Single-objective Minimization Research Articles

Multi-criteria optimization approach to the design of small dams’ systems along mountainous stream beds

Abstract This paper aims at the optimal design of a system of small solid barrier-type stone dams in a semi-realistic study case, determining the number, location and height of dams and a borrow-pit (BP)'s location for benefit maximization and cost minimization of objectives: (a) maximum flood protection, (b) maximum underlying aquifers' artificial recharge, (c) minimum dams' construction cost and (d) minimum stonework transportation cost. The simplified conceptual model involves no hydraulic simulation; flow characteristics are not considered, while no dam is assumed to affect another dam's benefit/cost values. Hence, all partial benefit/cost values can be separately pre-calculated, for each one of the available dam locations for all available heights and BP locations, deriving from data concerning topography, geology/soil, land uses, construction and transportation costs. Any solution proposing a system of dams of various heights and a BP exhibits a total management value equal to the sum of the respective partial benefit/cost values of each dam. The multi-objective optimization problem is formulated into a single-objective minimization problem; the difference of costs minus benefits is to be minimized. Simple, elitist genetic algorithms (GAs) are used, coupled with sophisticated post-processing of results, able to produce optimized design solutions and strategies.

Grey Wolf Optimization Based Demand Side Management in Solar PV Integrated Smart Grid Environment

Most of world’s electrical energy demand is fulfilled by natural resources (Oil, Coal, Gas, etc.) and there is a huge gap between demand and supply. Therefore, utilities are facing the problem of peak load burden. Broadly speaking, to sustain future electricity demand renewable/alternate sources (solar, wind etc.) of energy must be integrated with smart grid (SG) to cope with energy demand. These sources are freely available, inexhaustible and can be used as an alternate source of energy. For smart utilization of electrical energy, a balance between supply and demand is required at all instants of time. In the SG environment, the most promising solution to reduce the peak load burden on utility is demand side management (DSM) which is possible because of the property of smart grid inertia. DSM permits all types of consumers to alter their energy consumption pattern to reduce the cost of energy and it helps the utility to reduce peak load burden and reshape load profile. In this study, DSM has been formulated as a single objective minimization problem to reduce peak load burden on utility. Although several optimization techniques has been listed in the literature which reduces the peak load and cost of energy, but integration of renewable energy is limited to residential consumers only. In this paper, a robust optimization algorithm inspired by the lifestyle of grey wolves, popularly known as grey wolf optimization (GWO) algorithm is utilized to solve the proposed DSM minimization problem. The DSM minimization problem optimization using GWO is demonstrated on three different cases-residential, commercial, and industrial loads in time of use (TOU) pricing scheme with and without solar PV energy (SPVE). Validation of GWO displays remarkable reductions in peak load on utility and cost of energy of consumers with and without SPVE. Also, GWO optimization results are compared with existing research papers having identical data sets.

An efficient optimization approach for flexibility provisioning in community microgrids with an incentive-based demand response scheme

Flexibility provisioning through demand response (DR) programs has emerged as an efficient tool for the economic and reliable management of electricity grids. In this work, an incentive-based DR model of a community microgrid (CMG) is considered, where an aggregator provides flexibility to the CMG. The objective of the aggregator is to minimize the cost of flexibility management that comprises the incentives paid to the residential users for shifting demands and penalty payments to the CMG operator for violating contractual commitments. Instead of attempting to minimize the total cost as single objective minimization, we adopt a two-stage optimization approach, wherein a bi-objective formulation is used in the first stage and a single objective formulation is used in the next. The bi-objective formulation enhances diversity and preserves promising solutions during the course of the search. An evolutionary algorithm is used to solve the bi-objective formulation and the obtained solution is improved in the next stage using local search conforming to a memetic algorithm paradigm. The performance of the proposed algorithm is investigated through statistical analysis and comparison with existing algorithms. The proposed algorithm reduces the peak-to-average ratio of CMG load by 3.97% with at least 27.94% cost saving compared to the state-of-the-art algorithms.

Hybrid Bacterial Foraging Sine Cosine Algorithm for Solving Global Optimization Problems

This paper proposes a new hybrid algorithm between Bacterial Foraging Algorithm (BFA) and Sine Cosine Algorithm (SCA) called Hybrid Bacterial Foraging Sine Cosine Algorithm (HBFSCA) to solve global optimization problems. The proposed HBFSCA algorithm synergizes the strength of BFA to avoid local optima with the adaptive step-size and highly randomized movement in SCA to achieve higher accuracy compared to its original counterparts. The performances of the proposed algorithm have been investigated on a set of single-objective minimization problems consist of 30 benchmark functions, which include unimodal, multimodal, hybrid, and composite functions. The results obtained from the test functions prove that the proposed algorithm outperforms its original counterparts significantly in terms of accuracy, convergence speed, and local optima avoidance.

