a Course Portfolio with Industry- Institute Collaboration

The effective integration strategies of blended learning with traditional, designed a decade ago and proven effective, scalable, and flexible, now put forth several other challenges with delivery and evaluation. Especially for the elective courses, they demand assessments that add value to the course and the student's resume. The principles of elective design, the delivery tools, and techniques, the number of students, the significance of the course, etc., are some of the major evaluation parameters to be considered for the design of assessment strategies. This paper presents one such evaluation methodology, portfolio design, for the courses delivered in a blended learning model, which can also be adapted to the offline learning model. The model involved problem analysis, concept relation, design thinking, solution approaches, implementation, and presentation in the form of a portfolio. The portfolios were created online using various open source tools. The paper presents the model and design goals in detail. The first offering of the course had course projects, and the second offering had portfolio creation. The grades and attainment have improved in the second offering compared to the first one. There is also improvement in the course attainment where course learning objectives have remained the same. Portfolios are an effective strategy to evaluate one's course understanding. Portfolios can be an effective way to present the course realizations to the world. Keywords— assessment, blended-learning, elective design, portfolio

A novel evolutionary optimization algorithm based solution approach for portfolio selection problem

<span>The portfolio selection problem is one of the most common problems which drawn the attention of experts of the field in recent decades. The mean variance portfolio optimization aims to minimize variance (risk) and maximize the expected return. In case of linear constraints, the problem can be solved by variants of Markowitz. But many constraints such as cardinality, and transaction cost, make the problem so vital that conventional techniques are not good enough in giving efficient solutions. Stochastic fractal search (SFS) is a strong population based meta-heuristic approach that has derived from evolutionary computation (EC). In this paper, a novel portfolio selection model using SFS based optimization approach has been proposed to maximize Sharpe ratio. SFS is an evolutionary approach. This algorithm models the natural growth process using fractal theory. Performance evaluation has <span>been conducted to determine the effectiveness of the model by making comparison with other state of art models such as <a name="_Hlk101168095"></a>genetic algorithm (GA) and simulated</span> annealing (SA) on same objective and environment. The real datasets of the Bombay stock exchange (BSE) Sensex of Indian stock exchange have been taken in the study. Study reveals the superior performance of the SFS than GA and SA.</span>

Constraint programming-based solution approaches for three-dimensional loading capacitated vehicle routing problems

This paper presents constraint programming-based solution approaches for the three-dimensional loading capacitated vehicle routing problem (3l-CVRP) that consists of vehicle routing and three-dimensional loading problems in distribution logistics. Despite the practical benefits in the logistics world, the 3l-CVRP has not been extensively studied in the literature for its high combinatorial complexity. Therefore, we developed integrated and decomposed constraint programming-based solution methods in this study. The decomposed models outperformed the mixed-integer programming model proposed earlier in the literature for small-size problems. Furthermore, we solved the well-known benchmark problems with a decomposed model using constraint programming for the vehicle routing part of the problem and an evolutionary algorithm for the loading part. The computational study results show that the best-known results are improved in 36 of 93 problems.

Literature Review on Problem Models and Solution Approaches for Managing Real-Time Passenger Train Operations: The Perspective of Train Operating Companies

This study presents a comprehensive review of different problem models for managing railway operations by problem-type classification. Railway terminology was used to identify the studies that encompass the existing body of knowledge. The 28 articles analyzed showed that existing studies are focused on the individual schedule components, such as rolling stock, schedules, crews, and passengers. Few studies have adopted a broader scope by covering several of those components. Two of the most popular approaches include the integer linear program and the mixed integer linear program variant. The difference between them is that integer programming uses discrete decision-making variable data, while mixed integer programming also admits continuous variable data. In contrast, few studies involve combining computational algorithms with human knowledge-based approaches. This analysis reveals that the most significant variables for managing disruptive events are related to verifying suppressed circulation and the discrete events of real-time traffic, such as departures and arrivals at stations.

