Cost Objective Function Research Articles

The impact of using a naïve approach in the limited-stop bus service design problem

The proven benefits of limited-stop services have captured the attention of researchers, especially during the last decade. However, to solve the limited-stop service design problem many existing works directly impose a capacity constraint to a total social cost objective function. This “naïve approach” implicitly assumes that passengers behave altruistically, basing their decisions on what is best for the whole system. Although this issue has been identified in earlier works, the magnitude of the error induced by this simplification has not been studied yet. The objective of this work is to measure this error and to understand how it misrepresents passenger flows and bus occupation rates. To measure this error gap, we optimize a set of test scenarios by applying a naïve approach, and then take the resulting design and obtain a benchmark passenger assignment using a simple behavioral model. We propose two main indicators to compare both passenger assignment: the total passenger deviation, and the total capacity deficit. This comparison reveals that the assignment of the naïve approach may indeed be unrealistic, and raises concerns that a network design based on the naïve approach might have severe problems when implemented. Thus, the work highlights the importance of taking the results of the naïve approach with caution and verify them with a passenger assignment model before their implementation.

Identification of Two-shaft Gas Turbine Variables Using a Decoupled Multi-model Approach With Genetic Algorithm

In industrial practice, the representation of the dynamics of nonlinear systems by models linking their different operating variables requires an identification procedure to characterize their behavior from experimental data. This article proposes the identification of the variables of a two-shafts gas turbine based on a decoupled multi-model approach with genetic algorithm. Hence the multi-model is determined in the form of a weighted combination of the decoupled linear local state space sub-models, with optimization of an objective cost function in different modes of operation of this machine. This makes it possible to have robust and reliable models using input / output data collected on the examined system, limiting the influence of errors and identification noises.

Wind Electric System (WES) Design Using General and Simple Algorithm.(Dept.E)

It is intended in this paper to find the optimum design of a wind electric system by a general, but simple algorithm. It is a general since the proposal can be applied to any wind regime, site and design parameters. Its simplicity stems from the direct solution of the optimization problem without hard and numerous calculations. This is obtained although several parameters are involved. Thus, an objective cost function is deduced to express mathematically the energy cost figure against the foregoing variables. It will be minimized subjected to the most effective technical constraints. Two models are derived also, to describe the optimum normalized rated wind speed and the minimum energy cost figure in explicit forms as functions of wind regime parameters and the wind speeds ratios. A comparative study has been carried out to validate the proposed algorithm and the deduced models. The results are compared with those attained by applying the previously published methodology which depends on step-by-step calculations for specific conditions. The comparison demonstrates the flexibility of the proposal to any change in data and accuracy in estimating the optimum solution despite of its simplicity.

Sustainable Supplier Selection and Order Allocation Under Risk and Inflation Condition

The main objective of this paper is to develop an integrated multiobjective and multiperiod mathematical model for sustainable supplier selection and order allocation of an automotive manufacturer. In spite of the vast quantity of research on this area, integrated consideration of risk and inflation in sustainable supplier selection and order allocation problem is less investigated. To fill this gap, this paper aims to develop a multiobjective sustainable supplier selection and order allocation model considering risk and inflation. Particularly, six objective functions of total cost, economic score, environmental score, social score, inflation rate, and risk level along with related constraints are optimized in the model. The developed model is solved using weighted sum approach and augmented ε-constraint method. In addition, a sensitivity analysis has been conducted. The results provide the best sustainable suppliers and the optimum quantity of products to be purchase from each supplier in each period.

