Optimal Solution Value Research Articles

Optimization of the different controller parameters via OBL approaches based artificial ecosystem optimization involving fitness distance balance guiding mechanism for efficient motor speed regulation of DC motor

This study proposes a new optimization approach, which is called as artificial ecosystem optimization algorithm with fitness-distance balance guiding mechanism by using opposite based learning methods (FDBAEO_OBLs) for the speed regulation of direct current (DC) motor. The performance of the proposed FDBAEO_OBL algorithm is tested in two different experimental studies. In the first experimental study, the proposed approach is tested in the CEC2020 benchmark test functions and the FDBAEO algorithm, which included the best OBL approach, is determined using non-parametric Wilcoxon and Friedman statistical analysis methods. Second, the parameters of proportional integral derivative (PID), tilt integral derivative (TID), proportional integral derivative with filter (PIDF), tilt integral derivative with filter (TIDF), fractional-order proportional integral derivative (FOPID), fractional-order proportional integral derivative with filter (FOPIDF), proportional integral derivative with fractional-order filter (PIDFF) and fractional-order proportional integral derivative with fractional-order filter (FOPIDFF) controller structures to be used in DC motor closed loop speed control are determined with FDBAEO_OBL, and the performances of the controllers are investigated. Integral absolute error (IAE), integral time absolute error (ITAE), integral time squared error (ITSE) and integral squared error (ISE) performance indices are used as the objective function of the operation process in which the control parameters are determined. According to the comparative step response results of the controller structures, the four best controller structures for DC motor speed regulation are determined. The performances of these controllers are examined under different simulation conditions and according to the results obtained, it is seen that the best controller structure is FOPIDFF. The FDBAEO_OBL algorithm, which is used in both benchmark test functions and DC motor speed regulation, shows an effective, durable and superior performance in finding the optimal solution values during the optimization.

An Efficient Scenario Reduction Method for Problems with Higher Moment Coherent Risk Measures

In this paper, we present an efficient scenario reduction method for optimization problems whose objective function is the higher moment coherent risk (HMCR) measures. Compared with existing approaches, our method places greater emphasis on the characteristics of optimization problems. Because the value of HMCR measures only depends on a small subset of scenarios that correspond to high cost or loss, our approach is based mostly on the concept of ineffective scenarios previously proposed in the literature, which entails identifying the scenarios whose removal from the problem results in no change of the optimal value. We test our method on a simple portfolio optimization problem with only nine risky assets and a realistic one with 50 risky assets and cardinality constraints. Results show that our scenario reduction method can yield a more accurate optimal solution and optimal value, along with a smaller reduced-scenario set. Even at the same reduction level, our method continues to outperform the existing scenario reduction methods. Interestingly, the portfolio produced by our method is also more diversified than others. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the National Natural Science Foundation of China [Grants 71720107002 and U1901223]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0375 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0375 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Estimating optimal split delivery vehicle routing problem solution values

This paper explores the application of linear regression models to estimate the optimal solution value (i.e., the sum of tour lengths) for the Split Delivery Vehicle Routing Problem (SDVRP). We present novel models that integrate topological features along with the mean and standard deviation of feasible solution values, achieving an impressive accuracy with an error margin of approximately 3%. To obtain random feasible solutions for the SDVRP quickly, we propose a modified Clarke & Wright algorithm with split delivery (MCWSD). Our results demonstrate the potential of extending our earlier work to more complex routing problems, highlighting the importance of incorporating diverse features to obtain accurate approximations.

Heat flow topology-driven thermo-mass decoupling strategy: Cross-scale regularization modeling and optimization analysis

The liquid desiccant dehumidification (LDD) is both eco-friendly and highly effective in humidity control, widely investigated across diverse angles. This study expands the application of the newly devised heat current method to examine the liquid desiccant dehumidification process. It introduces a new regularized temperature, which includes using a heat flow topology driven thermo-mass decoupling strategy, and constructing the heat current model by defining both the thermal resistance and moisture resistance. It significantly extends the application of the heat current method, clarifying the thermo-mass coupling energy transfer mechanism. The findings indicate that key factors influencing system performance indicators include total thermal conductivity (αA), solution mass flow rate (ms), air-solution mass flow rate ratio (RA/S,D), and heat source temperature (tH). Furthermore, under the influence of distinct thermal conductivities, the optimal output values for performance indicators, including moisture removal rate, exergy efficiency and entransy efficiency, are determined as 8.4 g/s, 71.2%, and 12.3%, respectively. The results of synergistic influence analysis reveal that, for the performance indicator entransy efficiency, msand RA/S,D display a significant degree of synergistic influence, resulting in a strong positive effect and benefiting 68.53% of the total area. Multi-objective optimization indicates a trade-off relationship among the system performance evaluation indicators moisture removal rate, exergy efficiency and entransy efficiency, with optimal solution values of 3.25 g/s, 65.92%, and 12.01%, respectively.

