Abstract: A multicriteria linear programming problem with integer variables and parameterized optimality principle "from lexicographic to Slater" is considered. A situation in which initial coefficients of penalty cost functions are not fixed but may be potentially a subject to variations is studied. For any efficient solution, appropriate measures of the quality are introduced which incorporate information about variations of penalty cost function coefficients. These measures correspond to the so-called stability and accuracy functions defined earlier for efficient solutions of a generic multicriteria combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied and maximum norms of perturbations for which an efficient solution preserves the property of being efficient are calculated.
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: Project managers are the ultimate responsible for the
overall characteristics of a project, i.e. they should deliver the project
on time with minimum cost and with maximum quality. It is vital for
any manager to decide a trade-off between these conflicting
objectives and they will be benefited of any scientific decision
support tool. Our work will try to determine optimal solutions (rather
than a single optimal solution) from which the project manager will
select his desirable choice to run the project. In this paper, the
problem in project scheduling notated as
(1,T|cpm,disc,mu|curve:quality,time,cost) will be studied. The
problem is multi-objective and the purpose is finding the Pareto
optimal front of time, cost and quality of a project
(curve:quality,time,cost), whose activities belong to a start to finish
activity relationship network (cpm) and they can be done in different
possible modes (mu) which are non-continuous or discrete (disc), and
each mode has a different cost, time and quality . The project is
constrained to a non-renewable resource i.e. money (1,T). Because
the problem is NP-Hard, to solve the problem, a meta-heuristic is
developed based on a version of genetic algorithm specially adapted
to solve multi-objective problems namely FastPGA. A sample project
with 30 activities is generated and then solved by the proposed
method.
Abstract: Scheduling for the flexible job shop is very important
in both fields of production management and combinatorial
optimization. However, it quit difficult to achieve an optimal solution
to this problem with traditional optimization approaches owing to the
high computational complexity. The combining of several
optimization criteria induces additional complexity and new
problems. In this paper, a Pareto approach to solve the multi
objective flexible job shop scheduling problems is proposed. The
objectives considered are to minimize the overall completion time
(makespan) and total weighted tardiness (TWT). An effective
simulated annealing algorithm based on the proposed approach is
presented to solve multi objective flexible job shop scheduling
problem. An external memory of non-dominated solutions is
considered to save and update the non-dominated solutions during
the solution process. Numerical examples are used to evaluate and
study the performance of the proposed algorithm. The proposed
algorithm can be applied easily in real factory conditions and for
large size problems. It should thus be useful to both practitioners and
researchers.
Abstract: The shortest path routing problem is a multiobjective
nonlinear optimization problem with constraints. This problem has
been addressed by considering Quality of service parameters, delay
and cost objectives separately or as a weighted sum of both
objectives. Multiobjective evolutionary algorithms can find multiple
pareto-optimal solutions in one single run and this ability makes them
attractive for solving problems with multiple and conflicting
objectives. This paper uses an elitist multiobjective evolutionary
algorithm based on the Non-dominated Sorting Genetic Algorithm
(NSGA), for solving the dynamic shortest path routing problem in
computer networks. A priority-based encoding scheme is proposed
for population initialization. Elitism ensures that the best solution
does not deteriorate in the next generations. Results for a sample test
network have been presented to demonstrate the capabilities of the
proposed approach to generate well-distributed pareto-optimal
solutions of dynamic routing problem in one single run. The results
obtained by NSGA are compared with single objective weighting
factor method for which Genetic Algorithm (GA) was applied.
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: Environmental awareness and the recent
environmental policies have forced many electric utilities to
restructure their operational practices to account for their emission
impacts. One way to accomplish this is by reformulating the
traditional economic dispatch problem such that emission effects are
included in the mathematical model. This paper presents a Particle
Swarm Optimization (PSO) algorithm to solve the Economic-
Emission Dispatch problem (EED) which gained recent attention due
to the deregulation of the power industry and strict environmental
regulations. The problem is formulated as a multi-objective one with
two competing functions, namely economic cost and emission
functions, subject to different constraints. The inequality constraints
considered are the generating unit capacity limits while the equality
constraint is generation-demand balance. A novel equality constraint
handling mechanism is proposed in this paper. PSO algorithm is
tested on a 30-bus standard test system. Results obtained show that
PSO algorithm has a great potential in handling multi-objective
optimization problems and is capable of capturing Pareto optimal
solution set under different loading conditions.
Abstract: This article proposes a novel Pareto-based multiobjective
meta-heuristic algorithm named non-dominated ranking
genetic algorithm (NRGA) to solve multi-facility location-allocation
problem. In NRGA, a fitness value representing rank is assigned to
each individual of the population. Moreover, two features ranked
based roulette wheel selection including select the fronts and choose
solutions from the fronts, are utilized. The proposed solving
methodology is validated using several examples taken from the
specialized literature. The performance of our approach shows that
NRGA algorithm is able to generate true and well distributed Pareto
optimal solutions.