Optimized routing algorithm for maximizing transmission rate in D2D network

<span style="font-size: 9pt; font-family: 'Times New Roman', serif;">Wireless devices have been equiping extensive services over recent years. Since most of these devices are randomly distributed, a fundamental trade-off to be addressed is the transmission rate, latency, and packet loss of the ad hoc route selection in device to device (D2D) networks. Therefore, this paper introduces a notion of weighted transmission rate and total delay, as well as the probability of packet loss. By designing optimal transmission algorithms, this proposed algorithm aims to select the best path for device-to-device communication that maximizes the transmission rate while maintaining minimum delay and packet loss. Using the Lagrange optimization method, the lagrangian optimization of rate, delay, and the probability of packet loss algorithm (LORDP) is modeled. For practical designation, we consider the fading effect of the wireless channels scenario. The proposed optimal algorithm is modeled to compute the optimal cost objective function and represents the best possible solution for the corresponding path. Moreover, a simulation for the optimized algorithm is presented based on optimal cost objective function. Simulation results establish the efficiency of the proposed LORDP algorithm</span><span>.</span><span style="font-size: 9pt; font-family: 'Times New Roman', serif;">Wireless devices have been equiping extensive services over recent years. Since most of these devices are randomly distributed, a fundamental trade-off to be addressed is the transmission rate, latency, and packet loss of the ad hoc route selection in device to device (D2D) networks. Therefore, this paper introduces a notion of weighted transmission rate and total delay, as well as the probability of packet loss. By designing optimal transmission algorithms, this proposed algorithm aims to select the best path for device-to-device communication that maximizes the transmission rate while maintaining minimum delay and packet loss. Using the Lagrange optimization method, the lagrangian optimization of rate, delay, and the probability of packet loss algorithm (LORDP) is modeled. For practical designation, we consider the fading effect of the wireless channels scenario. The proposed optimal algorithm is modeled to compute the optimal cost objective function and represents the best possible solution for the corresponding path. Moreover, a simulation for the optimized algorithm is presented based on optimal cost objective function. Simulation results establish the efficiency of the proposed LORDP algorithm</span>

A Bayesian Optimization Approach for Multi-Function Estimation for Environmental Monitoring Using an Autonomous Surface Vehicle: Ypacarai Lake Case Study

Bayesian optimization is a sequential method that can optimize a single and costly objective function based on a surrogate model. In this work, we propose a Bayesian optimization system dedicated to monitoring and estimating multiple water quality parameters simultaneously using a single autonomous surface vehicle. The proposed work combines different strategies and methods for this monitoring task, evaluating two approaches for acquisition function fusion: the coupled and the decoupled techniques. We also consider dynamic parametrization of the maximum measurement distance traveled by the ASV so that the monitoring system balances the total number of measurements and the total distance, which is related to the energy required. To evaluate the proposed approach, the Ypacarai Lake (Paraguay) serves as the test scenario, where multiple maps of water quality parameters, such as pH and dissolved oxygen, need to be obtained efficiently. The proposed system is compared with the predictive entropy search for multi-objective optimization with constraints (PESMOC) algorithm and the genetic algorithm (GA) path planning for the Ypacarai Lake scenario. The obtained results show that the proposed approach is 10.82% better than other optimization methods in terms of R2 score with noiseless measurements and up to 17.23% better when the data are noisy. Additionally, the proposed approach achieves a good average computational time for the whole mission when compared with other methods, 3% better than the GA technique and 46.5% better than the PESMOC approach.

FIR FILTER DESIGN WITH INERTIA WEIGHT AND COMPRESSION FACTOR APPROACH USING ADVANCED OPTIMIZATION TECHNIQUES

This paper includes the design of Finite impulse response filter with inertia weight and compression factor approach. The objective function of filter design involves accurate control of various parameters of frequency spectrum and is thus highly non-uniform, non-linear, non-differentiable and multimodal in nature. Classical optimization methods cannot converge to solutions. Because they have disadvantages such as highly sensitive to starting points, frequent convergence to local optimum solution or divergence or revisiting the same solution, requirement of continuous and differentiable objective cost function, requirement of the piecewise linear cost approximation and problem of convergence and algorithm. Evolutionary optimization methods for the design of optimal digital filters have better control of parameters and the highest stop band attenuation.

Modeling and Parameter Subset Selection for Fibrin Polymerization Kinetics with Applications to Wound Healing.