Code and Data Repository for VRPSolverEasy: A Python Library for the Exact Solution of a Rich Vehicle Routing Problem

VRPSolverEasy is a Python package which provides a simple interface for VRPSolver, a state-of-the-art Branch-Cut-and-Price exact solver for vehicle routing problems (VRPs). The simplified interface is accessible for users without operations research background, meaning you do not need to know how to model your problem as an Integer Programming problem. As a price to pay for the simplicity, this interface is restricted to some standard VRP variants, which involve the following features and their combinations: capacitated vehicles customer time windows heterogeneous fleet multiple depots open routes optional customers with penalties parallel links to model transition time/cost trade-off incompatibilities between vehicles and customers customers with alternative locations and/or time windows To our knowledge, VRPSolver is the most efficient exact solver available for VRPs. Its particularity is to focus on finding and improving a lower bound on the optimal solution value of your instance. It is less efficient in finding feasible solutions but still can be better than available heuristic solvers for non-classic VRP variants.

Robust optimization for the integrated berth allocation and quay crane assignment problem

AbstractThis paper studies the berth allocation and quay crane assignment problem (denoted by BACAP) under uncertainty. We assume that the ships' arrival and operation time is uncertain in this problem. We merge the proactive and reactive strategies to address the two‐stage robust optimization (denoted by RO) model for the BACAP to obtain a complete schedule with robustness. We obtain the berth allocation and quay crane assignment with a proactive strategy in the first stage. In the second stage, we formulate a rescheduling model with a reactive strategy considering the sensitivity towards the change in the complete schedule. The second stage model is based on the prospect theory, a quantitative way to describe the stakeholders' perception, including the port managers and shipowners, of the deviation from the baseline plan. The two stages are iterated until a favorable schedule with high robustness is found. To illustrate the superiority of the two‐stage robust optimization model with the prospect theory for the complete schedule, we give an intuitive example to compare the performance among the related models. The two‐stage RO model with the prospect theory for the complete schedule can generate a lower cost and higher robustness schedule. As for the solution methods, the column and constraint generation (denoted by C&CG) algorithm is applied to obtain the exact solution for the two‐stage RO model. Moreover, we propose the scenario‐constrained C&CG (denoted by SC) algorithm, which can reduce constraints and variables for the master problem to accelerate the solving process of the two‐stage RO model. In addition, the optimality of the SC algorithm is verified by analyzing the pattern of the occurrence of the worst‐case scenarios. Besides, to tackle the large‐scale instances, we propose the schedule‐fixed (denoted by SF) algorithm, in which the results of the previous iterations are treated as fixed. The SF algorithm can increase computing efficiency with a small gap compared to the optimal solution value. Furthermore, extensive numerical experiments are conducted on both real‐life instances and randomly generated instances to verify the superiority and generality of our model and algorithms.

Managing Volunteers and Paid Workers in a Nonprofit Operation

Some nonprofit organizations (NPOs) manage a complex workforce composed of a mix of volunteers, part-time workers, and full-time workers. We study the NPO’s finite-horizon staffing problem to determine the optimal initial staff planning decisions and per period optimal hiring and assignment decisions given a budget, capacity constraints, and an uncertain supply of volunteers and part-time workers. Our main goal is to solve this problem in a way that is effective and easy to implement while obtaining interesting managerial insights. To this end, we first demonstrate that the optimal staffing policies are computationally challenging to identify in general. However, we demonstrate that a prioritization assignment policy and a hire-up-to policy for part-time workers can be conveniently applied and are close to optimal. These policies are, in fact, optimal under staff scarcity and staff sufficiency. In our numerical analysis, we study the value and impact of the general optimal solution that considers flexibility and turnover of part-time workers versus the prioritization assignment policy and a constant hire-up-to policy that omit flexibility and turnover behaviors. We further suggest two easy-to-implement heuristics and theoretically analyze them and run a numerical performance study. We observe that both heuristics have low relative optimality gaps. Finally, we extend our analysis by studying how the optimal policy varies under three different practical considerations: a concave social value objective, nonzero volunteer costs, and dynamic volunteer behaviors. This paper was accepted by Jayashankar Swaminathan, operations management. Funding: This work was supported by the Comunidad de Madrid [Grant EPUC3M12], the Ministerio de Ciencia e Innovación [Grant PID2021-127657NA-I00], and the Ramon y Cajal Fellowship [RYC2020-029303-I]. Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2023.4923 .