Abstract: In some real applications of Statistical Process Control
it is necessary to design a control chart to not detect small process
shifts, but keeping a good performance to detect moderate and large
shifts in the quality. In this work we develop a new quality control
chart, the synthetic T2 control chart, that can be designed to cope with
this objective. A multi-objective optimization is carried out employing
Genetic Algorithms, finding the Pareto-optimal front of
non-dominated solutions for this optimization problem.
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: We propose a multi-agent based utilitarian approach
to model and understand information flows in social networks that
lead to Pareto optimal informational exchanges. We model the
individual expected utility function of the agents to reflect the net
value of information received. We show how this model, adapted
from a theorem by Karl Borch dealing with an actuarial Risk
Exchange concept in the Insurance industry, can be used for social
network analysis. We develop a utilitarian framework that allows us
to interpret Pareto optimal exchanges of value as potential
information flows, while achieving a maximization of a sum of
expected utilities of information of the group of agents. We examine
some interesting conditions on the utility function under which the
flows are optimal. We illustrate the promise of this new approach to
attach economic value to information in networks with a synthetic
example.
Abstract: The design of a steam turbine is a very complex
engineering operation that can be simplified and improved thanks to
computer-aided multi-objective optimization. This process makes use
of existing optimization algorithms and losses correlations to identify
those geometries that deliver the best balance of performance (i.e.
Pareto-optimal points).
This paper deals with a one-dimensional multi-objective and
multi-point optimization of a single-stage steam turbine. Using a
genetic optimization algorithm and an algebraic one-dimensional
ideal gas-path model based on loss and deviation correlations, a code
capable of performing the optimization of a predefined steam turbine
stage was developed. More specifically, during this study the
parameters modified (i.e. decision variables) to identify the best
performing geometries were solidity and angles both for stator and
rotor cascades, while the objective functions to maximize were totalto-
static efficiency and specific work done.
Finally, an accurate analysis of the obtained results was carried
out.
Abstract: In the multi objective optimization, in the case when generated set of Pareto optimal solutions is large, occurs the problem to select of the best solution from this set. In this paper, is suggested a method to order of Pareto set. Ordering the Pareto optimal set carried out in conformity with the introduced distance function between each solution and selected reference point, where the reference point may be adjusted to represent the preferences of a decision making agent. Preference information about objective weights from a decision maker may be expressed imprecisely. The developed elicitation procedure provides an opportunity to obtain surrogate numerical weights for the objectives, and thus, to manage impreciseness of preference. The proposed method is a scalable to many objectives and can be used independently or as complementary to the various visualization techniques in the multidimensional case.
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.
Abstract: Plackett-Burman statistical screening of media
constituents and operational conditions for extracellular lipase
production from isolate Trichoderma viride has been carried out in
submerged fermentation. This statistical design is used in the early
stages of experimentation to screen out unimportant factors from a
large number of possible factors. This design involves screening of
up to 'n-1' variables in just 'n' number of experiments. Regression
coefficients and t-values were calculated by subjecting the
experimental data to statistical analysis using Minitab version 15.
The effects of nine process variables were studied in twelve
experimental trials. Maximum lipase activity of 7.83 μmol /ml /min
was obtained in the 6th trail. Pareto chart illustrates the order of
significance of the variables affecting the lipase production. The
present study concludes that the most significant variables affecting
lipase production were found to be palm oil, yeast extract, K2HPO4,
MgSO4 and CaCl2.
Abstract: Due to the deregulation of the Electric Supply
Industry and the resulting emergence of electricity market, the
volumes of power purchases are on the rise all over the world. In a
bid to meet the customer-s demand in a reliable and yet economic
manner, utilities purchase power from the energy market over and
above its own production. This paper aims at developing an optimal
power purchase model with two objectives viz economy and
environment ,taking various functional operating constraints such as
branch flow limits, load bus voltage magnitudes limits, unit capacity
constraints and security constraints into consideration.The price of
purchased power being an uncertain variable is modeled using fuzzy
logic. DEMO (Differential Evolution For Multi-objective
Optimization) is used to obtain the pareto-optimal solution set of the
multi-objective problem formulated. Fuzzy set theory has been
employed to extract the best compromise non-dominated solution.
The results obtained on IEEE 30 bus system are presented and
compared with that of NSGAII.
Abstract: In this study, we explore the use of information for inventory decision in the healthcare organization (HO). We consider the scenario when the HO can make use of the information collected from some correlated products to enhance its inventory planning. Motivated by our real world observations that HOs adopt RFID and bar-coding system for information collection purpose, we examine the effectiveness of these systems for inventory planning with Bayesian information updating. We derive the optimal ordering decision and study the issue of Pareto improvement in the supply chain. Our analysis demonstrates that RFID system will outperform the bar-coding system when the RFID system installation cost and the tag cost reduce to a level that is comparable with that of the barcoding system. We also show how an appropriately set wholesale pricing contract can achieve Pareto improvement in the HO supply chain.