During the hemostatic phase of wound healing, vascular injury leads to endothelial cell damage, initiation of a coagulation cascade involving platelets, and formation of a fibrin-rich clot. As this cascade culminates, activation of the protease thrombin occurs and soluble fibrinogen is converted into an insoluble polymerized fibrin network. Fibrin polymerization is critical for bleeding cessation and subsequent stages of wound healing. We develop a cooperative enzyme kinetics model for in vitro fibrin matrix polymerization capturing dynamic interactions among fibrinogen, thrombin, fibrin, and intermediate complexes. A tailored parameter subset selection technique is also developed to evaluate parameter identifiability for a representative data curve for fibrin accumulation in a short-duration in vitro polymerization experiment. Our approach is based on systematic analysis of eigenvalues and eigenvectors of the classical information matrix for simulations of accumulating fibrin matrix via optimization based on a least squares objective function. Results demonstrate robustness of our approach in that a significant reduction in objective function cost is achieved relative to a more ad hoc curve-fitting procedure. Capabilities of this approach to integrate non-overlapping subsets of the data to enhance the evaluation of parameter identifiability are also demonstrated. Unidentifiable reaction rate parameters are screened to determine whether individual reactions can be eliminated from the overall system while preserving the low objective cost. These findings demonstrate the high degree of information within a single fibrin accumulation curve, and a tailored model and parameter subset selection approach for improving optimization and reducing model complexity in the context of polymerization experiments.

Benders decomposition for a period-aggregated resource leveling problem with variable job duration

We consider a special case of resource leveling problem with variable job duration and period-aggregated resource consumption. The objective function is to minimize the total extra resource cost required to complete all jobs before the hard project deadline. All jobs must be implemented without any preemption. The planning horizon is divided into periods, each period is characterized by an available level of resources of each type. For each job, resource consumption varies from one period to another. It is possible to control the speed of the job execution: if more resources are allocated to a job, then the job is executed faster if fewer resources are used, the job takes more time. A problem solution defines the start and end times for each job, but also its resource usage per period. On contrary to former models of this problem, our formulation allows an independent resource usage for each resource type. This approach can reach more flexible solutions with lower cost objective function value. We develop a Benders decomposition algorithm to solve this new formulation. Several enhancements are also implemented, such as the construction of effective bounds and multi-cut generation with the single search tree (Branch&Benders cuts). Numerical experiments on several sets of instances demonstrate the advantage of the algorithm in comparison with the basic model and a CPLEX built-in Benders decomposition.

Optimal Control in Fluid Models of nxn Input-Queued Switches under Linear Fluid-Flow Costs

We consider a fluid model of n x n input-queued switches with associated fluid-flow costs and derive an optimal scheduling control policy to an infinite horizon discounted control problem with a general linear objective function of fluid cost. Our optimal policy coincides with the cμ-rule in certain parameter domains, but more generally, takes the form of the solution to a flow maximization problem. Computational experiments demonstrate the benefits of our optimal scheduling policy over variants of max-weight scheduling and the cμ-rule.

Robust Multiobjective Nonlinear Constrained Optimization with Ensemble Stochastic Gradient Sequential Quadratic Programming-Filter Algorithm

Summary As the crucial step in closed-loop reservoir management, robust life-cycle production optimization is defined as maximizing/minimizing the expected value of a predefined objective (cost) function over geological uncertainties (i.e., uncertainties in the reservoir permeability, porosity, endpoint relative permeability, etc.). However, with robust optimization, there is no control over downside risk defined as the minimum net present value (NPV) among the individual NPVs of the different reservoir models. Yet, field operators generally wish to keep this minimum NPV reasonably large to try to ensure that the reservoir is commercially viable. In addition, the field operator may desire to maximize the NPV of production over a much shorter time period than the life of the reservoir under the limitation of surface facilities (e.g., field liquid and water production rates). Thus, it is important to consider multiobjective robust production optimization with nonlinear constraints and when geological uncertainties are incorporated. The three objectives considered in this paper are; to maximize the average life-cycle NPV, to maximize the average short-term NPV, and to maximize the minimum NPV of the set of realizations. Generally, these objectives are in conflict; for example, the well controls that give a global maximum for robust life-cycle production optimization do not usually correspond to the controls that maximize the short-term average NPV of production. Moreover, handling the nonlinear state constraints (e.g., field liquid production rates and field water production rates for the bottom-hole pressure controlled producers in the robust production optimization) is also a challenge because those nonlinear constraints should be satisfied at each control steps for each geological realization. To provide potential solutions to the multiobjective robust optimization problem with state constraints, we developed a modified lexicographic method with a minimizing-maximum scheme to attempt to obtain a set of Pareto optimal solutions and to satisfy all nonlinear constraints. We apply the sequential quadratic programming filter with modified stochastic gradients to solve a sequence of optimization problems, where each solution is designed to generate a single point on the Pareto front. In the modified lexicographic method, the objective is always considered to be the primary objective, and the other objectives are considered by specifying bounds on them to convert them to state constraints. The temporal damping and truncation schemes are applied to improve the quality of the stochastic gradient on nonlinear constraints, and the minimizing–maximum procedure is applied to enforce constraints on the normal state constraints. The main advantage that the modified lexicographic method has over the standard lexicographic method is that it allows for the generation of potential Pareto optimal points, which are uniformly spaced in the values of the second and/or third objective that one wishes to improve by multiobjective optimization.

