Abstract: This paper presents a multi-objective optimal design of
a cascade control system for an underactuated mechanical system.
Cascade control structures usually include two control algorithms
(inner and outer). To design such a control system properly, the
following conflicting objectives should be considered at the same
time: 1) the inner closed-loop control must be faster than the outer
one, 2) the inner loop should fast reject any disturbance and prevent
it from propagating to the outer loop, 3) the controlled system
should be insensitive to measurement noise, and 4) the controlled
system should be driven by optimal energy. Such a control problem
can be formulated as a multi-objective optimization problem such
that the optimal trade-offs among these design goals are found.
To authors best knowledge, such a problem has not been studied
in multi-objective settings so far. In this work, an underactuated
mechanical system consisting of a rotary servo motor and a ball
and beam is used for the computer simulations, the setup parameters
of the inner and outer control systems are tuned by NSGA-II
(Non-dominated Sorting Genetic Algorithm), and the dominancy
concept is used to find the optimal design points. The solution of
this problem is not a single optimal cascade control, but rather a set
of optimal cascade controllers (called Pareto set) which represent the
optimal trade-offs among the selected design criteria. The function
evaluation of the Pareto set is called the Pareto front. The solution
set is introduced to the decision-maker who can choose any point
to implement. The simulation results in terms of Pareto front and
time responses to external signals show the competing nature among
the design objectives. The presented study may become the basis for
multi-objective optimal design of multi-loop control systems.
Abstract: This paper presents the techno-economic evaluation of run-of-river small-hydropower plants. In this regard, a multi-objective optimization procedure is proposed for the optimal sizing of the hydropower plants, and NSGAII is employed as the optimization algorithm. Annual generated energy and investment cost are considered as the objective functions, and number of generator units (n) and nominal turbine flow rate (QT) constitute the decision variables. Site of Yeripao in Benin is considered as the case study. We have categorized the river of this site using its environmental characteristics: gross head, and first quartile, median, third quartile and mean of flow. Effects of each decision variable on the objective functions are analysed. The results gave Pareto Front which represents the trade-offs between annual energy generation and the investment cost of hydropower plants, as well as the recommended optimal solutions. We noted that with the increase of the annual energy generation, the investment cost rises. Thus, maximizing energy generation is contradictory with minimizing the investment cost. Moreover, we have noted that the solutions of Pareto Front are grouped according to the number of generator units (n). The results also illustrate that the costs per kWh are grouped according to the n and rise with the increase of the nominal turbine flow rate. The lowest investment costs per kWh are obtained for n equal to one and are between 0.065 and 0.180 €/kWh. Following the values of n (equal to 1, 2, 3 or 4), the investment cost and investment cost per kWh increase almost linearly with increasing the nominal turbine flowrate while annual generated. Energy increases logarithmically with increasing of the nominal turbine flowrate. This study made for the Yeripao river can be applied to other rivers with their own characteristics.
Abstract: Nowadays, in advanced countries, agriculture as one of the most significant sectors of the economy, plays an important role in its political and economic independence. Due to farmers' lack of information about products' demand and lack of proper planning for harvest time, annually the considerable amount of products is corrupted. Besides, in this paper, we attempt to improve these unfavorable conditions via designing an effective supply chain network that tries to minimize total costs of agricultural products along with minimizing shortage in demand points. To validate the proposed model, a stochastic optimization approach by using a branch and bound solver of the LINGO software is utilized. Furthermore, to accumulate the data of parameters, a case study in Mazandaran province placed in the north of Iran has been applied. Finally, using ɛ-constraint approach, a Pareto front is obtained and one of its Pareto solutions as best solution is selected. Then, related results of this solution are explained. Finally, conclusions and suggestions for the future research are presented.
Abstract: Composite patching is a common way for reinforcing the cracked pipes and cylinders. The effects of composite patch reinforcement on fracture parameters of a cracked pipe depend on a variety of parameters such as number of layers, angle, thickness, and material of each layer. Therefore, stacking sequence optimization of composite patch becomes crucial for the applications of cracked pipes. In this study, in order to obtain the optimal stacking sequence for a composite patch that has minimum weight and maximum resistance in propagation of cracks, a coupled Multi-Objective Genetic Algorithm (MOGA) and Finite Element Method (FEM) process is proposed. This optimization process has done for longitudinal and transverse semi-elliptical cracks and optimal stacking sequences and Pareto’s front for each kind of cracks are presented. The proposed algorithm is validated against collected results from the existing literature.