Magnetorheological valves based on Herschel–Bulkley fluid model: modelling, magnetostatic analysis and geometric optimization

Magnetorheological (MR) fluids find wide application in various engineering applications. At the design stage of any MR devices, choosing a suitable rheological model for describing the flow behaviour is very critical. Since, the Herschel–Bulkley (H–B) is the most suitable model to describe the flow behaviour of MR fluids, the present study models the flow of MR fluid in the annular valve using the H–B model and does geometric optimization of the valve for three different commercially available MR fluids. The work discussed in the paper consist of three broader parts viz. (i) flow modelling, (ii) magnetostatic analysis and (iii) geometric optimization. In flow modelling, MR fluid flow is modelled using the H–B fluid model and validated by computational fluid dynamic analysis in ANSYS environment. Further, in magnetostatic analysis, for calculating the values of objective functions during the optimization process, magnetic flux density in the MR valve has been calculated using a polynomial model for the relative magnetic permeability for three different MR fluids, rather than conventionally choosing a constant value which is valid only for low ranges of current. The magnetostatic analysis has been validated through finite element modelling in ANSYS software package for different valve geometries. After defining the magnetization model for the chosen MR fluids and geometric design of the valve, variation of valve mass and performance indices such as damping force, dynamic range, inductive time constant and control energy, have been shown for all chosen fluids. In geometric optimization, the performance indices of the valve have been kept as objective functions which incorporate H–B fluid model for its definition. Such work has not been reported in the literature. Finally, a single-objective minimization problem has been formulated for the optimization with application-specific weight factors and solved using Genetic Algorithm in MATLAB® environment. The optimal results are then discussed and the best possible MR fluid has been suggested for the chosen applications.

Multi-objective optimization of the two-stage helical gearbox with tribological constraints

In this study, a novel multi-objective optimization of a two-stage helical gearbox is carried out with a comprehensive range of constraints. Two objective functions are formulated, the first minimizes the volume and the second minimizes the total power loss in the gearbox. Various design constraints such as bending stress, pitting stress, etc., and tribological constraints namely, scuffing and wear are included. By using a specially formulated discrete version of Non-Dominated Sorting Genetical Algorithm II (NSGA-II) these objective functions are minimized for three different gear profiles (unmodified profile, smooth meshing profile and high load capacity profile) and four ISO oil grades and at two speeds. The results are compared with standard single objective minimization without tribological constraints as per existing literature and single objective minimization with tribological constraints. It is shown that there is a high probability of wear failure for solutions obtained from single objective minimization without tribological constraints and the total power loss of the gearbox is reduced by half when using the multi-objective approach. Multi-objective optimization was also shown to give lower power losses when compared to the case of single objective optimization with tribological constraints.

单目标极小值优化法的多波长真温反演研究

单目标极小值优化法的多波长真温反演研究

Multi-Objective Optimization of Spur Gearbox with Inclusion of Tribological Aspects

In this paper, a novel multi-objective optimization of a two-stage spur gearbox is carried out with a comprehensive range of constraints. The first objective function aims to reduce the weight/volume and second aims to minimize the power losses in the gearbox. Various design constraints and tribological constraints such as scuffing and wear are included. By using a specially formulated discrete version of NSGA-II optimization code, these objective functions are minimized for three different gear profiles (unmodified profile, smooth meshing, and high load) and for different SAE oil grades. Optimization is first carried out based on standard single objective minimization using regular constraints based on existing literature and then based on multi-objective optimization with comprehensive constraints which include tribological aspects. Finally, these two cases are compared for different gear profiles and oils. The results indicate that there is a high probability of wear failure, for solutions obtained from single objective minimization. The total power loss is reduced by half when using multi-objective compared to single objective optimization.

Engine calibration: multi-objective constrained optimization of engine maps

We present two new approaches to address the optimization problem associated with engine calibration. In this area, the tuning parameters are traditionally determined in a local way, i.e., at each engine operating point, via a single-objective minimization problem. To overcome these restrictions, the first method we propose is able to cope with several objective functions simultaneously in the local formulation. The second method we put forward relies on a global formulation, which allows the whole driving cycle to be taken into account while remaining single-objective. At the practical level, the two methods are implemented by combining various existing techniques such as the LoLiMoT (Local Linear Model Tree) parameterization and the MO-CMA-ES (Multi-Objective Covariance Matrix Adaptation Evolution Strategy) algorithm. A better compromise appears to be achieved on real case applications.