Design optimization and sensitivity analysis of simply supported prestressed concrete girders: A two dimensional non-linear paradigm

This paper presents a practical optimum design solution of prismatic simply supported prestressed concrete girders that are subjected to uniformly distributed static loads. The process is formulated as a nonlinear optimization model while assuming linear elastic behavior and employing the working stresses method. The process produces the optimum values of two design variables, namely the cross-sectional dimensions and the prestressing force. Those optimized values are computed to satisfy either a minimum weight or a minimum cost objective function. To solve the nonlinear programming models, a program named Nonlinear Programming Prestressed Concrete Optimizer (NLPRECO) was coded in MATLAB® programming environment. Some illustrative design problems were solved using NLPRECO, and their results are demonstrated herein. Sensitivity analysis of the optimized design variables, to variations in design parameters, was also investigated, and the results are presented. Results show substantial improvement over the regular un-optimized solutions and moderate improvement over linear programming optimization solutions.

Robust multi-objective thermal and electrical energy hub management integrating hybrid battery-compressed air energy storage systems and plug-in-electric-vehicle-based demand response

A compressed air energy storage (CAES) can operate together with a battery energy storage system (BESS) to enhance the economic and environmental features of the energy hubs (EH). In this regard, this paper investigates their mutual cooperation in a multi-objective thermal and electrical residential EH optimization problem, which aims to diminish the total operational cost and emission. The proposed formulation also includes a PEV-based demand response program (DRP), renewable energy production units, solar heat collectors (SHE), thermal energy storage (TES), and hot water storage. Additionally, the CAES is operated as a combined heat and power unit in discharging and simple cycle modes. A linearized battery degradation cost model is integrated into the cost objective function, which ensures global optimization. Moreover, the inherent uncertainties of wind speed, solar irradiation, residential loads, electricity market price and PEVs’ load demand are handled by the computationally effective robust mixed-integer linear programming (RMILP) method. The PEVs’ uncertain load demand is obtained from their corresponding arrival–departure time, daily traveled miles, and vehicle type. The optimal Pareto front of the multi-objective problem is obtained by ε-constrained method for different robustness adjustments. Different deterministic and robust case studies are designed to evaluate the functionality of the proposed formulation.

A fair and EMG-validated comparison of recruitment criteria, musculotendon models and muscle coordination strategies, for the inverse-dynamics based optimization of muscle forces during gait