A bicriteria approximation algorithm for the minimum hitting set problem in measurable range spaces

We consider the problem of finding a minimum-size hitting set in a range space F=(Q,R) defined by a measure on a family of subsets of an infinite set R. We observe that, under reasonably general assumptions, the infinite-dimensional convex relaxation can be solved (approximately) efficiently by multiplicative weight updates. As a consequence, we get an algorithm that finds, for any δ>0, a set of size O(αFzF⁎) that hits a (1−δ)-fraction of the ranges in R (with respect to the given measure) in time proportional to log⁡1δ, where zF⁎ is the value of the fractional optimal solution and αF is the integrality gap of the standard LP relaxation of the hitting set problem for the restriction of F on a set of points of size O(zF⁎log⁡1δ). Some applications of this result in Computational Geometry are given.

Estimating optimal objective values for the TSP, VRP, and other combinatorial problems using randomization

AbstractApproximation of the optimal tour length in a Euclidean traveling salesman problem (TSP) has been studied by many researchers. In a previous study, we used the standard deviation in random tour lengths to approximate the optimal tour length in both Euclidean and non‐Euclidean TSPs and we obtained good estimates. In this paper, we show that the strong power‐law relationship between the standard deviation in random feasible solution values and the optimal solution value also holds for other Euclidean and near‐Euclidean combinatorial optimization problems like the minimum spanning tree (MST) and maximum weight matching (MWM) problems. We then enhance the estimation ability of the model by considering a second predictor: the mean in random feasible solution values. Experimental results show that by using the mean, standard deviation, and randomization, we can accurately predict the optimal solution values for the TSP, MST, MWM, and the capacitated vehicle routing problem (VRP).

Sensitivity analysis of combinatorial optimization problems using evolutionary bilevel optimization and data mining

Sensitivity analysis in general deals with the question of how changes in input data of a model affect its output data. In the context of optimization problems, such an analysis could, for instance, address how changes in capacity constraints affect the optimal solution value. Although well established in the domain of linear programming, sensitivity analysis approaches for combinatorial optimization problems are model-specific, limited in scope and not applicable to practical optimization problems. To overcome these limitations, Schulte et al. developed the concept of bilevel innovization. By using evolutionary bilevel optimization in combination with data mining and visualization techniques, bilevel innovization provides decision-makers with deeper insights into the behavior of the optimization model and supports decision-making related to model building and configuration. Originally introduced in the field of evolutionary computation, most recently bilevel innovization has been proposed as an approach to sensitivity analysis for combinatorial problems in general. Based on previous work on bilevel innovization, our paper illustrates this concept as a tool for sensitivity analysis by providing a comprehensive analysis of the generalized assignment problem. Furthermore, it is investigated how different algorithms for solving the combinatorial problem affect the insights gained by the sensitivity analysis, thus evaluating the robustness and reliability of the sensitivity analysis results.

Single machine scheduling with assignable due dates to minimize maximum and total late work

A single machine scheduling problem with assignable job due dates to minimize total late work has recently been introduced by Mosheiov, Oron, and Shabtay (2021). The problem was proved NP-hard in the ordinary sense, and no solution algorithm was proposed. In this note, we present two pseudo-polynomial dynamic programming algorithms and an FPTAS for this problem. Besides, we introduce a new single machine scheduling problem to minimize maximum late work of jobs with assignable due dates. We develop an O(nlogn) time algorithm for it, where n is the number of jobs. An optimal solution value of this new problem is a lower bound for the optimal value of the total late work minimization problem, and it is used in the FPTAS.

Simultaneous minimisation of mean and variation of waiting times in a two-stage proportionate blocking flow shop

We consider the two-stage proportionate blocking flow shop scheduling problem with the objective of simultaneously minimising the mean and the variation of job waiting times. We show that the problem can be solved in time by evaluating at most two candidate optimal sequences. In some cases, the shortest processing time (SPT) sequence is optimal for any set of processing times. In all other cases, the optimal sequence is either the SPT sequence or a V-shaped sequence. We show that the optimal solution value for the corresponding no-wait flow shop scheduling problem is no worse than the optimal solution value for the blocking flow shop problem. We then analyse the blocking flow shop problem with the option of rejecting jobs from the sequence by paying their job-specific rejection penalties. We show that the problem with the job rejection option can be solved in time by dynamic programming (DP). Finally, we show that our results also apply to the corresponding flow shop scheduling problem with synchronous job transfers.