Abstract: Terms set in power purchase agreements (PPA) challenge power utility companies in balancing between the returns (from maximizing power production) and securing long term supply contracts at capped production. The production limitation set in the PPA has driven efforts to maximize profits through efficient and economic power production. In this paper, a combined industrial-scale gas turbine (GT) - absorption chiller (AC) system is considered to cool the GT air intake for reducing the plant’s heat rate (HR). This GT-AC system is optimized while considering power output limitations imposed by the PPA. In addition, the proposed formulation accounts for uncertainties in the ambient temperature using Type-2 fuzzy programming. Using the enhanced chaotic differential evolution (CEDE), the Pareto frontier was constructed and the optimization results are analyzed in detail.
Abstract: Concurrent planning of project scheduling and
material ordering has been increasingly addressed within last decades
as an approach to improve the project execution costs. Therefore, we
have taken the problem into consideration in this paper, aiming to
maximize schedules quality robustness, in addition to minimize the
relevant costs. In this regard, a bi-objective mathematical model is
developed to formulate the problem. Moreover, it is possible to
utilize the all-unit discount for materials purchasing. The problem is
then solved by the E-constraint method, and the Pareto front is
obtained for a variety of robustness values. The applicability and
efficiency of the proposed model is tested by different numerical
instances, finally.
Abstract: Assembly line balancing problem is aimed to divide
the tasks among the stations in assembly lines and optimize some
objectives. In assembly lines the workload on stations is different
from each other due to different tasks times and the difference in
workloads between stations can cause blockage or starvation in some
stations in assembly lines. Buffers are used to store the semi-finished
parts between the stations and can help to smooth the assembly
production. The assembly line balancing and buffer sizing problem
can affect the throughput of the assembly lines. Assembly line
balancing and buffer sizing problems have been studied separately in
literature and due to their collective contribution in throughput rate of
assembly lines, balancing and buffer sizing problem are desired to
study simultaneously and therefore they are considered concurrently
in current research. Current research is aimed to maximize
throughput, minimize total size of buffers in assembly line and
minimize workload variations in assembly line simultaneously. A
multi objective optimization objective is designed which can give
better Pareto solutions from the Pareto front and a simple example
problem is solved for assembly line balancing and buffer sizing
simultaneously. Current research is significant for assembly line
balancing research and it can be significant to introduce optimization
approaches which can optimize current multi objective problem in
future.
Abstract: This study presents an Expert System specially designed to be used with Multiobjective Evolutionary Algorithms (MOEAs) for the solution of the portfolio selection problem. The validation of the proposed hybrid System is done by using data sets from Hang Seng 31 in Hong Kong, DAX 100 in Germany and FTSE 100 in UK. The performance of the proposed system is assessed in comparison with the Non-dominated Sorting Genetic Algorithm II (NSGAII). The evaluation of the performance is based on different performance metrics that evaluate both the proximity of the solutions to the Pareto front and their dispersion on it. The results show that the proposed hybrid system is efficient for the solution of this kind of problems.
Abstract: In this paper the multi-mode resource-constrained project scheduling problem with discounted cash flows is considered. Minimizing the makespan and maximization the net present value (NPV) are the two common objectives that have been investigated in the literature. We apply one evolutionary algorithm named multiobjective particle swarm optimization (MOPSO) to find Pareto front solutions. We used standard sets of instances from the project scheduling problem library (PSPLIB). The results are computationally compared respect to different metrics taken from the literature on evolutionary multi-objective optimization.
Abstract: Stock portfolio selection is a classic problem in finance,
and it involves deciding how to allocate an institution-s or an individual-s
wealth to a number of stocks, with certain investment objectives
(return and risk). In this paper, we adopt the classical Markowitz
mean-variance model and consider an additional common realistic
constraint, namely, the cardinality constraint. Thus, stock portfolio
optimization becomes a mixed-integer quadratic programming problem
and it is difficult to be solved by exact optimization algorithms.