Experimental studies and EMG collections suggest that a specific strategy of muscle coordination is chosen by the central nervous system to perform a given motor task. A popular mathematical approach for solving the muscle recruitment problem is optimization. Optimization-based methods minimize or maximize some criterion (objective function or cost function) which reflects the mechanism used by the central nervous system to recruit muscles for the movement considered. The proper cost function is not known a priori, so the adequacy of the chosen function must be validated according to the obtained results. In addition of the many criteria proposed, several physiological representations of the musculotendon actuator dynamics (that prescribe constraints for the forces) along with different musculoskeletal models can be found in the literature, which hinders the selection of the best neuromusculotendon model for each application. Seeking to provide a fair base for comparison, this study measures the efficiency and accuracy of: (i) four different criteria within the static optimization approach (where the physiological character of the muscle, which affects the constraints of the forces, is not considered); (ii) three physiological representations of the musculotendon actuator dynamics: activation dynamics with elastic tendon, simplified activation dynamics with rigid tendon and rigid tendon without activation dynamics; (iii) a synergy-based method; all of them within the framework of inverse-dynamics based optimization. Motion/force/EMG gait analyses were performed on ten healthy subjects. A musculoskeletal model of the right leg actuated by 43 Hill-type muscles was scaled to each subject and used to calculate joint moments, musculotendon kinematics and moment arms. Muscle activations were then estimated using the different approaches, and these estimates were compared with EMG measurements. Although no significant differences were obtained with all the methods at statistical level, it must be pointed out that a higher complexity of the method does not guarantee better results, as the best correlations with experimental values were obtained with two simplified approaches: the static optimization and the physiological approach with simplified activation dynamics and rigid tendon, both using the sum of the squares of muscle forces as objective function.

Sizing and Cost Minimization of Standalone Hybrid WT/PV/Biomass/Pump-Hydro Storage-Based Energy Systems

In this study, a standalone hybrid wind turbine (WT)/photovoltaic (PV)/biomass/pump-hydro-storage energy system was designed and optimized based on technical, economic, and environmental parameters to provide the load demand with an objective function of minimum cost of energy (COE). The constraints of the proposed approach are the loss of power supply probability, and the excess energy fraction. The proposed approach allows the combination of different sources of energy to provide the best configuration of the hybrid system. Therefore, the proposed system was optimized and compared with a WT/PV/biomass/battery storage-based hybrid energy system. This study proposes three different optimization algorithms for sizing and minimizing the COE, including the whale optimization algorithm (WOA), firefly algorithm (FF) and particle swarm optimization (PSO) and the optimization procedure was executed using MATLAB software. The outcomes of these algorithms are contrasted to select the most effective, and the one providing the minimum COE is chosen based on statistical analysis. The results indicate that the proposed hybrid WT/PV/biomass/pump-hydro storage energy system is environmentally and economically practical. Meanwhile, the outcomes demonstrated the technical feasibility of a pump-hydro energy storage system in expanding the penetration of renewable energy sources compared to other existing systems. The COE of the pumped-hydro storage hybrid system was found to be lower (0.215 $/kWh) than that with batteries storage hybrid system (0.254 $/kWh) which was determined using WOA at the same load demand.

A globally convergent method to accelerate topology optimization using on-the-fly model reduction

We present a globally convergent method to accelerate density-based topology optimization using projection-based reduced-order models (ROMs) and trust-region methods. To accelerate topology optimization, we replace the large-scale finite element simulation, which dominates the computational cost, with ROMs that reduce the cost of objective function and gradient evaluations by orders of magnitude. To guarantee convergence, we first introduce a trust-region method that employs generalized trust-region constraints and prove it is globally convergent. We then devise a class of globally convergent ROM-accelerated topology optimization methods informed by two theories: the aforementioned trust-region theory, which identifies the ROM accuracy conditions required to guarantee the method converges to a critical point of the original topology optimization problem; a posteriori error estimation theory for projection-based ROMs, which informs ROM construction procedure to meet the accuracy conditions. This leads to trust-region methods that construct and update the ROM on-the-fly during optimization; the methods are guaranteed to converge to a critical point of the original, unreduced topology optimization problem, regardless of starting point. Numerical experiments on three different structural topology optimization problems demonstrate the proposed reduced topology optimization methods accelerate convergence to the optimal design by up to an order of magnitude.

Optimisation of the Automated buffer positioning model under DDMRP logic

Abstract This paper discusses the buffer positioning problem in a hybrid Make-To-Order/Make-To-Stock (MTO/MTS) setting with deterministic lead times. With a more demanding market, delivery times have become more competitive. A dynamic amount of inventory is made immediately available at certain points of the manufacturing process, including the final product, allowing to improve the flow of materials and meet more competitive deadlines. This work is particularly interested in optimizing buffer positioning in the context of Demand Driven Material Requirement Planning (DDMRP), where the decision maker can process the location and the sizing of the inventory buffers in complex Bills of materials (BOMs) in the most efficient strategy all while minimizing inventory costs under service time constraint. To do so, an improvement of the existing model of the two first steps of DDMRP: the strategic inventory positioning and calculating the buffer levels, is proposed. A linearization of the model and better solutions in shorter computational times compared to the literature are given by the enhanced model which is proven through various simulations. A cost objective function was evaluated in this model, and was solved using CPLEX and its CP Optimizer. These simulations would prove a better and more efficient approach for an enhanced DDMRP implementation.