The continuous delayed distribution problem

Nowadays, decision makers (DMs) at companies have access to extensive and accurate data, which means they have the opportunity to grow and improve if they use the latent potential effectively. We address the complex problem of optimizing decisions in a multi-period one-warehouse multi-retailer inventory system with stochastic continuous demand and an option of delayed distributions. At the beginning of each period, the DM determines each retailer’s target stock levels, as well as the number of items to be held back at a central location for later distribution(s). Such a policy offers partial inventory pooling through the holdback quantity. The decisions in each period are data-driven, i.e., made based on sales data available through an information system up to that point in time.We model the problem as a multi-stage stochastic program with recourse. For the general case, we develop a new recursive solution algorithm, which is based on subgradient optimization and an analysis of system dynamics. For the special case of two identical retailers and two periods, we provide explicit optimality conditions based on the subgradients. Using a large numerical study, we evaluate the performance of our proposed policy and compare it to two benchmark policies. We also demonstrate the impact of various problem parameters on the optimal solution and objective value.

The Application of Particle Swarm Optimization in Neural Networks

The birth of the neural network model has provided a technological platform for the development of various industries. Among them, the branch network scientific research management model represented by the scientific research field is particularly profitable. China’s traditional research management system has been unable to meet the requirements of the present era and the management system reform is imperative. Therefore, based on Particle Swarm Optimization (PSO), this dissertation studies the neural network model based on the prerequisite that the branch network research management system retains the advantages of the traditional model. It tracks the optimal value of current search through cross and mutation. The optimal solution value is finally determined by solving the relationship between particle weight and inertia weight. In the final test, we establish the feasibility of the program.

Bifactor approximation for location routing with vehicle and facility capacities

Location Routing is a fundamental planning problem in logistics, in which strategic location decisions on the placement of facilities (depots, distribution centers, warehouses etc.) are taken based on accurate estimates of operational routing costs. We present an approximation algorithm, i.e., an algorithm with proven worst-case guarantees both in terms of running time and solution quality, for the general capacitated version of this problem, in which both vehicles and facilities are capacitated. Before, such approximation algorithms were only known for the special case where facilities are uncapacitated or where their capacities can be extended arbitrarily at linear cost. Previously established lower bounds that are known to approximate the optimal solution value well in the uncapacitated case can be off by an arbitrary factor in the general case. We show that this issue can be overcome by a bifactor approximation algorithm that may slightly exceed facility capacities by an adjustable, arbitrarily small fraction of the vehicle capacity while approximating the optimal cost by a constant factor. In addition to these proven worst-case guarantees, we also assess the practical performance of our algorithm in a comprehensive computational study, showing that the approach allows efficient computation of near-optimal solutions for instance sizes beyond the reach of current state-of-the-art heuristics.

Robust method of shared parking allocation based on buffer time

Shared parking platform determines the parking allocation schemes according to the time windows of parking supplies and parking demands. In order to deal with uncertain situations such as early arrival or delayed departure during parking, the robustness of the parking allocation scheme is enhanced by reserving appropriate buffer time. This paper builds a bi-objective optimization model of parking space allocation problem that maximizes the platform revenue and the robustness. The bi-objective function is transformed into a single objective function by the weighted sum method, and the nonlinear model is transformed into a linear model by adding auxiliary decision variables. Finally, the effectiveness of the method is verified by a numerical example, and the sensitivity analysis of key parameters is carried out. The results show that within a reasonable time, the method can obtain the optimal solution and various index values of the example. With the increase of the dual-objective adjustment coefficient, the platform revenue segment increases, while the robustness segment decreases. The non-dominated solutions are screened out from the optimal solutions obtained by different adjustment coefficients, and the approximate Pareto frontier curve is obtained by fitting. The robustness reduction varies in the range of [0.02, 6.75].