Multi-objective optimization in variably saturated fluid flow

A general purpose multi-objective inverse modeling strategy was developed and implemented to quantify fluid flow parameters in variably saturated porous materials. The strategy combines a robust and mass-conservative numerical simulator of the flow equation with an optimization algorithm and an experimental data set to estimate the parameters. The numerical simulator of the direct problem shows excellent agreement with a reference solution and conserves global mass with near perfection. An adaptive method was proposed in which the sensitivity matrix was calculated by one-sided finite difference approximation at the early stages of the optimization and the more accurate two-sided differentiation as the search approaches the minimum. A combined termination criterium was developed to stop the inverse code at the solution. The results of the multi-objective optimization were compared with those of single-objective minimization. While single-objective optimization generates reasonable results for either the fluid pressure head profile or the fluid content data, the proposed multi-objective optimization shows excellent agreement with both profiles simultaneously.

Optimization study of stacked micro-channel heat sinks for micro-electronic cooling

With smaller inlet flow velocity, a micro-channel stack requires less pumping power to remove a certain rate of heat than a single-layered micro-channel, because it provides a larger heat transfer area. A simple thermal resistance network model was developed to evaluate the overall thermal performance of a stacked micro-channel heat sink. Based on this simple model, in this study, a single objective minimization of overall thermal resistance is carried out using genetic algorithms. The aspect ratio, fin thickness and the ratio of channel width to fin thickness are the variables to be optimized, subject to constraints of maximum pressure drop (4 bar) and maximum volumetric flow rate (1000 ml/min). During the optimization, the overall dimensions, number of layers and pumping power (product of pressure drop and flow rate) are fixed. The study indicates that reduction in thermal resistance can be achieved by optimizing the channel configuration. The effects of number of layers in the stack, pumping power per unit area, and the channel length are also investigated.

A STUDY ON PROJECT CRASHING DECISION WITH MULTIPLE FUZZY GOALS

ABSTRACT This article constructs a multiple fuzzy objective linear programming (MFOLP) model to solve single objective minimization problems on direct costs and total completed time relevant with crashing and resource allocation decisions on financial, manpower, and inputs for production resources. Factors considered in the proposed model are multiple objective functions, flexible decision procedures, resource limitations, and decision information indications. By using these factors as objective trade-off components with multiple fuzzy goals, the proposed model is practically developed to provide various scenarios on specific satisfactory levels in decision making. The model involves two novel minimization goals, total costs and total crashing costs, and factors on direct and indirect costs, resource supply/demand limitations, capacity planning, and total budget restrictions as well. The expansion schedule case from a plastic factory is used to implement the proposed model. The implementation is designed as several scenarios to survey the objective variations of goal components. The implementation results demonstrate that the use of MFOLP models could help decision planners easily explain to the theoretical rigor not found in simpler decision models.

CHESS—Changing Horizon Efficient Set Search: A Simple Principle for Multiobjective Optimization

This paper presents a new concept for generating approximations to the non-dominated set in multiobjective optimization problems. The approximation set A is constructed by solving several single-objective minimization problems in which a particular function D(A, z) is minimized. A new algorithm to calculate D(A, z) is proposed. No general approach is available to solve the one-dimensional optimization problems, but metaheuristics based on local search procedures are used instead. Tests with multiobjective combinatorial problems whose non-dominated sets are known confirm that CHESS can be used to approximate the non-dominated set. Straightforward parallelization of the CHESS approach is illustrated with examples. The algorithm to calculate D(A, z) can be used in any other applications that need to determine Tchebycheff distances between a point and a dominant-free set.

Transboundary air pollution in Europe: An interactive multicriteria tradeoff analysis

In this paper, the acid rain problem in Europe is discussed, stressing the transboundary tradeoffs between abatement costs of sulphur emission reduction and corresponding deposition levels in the different countries. An interactive decision support methodology is proposed which utilizes a powerful nonlinear multicriteria software package to evaluate various scenarios and tradeoffs. This methodology provides a more appropriate tool for policy making than single-objective minimization of costs with given target deposition levels, because in the latter the tradeoffs cannot be analyzed directly. The results from a tradeoff analysis using previously published data suggest that reasonable deposition levels can be reached with limited transfers of funds between countries. The extent of these transfers can be controlled by selecting appropriate target levels for the criteria across countries.