Machine Learning: A Solution Approach for Complex Problems

Abstract—Machine learning is a growing technology which enables computers to learn automatically from past data. Machine learning uses various algorithms for building mathematical models and making predictions using historical data or information.It is being used for various tasks such as image recognition, speech recognition, email filtering, Facebook auto- tagging, recommender system, and many more. Machine Learning is said as a subset of artificial intelligence that is mainly concerned with the development of algorithms which allow a computer to learn from the data and past experiences on their own.Machine learning enables a machine to automatically learn from data, improve performance from experiences, and predict things without being explicitly programmed.Machine learning brings computer science and statistics together for creating predictive models. Machine learning constructs or uses the algorithms that learn from historical data. This paper provides over all views of Machine Learning. Keywords—machine learning, artificial intelligence, data,learning,algorithm.

A Vectorization Scheme for Nonconvex Set Optimization Problems

In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from multiobjective optimization. Our strategy consists of deriving a parametric family of multiobjective optimization problems whose optimal solution sets approximate, in a specific sense, that of the set-valued problem with arbitrary accuracy. We also examine particular classes of set-valued mappings for which the corresponding set optimization problem is equivalent to a multiobjective optimization problem in the generated family. Surprisingly, this includes set-valued mappings with a convex graph.

A two-stage solution approach for unequal area facility layout problem with bi-directional relaxed flexible bay structure

PurposeThe purpose of this article is to develop a bi-directional relaxed flexible bay structure (BRFBS) in the layout for the unequal area facility layout problems (UA-FLPs) and test the suitability of the proposed approach using literature data.Design/methodology/approachThis research adopts a two-stage solution approach for UA-FLPs to form BRFBS in the layout. The solution to UA-FLPs is carried out in discrete space. The proposed heuristic method optimises the layout plan for minimising the material handling cost (MHC), and also, it indirectly optimises the space utilisation by reducing the empty space in the layout. The first stage of layout design assumes that all facilities are equal in size and uses quadratic assignment problem (QAP) model. QAP is solved with a simulated annealing heuristic method. In the second stage, a heuristic method is proposed to find the optimum width for each bay and the dimension for facilities. The proposed heuristic method is tested with numerical data available in the literature. Results are compared with the results obtained by layout planning software, and with the simulated annealing algorithm for flexible bay structure (SA-FBS) heuristic procedure for continuous space UA-FLPs.FindingsThe proposed two-stage solution approach gives the BRFBS for the UA-FLPs. BRFBS helps to create proper aisle structure in the layout plan. The layout configuration and solution of the proposed method is better than the layout planning software solution and SA-FBS solution. The application of the proposed heuristic method to case data gave lesser MHC, better space utilisation and better aisle formation than the existing layout.Research limitations/implicationsThe proposed approach has the limitation that it can be applied only to UA-FLPs solved in discrete space. When the UA-FLPs are solved in continuous space, then it is not possible to make application of this approach to form bi-directional relaxed flexible bays in the layout plan.Practical implicationsMost of the modern industries are automated, and they use material handling equipment (MHE) like automated guided vehicles (AGVs). Design of layout plans that help to create proper aisle structure for AGV’s in the layout plan is a challenging to the researchers. The BRFBS configuration is more suitable in the flexible manufacturing system where AGVs are used for material transportation.Originality/valueThis paper proposes a novel two-stage heuristic method for solving the UA-FLPs in discrete space. The proposed approach generates a BRFBS in the layout plan. The BRFBS helps to create a proper aisle structure suitable for better material handling operations. Hence, this type of layout helps in easy interaction of the MHE (e.g. AGVs) with the boundaries of the facilities touching the aisle.