Chemical Reaction Optimization (CRO), which mimics the molecular
interactions in a chemical reaction process, is a population-based
metaheuristic method. Two different types of CRO, named canonical
CRO and Super Molecule-based CRO (S-CRO), are proposed to solve
the stock portfolio selection problem. We test both canonical CRO
and S-CRO on a benchmark and compare their performance under
two criteria: Markowitz efficient frontier (Pareto frontier) and Sharpe
ratio. Computational experiments suggest that S-CRO is promising
in handling the stock portfolio optimization problem.
Abstract: Graph partitioning is a NP-hard problem with multiple
conflicting objectives. The graph partitioning should minimize the
inter-partition relationship while maximizing the intra-partition
relationship. Furthermore, the partition load should be evenly
distributed over the respective partitions. Therefore this is a multiobjective
optimization problem (MOO). One of the approaches to
MOO is Pareto optimization which has been used in this paper. The
proposed methods of this paper used to improve the performance are
injecting best solutions of previous runs into the first generation of
next runs and also storing the non-dominated set of previous
generations to combine with later generation's non-dominated set.
These improvements prevent the GA from getting stuck in the local
optima and increase the probability of finding more optimal
solutions. Finally, a simulation research is carried out to investigate
the effectiveness of the proposed algorithm. The simulation results
confirm the effectiveness of the proposed method.
Abstract: In this paper multi-objective genetic algorithms are
employed for Pareto approach optimization of ideal Turboshaft
engines. In the multi-objective optimization a number of conflicting
objective functions are to be optimized simultaneously. The
important objective functions that have been considered for
optimization are specific thrust (F/m& 0), specific fuel consumption
( P S ), output shaft power 0 (& /&) shaft W m and overall efficiency( ) O
η .
These objectives are usually conflicting with each other. The design
variables consist of thermodynamic parameters (compressor pressure
ratio, turbine temperature ratio and Mach number).
At the first stage single objective optimization has been
investigated and the method of NSGA-II has been used for multiobjective
optimization. Optimization procedures are performed for
two and four objective functions and the results are compared for
ideal Turboshaft engine. In order to investigate the optimal
thermodynamic behavior of two objectives, different set, each
including two objectives of output parameters, are considered
individually. For each set Pareto front are depicted. The sets of
selected decision variables based on this Pareto front, will cause the
best possible combination of corresponding objective functions.
There is no superiority for the points on the Pareto front figure,
but they are superior to any other point. In the case of four objective
optimization the results are given in tables.
Abstract: A new design of a planar passive T-micromixer with fin-shaped baffles in the mixing channel is presented. The mixing efficiency and the level of pressure loss in the channel have been investigated by numerical simulations in the range of Reynolds number (Re) 1 to 50. A Mixing index (Mi) has been defined to quantify the mixing efficiency, which results over 85% at both ends of the Re range, what demonstrates the micromixer can enhance mixing using the mechanisms of diffusion (lower Re) and convection (higher Re). Three geometric dimensions: radius of baffle, baffles pitch and height of the channel define the design parameters, and the mixing index and pressure loss are the performance parameters used to optimize the micromixer geometry with a multi-criteria optimization method. The Pareto front of designs with the optimum trade-offs, maximum mixing index with minimum pressure loss, is obtained. Experiments for qualitative and quantitative validation have been implemented.
Abstract: Vehicle suspension design must fulfill
some conflicting criteria. Among those is ride comfort
which is attained by minimizing the acceleration
transmitted to the sprung mass, via suspension spring
and damper. Also good handling of a vehicle is a
desirable property which requires stiff suspension and
therefore is in contrast with a vehicle with good ride.
Among the other desirable features of a suspension is
the minimization of the maximum travel of suspension.
This travel which is called suspension working space in
vehicle dynamics literature is also a design constraint
and it favors good ride. In this research a full car 8
degrees of freedom model has been developed and the
three above mentioned criteria, namely: ride, handling
and working space has been adopted as objective
functions. The Multi Objective Programming (MOP)
discipline has been used to find the Pareto Front and
some reasoning used to chose a design point between
these non dominated points of Pareto Front.