Research on Design of Cross-Aisles Shuttle-Based Storage/Retrieval System Based on Improved Particle Swarm Optimization

The cross-aisles shuttle-based storage/retrieval system has not only storage function but also the sorting function and makes full use of warehouse space to achieve high-density storage. It uses “part-to-picker” order picking mode to respond quickly to orders and shorten sorting time. In this paper, through the analysis of the system, an effective evaluation method for the efficiency and time of system picking under a single instruction operation cycle is presented. The objective function of system minimum cost under the condition of satisfying customer’s demand is constructed. The objective function is solved by an improved particle swarm algorithm based on the optimized initial particle swarm optimization. By optimizing, we can find the optimal configuration of the system (i.e., the number of tiers, number of aisles and number of bays, number of picking stations, and number of lifts with minimal system cost). Finally, the impact of different configurations on system performance is summarized. This method can guide the design planner to design a more reasonable system under minimum cost control.

Multiobjective Optimal Power Flow for Static Voltage Stability Margin Improvement

The prevailing economic and environmental pressures have pushed the operation of power systems to close to stability limits. In such situations, utilities are aiming to increase the network’s stability during system disturbances. Optimized generation scheduling in contingency and stressed conditions can improve system security while lowering losses and generation costs. This paper focuses on incorporating Voltage Collapse Proximity Index in the conventional optimal power flow problem for multiobjective optimization. Multiobjective Particle Swarm Optimization (MOPSO) algorithm is utilized for its fast convergence and strong exploration and exploitation capabilities. The minimization of three competing objective functions of generation cost, power loss, and voltage stability is assessed in different case studies to evaluate the impact on the control variables. To select the best case study for optimal system operation a Preference Selection index (PSI) is utilized. The effectiveness of the proposed approach is tested on standard IEEE 30-bus and IEEE 57-bus during normal, contingency, and stressed conditions using MATPOWER. The results indicate that an average voltage stability improvement of 53.80%, 66.90%, and 54.15% is achieved in normal, contingency, and stressed system conditions respectively when the three objective functions are optimized simultaneously. Additionally, a possible voltage collapse is prevented during system disturbances.

Hardness of an Asymmetric 2-Player Stackelberg Network Pricing Game

Consider a communication network represented by a directed graph G=(V,E) of n nodes and m edges. Assume that edges in E are partitioned into two sets: a set C of edges with a fixed non-negative real cost, and a set P of edges whose costs are instead priced by a leader. This is done with the final intent of maximizing a revenue that will be returned for their use by a follower, whose goal in turn is to select for his communication purposes a subnetwork of Gminimizing a given objective function of the edge costs. In this paper, we study the natural setting in which the follower computes a single-source shortest paths tree of G, and then returns to the leader a payment equal to the sum of the selected priceable edges. Thus, the problem can be modeled as a one-round two-player Stackelberg Network Pricing Game, but with the novelty that the objective functions of the two players are asymmetric, in that the revenue returned to the leader for any of her selected edges is not equal to the cost of such an edge in the follower’s solution. As is shown, for any ϵ>0 and unless P=NP, the leader’s problem of finding an optimal pricing is not approximable within n1/2−ϵ, while, if G is unweighted and the leader can only decide which of her edges enter in the solution, then the problem is not approximable within n1/3−ϵ. On the positive side, we devise a strongly polynomial-time O(n)-approximation algorithm, which favorably compares against the classic approach based on a single-price algorithm. Finally, motivated by practical applications, we consider the special cases in which edges in C are unweighted and happen to form two popular network topologies, namely stars and chains, and we provide a comprehensive characterization of their computational tractability.