Feasible Dispatch Limits of PV Generation With Uncertain Interconnection of EVs in the Unbalanced Distribution Network

This paper presents a framework to determine the feasible dispatch limits of solar photovoltaic (PV) generation in the unbalanced distribution network considering the interconnection of electric vehicles (EVs) and associated uncertainties. The proposed framework determines the lower and upper dispatch limits of PV generation considering the worst-case realization of a) the minimum and maximum storage capacity of EVs, b) the minimum and maximum power dispatch of EVs, c) the lower and upper bounds for the arrival and departure times, and d) the available energy at arrival and departure times. The unbalanced operation of the distribution network as well as the uncertainty in the maximum PV generation and demand forecasts were considered. The problem formulation and solution approach are validated using the modified IEEE 34-bus and IEEE 123-bus distribution systems. The impacts of the budget of uncertainty and the vehicle-to-grid operation mode of EV clusters were addressed in the case studies. It is shown that integrating EVs with charging capability will increase the lower dispatch limit or increase the upper dispatch limit of the PV generation. Moreover, the increase in the budget of uncertainty will reduce the difference between the upper and lower dispatch limits by increasing the lower dispatch or decreasing the upper dispatch limit of the PV generation. Finally, it is shown that the vehicle-to-grid capability will reduce the total lower dispatch limit or increase the total upper dispatch limit of the PV generation in the operation horizon.

A solution approach for cardinality minimization problem based on fractional programming

A solution approach for cardinality minimization problem based on fractional programming

The problem-solution approach revisited

The problem-solution approach revisited

Alternate solution approach for ML-MOLFPP problems

This article presents an alternate solution approach for multi-level multi objective linear fractional programming problems (ML-MOLFPPs) with modifications in the modified fuzzy goal programming (FGP) approach suggested by Lachhwani [1]. In the proposed alternate technique, fractional objective functions at every level are individually considered and converted into individual membership function instead of treating numerator and denominator part of objective function separately for formulation of membership function. The proposed alternate approach for obtaining compromise optimal solution for ML-MOLFPPs is comparatively less computational and efficient. This is demonstrated with the use of proposed technique over numerical example and comparative analysis with earlier method.

OUP accepted manuscript

According to Art 56 of the European Patent Convention (EPC) (and equivalent national provisions), an invention involves an inventive step if, having regard to prior art, it is not obvious to a person skilled in the art. There are different tests for inventive step. The European Patent Office (EPO) uses the problem–solution approach, which comprises three main stages: The English Pozzoli test (Pozzoli v BDMO [2007] EWCA Civ 588; [2007] FSR 37) and the German test for inventive step (reviewed by Gröning, GRUR 2021, 206) do not necessarily require that the starting point be ‘closest’ (if they consider a single starting point at all), and they define the problem more broadly (Germany) or not at all (UK). Another difference is the approach to the statutory question of obviousness: English and German courts adhere more strictly to the wording of the statutes, focusing on the question whether the features distinguishing...

Hybrid Classical-Quantum Optimization Techniques for Solving Mixed-Integer Programming Problems in Production Scheduling

Quantum computing (QC) holds great promise to open up a new era of computing and has been receiving significant attention recently. To overcome the performance limitations of near-term QC, utilizing the current quantum computers to complement classical techniques for solving real-world problems is of utmost importance. In this paper, we develop QC-based solution strategies that exploit quantum annealing and classical optimization techniques for solving large-scale scheduling problems in manufacturing systems. The applications of the proposed algorithms are illustrated through two case studies in production scheduling. First, we present a hybrid QC-based solution approach for the job-shop scheduling problem. Second, we propose a hybrid QC-based parametric method for the multi-purpose batch scheduling problem with a fractional objective. The proposed hybrid algorithms can tackle optimization problems formulated as mixed-integer linear and mixed-integer fractional programs, respectively, and provide feasibility guarantees. Performance comparison between state-of-the-art exact and heuristic solvers and the proposed QC-based hybrid solution techniques is presented for both job-shop and batch scheduling problems. Unlike conventional classical solution techniques, the proposed hybrid frameworks harness quantum annealing to supplement established deterministic optimization algorithms and demonstrate performance efficiency over standard off-the-shelf optimization solvers.