Abstract: Because of importance of energy, optimization of
power generation systems is necessary. Gas turbine cycles are
suitable manner for fast power generation, but their efficiency is
partly low. In order to achieving higher efficiencies, some
propositions are preferred such as recovery of heat from exhaust
gases in a regenerator, utilization of intercooler in a multistage
compressor, steam injection to combustion chamber and etc.
However thermodynamic optimization of gas turbine cycle, even
with above components, is necessary. In this article multi-objective
genetic algorithms are employed for Pareto approach optimization of
Regenerative-Intercooling-Gas Turbine (RIGT) cycle. In the multiobjective
optimization a number of conflicting objective functions
are to be optimized simultaneously. The important objective
functions that have been considered for optimization are entropy
generation of RIGT cycle (Ns) derives using Exergy Analysis and
Gouy-Stodola theorem, thermal efficiency and the net output power
of RIGT Cycle. These objectives are usually conflicting with each
other. The design variables consist of thermodynamic parameters
such as compressor pressure ratio (Rp), excess air in combustion
(EA), turbine inlet temperature (TIT) and inlet air temperature (T0).
At the first stage single objective optimization has been investigated
and the method of Non-dominated Sorting Genetic Algorithm
(NSGA-II) has been used for multi-objective optimization.
Optimization procedures are performed for two and three objective
functions and the results are compared for RIGT Cycle. In order to
investigate the optimal thermodynamic behavior of two objectives,
different set, each including two objectives of output parameters, are
considered individually. For each set Pareto front are depicted. The
sets of selected decision variables based on this Pareto front, will
cause the best possible combination of corresponding objective
functions. There is no superiority for the points on the Pareto front
figure, but they are superior to any other point. In the case of three
objective optimization the results are given in tables.
Abstract: The Prediction of aerodynamic characteristics and
shape optimization of airfoil under the ground effect have been carried
out by integration of computational fluid dynamics and the multiobjective
Pareto-based genetic algorithm. The main flow
characteristics around an airfoil of WIG craft are lift force, lift-to-drag
ratio and static height stability (H.S). However, they show a strong
trade-off phenomenon so that it is not easy to satisfy the design
requirements simultaneously. This difficulty can be resolved by the
optimal design. The above mentioned three characteristics are chosen
as the objective functions and NACA0015 airfoil is considered as a
baseline model in the present study. The profile of airfoil is
constructed by Bezier curves with fourteen control points and these
control points are adopted as the design variables. For multi-objective
optimization problems, the optimal solutions are not unique but a set
of non-dominated optima and they are called Pareto frontiers or Pareto
sets. As the results of optimization, forty numbers of non- dominated
Pareto optima can be obtained at thirty evolutions.
Abstract: The necessity of solving multi dimensional
complicated scientific problems beside the necessity of several
objective functions optimization are the most motive reason of born
of artificial intelligence and heuristic methods.
In this paper, we introduce a new method for multiobjective
optimization based on learning automata. In the proposed method,
search space divides into separate hyper-cubes and each cube is
considered as an action. After gathering of all objective functions
with separate weights, the cumulative function is considered as the
fitness function. By the application of all the cubes to the cumulative
function, we calculate the amount of amplification of each action and
the algorithm continues its way to find the best solutions. In this
Method, a lateral memory is used to gather the significant points of
each iteration of the algorithm. Finally, by considering the
domination factor, pareto front is estimated. Results of several
experiments show the effectiveness of this method in comparison
with genetic algorithm based method.
Abstract: In this paper, an attempt has been made to obtain nonsensitive
solutions in the multi-objective optimization of a
photovoltaic/thermal (PV/T) air collector. The selected objective
functions are overall energy efficiency and exergy efficiency.
Improved thermal, electrical and exergy models are used to calculate
the thermal and electrical parameters, overall energy efficiency,
exergy components and exergy efficiency of a typical PV/T air
collector. A computer simulation program is also developed. The
results of numerical simulation are in good agreement with the
experimental measurements noted in the previous literature. Finally,
multi-objective optimization has been carried out under given
climatic, operating and design parameters. The optimized ranges of
inlet air velocity, duct depth and the objective functions in optimal
Pareto front have been obtained. Furthermore, non-sensitive solutions
from energy or exergy point of view in the results of multi-objective
optimization have been shown.