Techno-economic versus energy optimization of natural gas liquefaction processes with different heat exchanger technologies

The energy intensity of the natural gas liquefaction process in LNG value chains is considerable, and therefore a number of energy optimization studies have been conducted to obtain optimal operating conditions and maximize process efficiency. In order to limit the size and cost of heat exchangers during energy optimization, a minimum temperature approach constraint is used for heat exchangers, primarily as an economic trade-off parameter. However, the cost optimal solution and appropriate values for the minimum temperature approach constraints depend on the process concept and the heat exchanger type. In this study, techno-economic optimization and energy optimization are performed for three different natural gas liquefaction processes and two different heat exchanger types with different unit cost and heat transfer performance. The results indicate that the techno-economic optimization can provide a better distribution of temperature driving forces in the heat exchangers and thereby lower total annualized cost irrespective of the minimum temperature approach constraint. The energy optimization performs better for low-efficiency processes than high-efficiency processes in terms of the total annualized cost. In addition, based on the techno-economic optimization results, appropriate values for the minimum temperature approach constraints as economic trade-off parameters in the energy optimization are investigated for the two heat exchanger types.

A revisit of the proposed model for solving fuzzy linear fractional programming problem

Linear fractional programming (LFP) problem is used worldwide in solving real world problems. In real life situations the parameters of the problem are imprecise instead of fixed real numbers. So, a procedure for modelling these impreciseness in mathematical form is required. Fuzzy set theory is a best tool to deal with such situations. In this paper LFP problem with fuzzy parameters are studied. A fuzzy linear fractional programming (FLFP) problem is considered by Das et al. (2018) where a simple ranking approach between two triangular fuzzy numbers is provided. Then, in their study a tri-objective LFP problem is formulated to calculate the upper, middle and the lower bounds of the fuzzy optimal value. There are some errors and shortcomings in Das et al. method. Hence, in this study errors and shortcomings of Das et al. method are pointed out. Also, to overcome these errors, a simple method is presented to obtain optimal solution and fuzzy optimal value of the objective function. Moreover, by solving some numerical examples these errors are demonstrated and using the new proposed algorithm the correct optimal solution and the fuzzy optimal value of objective function are obtained.

On Multistage Multiscale Stochastic Capacitated Multiple Allocation Hub Network Expansion Planning

The hub location problem (HLP) basically consists of selecting nodes from a network to act as hubs to be used for flow traffic directioning, i.e., flow collection from some origin nodes, probably transfer it to other hubs, and distributing it to destination nodes. A potential expansion on the hub building and capacitated modules increasing along a time horizon is also considered. So, uncertainty is inherent to the problem. Two types of time scaling are dealt with; specifically, a long one (viz., semesters, years), where the strategic decisions are made, and another whose timing is much shorter for the operational decisions. Thus, two types of uncertain parameters are also considered; namely, strategic and operational ones. This work focuses on the development of a stochastic mixed integer linear optimization modeling framework and a matheuristic approach for solving the multistage multiscale allocation hub location network expansion planning problem under uncertainty. Given the intrinsic difficulty of the problem and the huge dimensions of the instances (due to the network size of realistic instances as well as the cardinality of the strategic scenario tree and operational ones), it is unrealistic to seek an optimal solution. A matheuristic algorithm, so-called SFR3, is introduced, which stands for scenario variables fixing and iteratively randomizing the relaxation reduction of the constraints and variables’ integrality. It obtains a (hopefully, good) feasible solution in reasonable time and a lower bound of the optimal solution value to assess the solution quality. The performance of the overall approach is computationally assessed by using stochastic-based perturbed well-known CAB data.

Thermal Analysis of Cylindrical Parabolic Trough Collector Using Particle Swarm Optimization

For about the first instance, a revolutionary Multi-objective Particle Swarm Optimization (PSO) method is applied to achieve a relatively close CPTC design for improving batter thermal performance and output warmth. Optimized design of parabolic trough collectors serves an important part in today's marketplace and is a rising area of concern for experts and academics. Particle swarm optimization (PSO) is an unique approach for enhancing a solar power trough collector's heat transfer analysis. Nanofluid has received a lot of interest as a way to increase convective heat transfer. They surpassed the previously used fluid. The thermal conductivity and convection temperature transfer coefficients are increased by employing nanofluid as the heat transport fluid and changing the base fluid. Particle concentration, thermal dispersion consistency, and nanofluid dimension are the important parameters for enhancing thermal conductivity, according to a prior study. As a preliminary step, keep these points in mind. Except perhaps the concentration fluid intake velocity and pipe diameter, the optimal solution value is determined using the tested model characteristics and the Dimethyl Polysiloxane Molecular as a base fluid. The results are exhibited at different temperatures. To determine if the recommended solution approach is appropriate, the outcomes of two research publications are compared