A Constraint Programming Approach to Solve Multi-skill Resource-constrained Project Scheduling Problem with Calendars

The multi-skill resource constrained project scheduling is an important and challenging problem in project management. Two key issues that turn this topic into a challenging problem are the assumptions that are considered to approximate the model to a real-world problem and exact solution approach for the model. In this paper, we deal with this two issues. To consider real-word situations, we take into account calendars specifying time intervals during which the resources are available. We proposed a constraint programming approach to solve the problem exactly. The problem with and without resource calendars are modeled with mathematical programming (MP) and constraint programming (CP). In addition, the performance of CP approach is evaluated by comparing Time-Indexed Model (TIM) and Branch and Price (B&P) approaches. Computational results show that the proposed approach can efficiently solve real-size instances.

Prediction of uniaxial compressive strength and modulus of elasticity for Travertine samples using an explainable artificial intelligence

The durability of rocks is a substantial rock property that has to be considered for designing geotechnical structures. Uniaxial compressive strength (UCS) and Young's modulus (E) are key indexes for measuring rocks’ durability. Several types of artificial intelligence (AI) methods have been used for modeling these key indexes; however, surprisingly, no explainable AI (XAI) has been considered for their model developments. An XAI is a model whose assessment is not a black box, and humans could understand its problem solution approach. This study has filled this gap and presented SHAP (Shapley Additive Explanations) as one of the most recent XAI methods for modeling UCS, and E. SHAP value could successfully illustrate intercorrelations between rock properties (porosity, point load index, P-wave velocity, and Schmidt hammer rebound number) and their representative UCS and E for each individual record and also together as variables. Results indicated that P-wave velocity has the highest importance for UCS and E prediction. eXtreme gradient boosting (XGBoost) was used as a solid predictive AI system for UCS and E estimation. Outcomes (R2> 0.99) confirmed the high accuracy of the SHAP-XGBoost model comparing with other typical AI models (Random Forest and Support Vector Regression). These results indicated XAI could be considered for illustrating complicated relationships within rock mechanics and energy-resource developments.

Network Models for Multiobjective Discrete Optimization

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework represents these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest-path problem in an auxiliary network. We design techniques for exploiting network models in order to accelerate the identification of the Pareto frontier, most notably a number of operations to simplify the network by removing nodes and arcs while preserving the set of nondominated solutions. We show that the proposed framework yields orders-of-magnitude performance improvements over existing state-of-the-art algorithms on five problem classes containing both linear and nonlinear objective functions. Summary of Contribution: Multiobjective optimization has a long history of research with applications in several domains. Our paper provides an alternative modeling and solution approach for multiobjective discrete optimization problems by leveraging graphical structures. Specifically, we encode the decision space of a problem as a layered network and propose graph reduction operators to preserve only solutions whose image are part of the Pareto frontier. The nondominated solutions can then be extracted through shortest-path algorithms on such a network. Numerical results comparing our method with state-of-the-art approaches on several problem classes, including the knapsack, set covering, and the traveling salesperson problem (TSP), suggest orders-of-magnitude runtime speed-ups for exactly enumerating the Pareto frontier, especially when the number of objective functions grows.

A Continuous Model for Designing Corridor Systems with Modular Autonomous Vehicles Enabling Station-wise Docking

The “asymmetry” between spatiotemporally varying passenger demand and fixed-capacity transportation supply has been a long-standing problem in urban mass transportation (UMT) systems around the world. The emerging modular autonomous vehicle (MAV) technology offers us an opportunity to close the substantial gap between passenger demand and vehicle capacity through station-wise docking and undocking operations. However, there still lacks an appropriate approach that can solve the operational design problem for UMT corridor systems with MAVs efficiently. To bridge this methodological gap, this paper proposes a continuum approximation (CA) model that can offer near-optimal solutions to the operational design for MAV-based transit corridors very efficiently. We investigate the theoretical properties of the optimal solutions to the investigated problem in a certain (yet not uncommon) case. These theoretical properties allow us to estimate the seat demand of each time neighborhood with the arrival demand curves, which recover the “local impact” property of the investigated problem. With the property, a CA model is properly formulated to decompose the original problem into a finite number of subproblems that can be analytically solved. A discretization heuristic is then proposed to convert the analytical solution from the CA model to feasible solutions to the original problem. With two sets of numerical experiments, we show that the proposed CA model can achieve near-optimal solutions (with gaps less than 4% for most cases) to the investigated problem in almost no time (less than 10 ms) for large-scale instances with a wide range of parameter settings (a commercial solver may even not obtain a feasible solution in several hours). The theoretical properties are verified, and managerial insights regarding how input parameters affect system performance are provided through these numerical results. Additionally, results also reveal that, although the CA model does not incorporate vehicle repositioning decisions, the timetabling decisions obtained by solving the CA model can be easily applied to obtain near-optimal repositioning decisions (with gaps less than 5% in most instances) very efficiently (within 10 ms). Thus, the proposed CA model provides a foundation for developing solution approaches for other problems (e.g., MAV repositioning) with more complex system operation constraints whose exact optimal solution can hardly be found with discrete modeling methods.

Exact solutions for the two-machine robust flow shop with budgeted uncertainty

This work proposes an exact solution approach for the two-machine robust flow shop problem, where operation processing times are uncertain and vary in a given interval. Based on the concept of budgeted uncertainty, the objective is to obtain a robust scheduling that minimizes the makespan of the restricted worst-case scenario, where only a subset of job processing times will oscillate to their worst-case values. To our knowledge, this is the first work to obtain optimal solutions to this problem, by extending two classical MILP formulations for the deterministic case and combining them with a Column-and-Constraint Generation framework. For this purpose, a dynamic programming algorithm was also developed, allowing the identification of worst-case scenarios in polynomial time. Experiments on a set of literature instances confirm the efficacy of our approach, including a case study that shows little overhead in the expected solution value of obtained robust solutions.

Centralized collaborative production scheduling with evaluation of a practical order-merging strategy

We study a collaborative scheduling problem where the dominant manufacturer (DM) outsources several processes to collaborative manufacturers (CMs). We consider multiple types of products defined by different collaborative production networks which may share some common CMs. The DM assigns the orders to the CMs and coordinates the production scheduling among the CMs. We analyse a practical order-merging strategy which combines a subset of same-type orders throughout the production aming at the cost benefit by continuous processing. Such a strategy is easy to implement but may increase the scheduling cost because of increased deviation between the completion time and the required delivery window of some orders. To this end, a heuristic algorithm based on a learning mechanism and ant colony optimisation is proposed for solving the collaborative scheduling problem under the order-merging plans. Simulation case study was carried out to compare the costs under different merging options. We conclude that merging more orders could lead to a better cost in a few cases, and the overall system performance is more sensitive to the merging schemes when the network capacity is tighter due to disruption. Our study provides an effective solution approach and managerial insights for collaborative scheduling problems with practical order-merging strategies.

A Comprehensive Solution Approach for CNC Machine Tool Selection Problem

A proper CNC machine selection problem is an important issue for manufacturing companies under competitive market conditions. The selection of an improper machine tool can cause many problems such as production capabilities and productivity indicators considering time and money industrially and practically. In this paper, a comprehensive solution approach is presented for the CNC machine tool selection problem according to the determined criteria. Seven main and thirteen sub-criteria were determined for the evaluation of the seven alternatives. To purify the selection process from subjectivity, instead of a single decision-maker, the opinions of six different experts on the importance of the criteria were taken and evaluated using the Best-Worst method. According to the evaluations, the order of importance of the main criteria has been determined as cost, productivity, flexibility, and dimensions. After the weighting of the criteria, three different ranking methods (GRA, COPRAS, and MULTIMOORA) were preferred due to the high investment costs of the selected alternatives. The findings obtained by solving the problem of selection of the CNC machine are close to those obtained by past researchers. As a result, using the suggested methodology, effective alternative decision-making solutions are obtained.