Jaya算法：高级优化技术与工程应用综述

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"《Jaya算法：一种高级优化算法及其工程应用》一书由Ravipudi Venkata Rao博士等人编著，探讨了一种先进的优化工具——Jaya算法。该算法以其高效性和适应性，在工程领域中得到了广泛应用。本书分为多个章节，深入解析了Jaya算法的核心原理和工作流程。首先，作者对Jaya算法进行了介绍，包括其起源和基本思想，它是一种基于生物进化策略的搜索算法，灵感来源于印度的女神Jayamahalakshmi，以其寻找财富的能力象征着算法在优化问题上的探索特性。Jaya算法通过模拟自然选择和种群更新过程，能够寻找到全局最优或近似最优解。接下来，书中详细讨论了Jaya算法的变体，这些改进版旨在提高算法的性能，如处理局部最优陷阱的能力，或者在处理大规模优化问题时的效率。此外，作者比较了Jaya算法与传统优化算法的优缺点，突出了其在复杂工程问题中的优势。书中着重介绍了Jaya算法在各种工程领域的应用，例如在换热器、热管和散热器的设计优化中，它被用于单目标和多目标决策，帮助工程师在满足性能指标的同时，考虑成本和其他约束条件。在冰蓄热系统的设计优化中，Jaya算法展现了其在解决多目标优化问题上的有效性。进一步，作者探讨了Jaya算法在现代制造工艺，如纳米精加工和铸造工艺中的应用，这些领域对精度和效率有高要求，Jaya算法的全局搜索特性使其成为理想的选择。无论是单目标还是多目标优化，Jaya算法都展示了其在提升生产效率和产品质量方面的潜力。最后，本书总结了Jaya算法在工程科学领域的广泛使用，强调了其在当今科技快速发展的背景下，作为优化工具的重要性。同时，版权信息表明，所有内容受到Springer International Publishing AG的保护，未经许可不得擅自复制或传播。《Jaya算法：一种高级优化算法及其工程应用》是一本深度解析该优化算法理论和实践应用的专业书籍，对于工程师、研究人员以及对优化技术感兴趣的读者来说，提供了宝贵的参考和实践指导。"

Chapter 1

Introduction

Abstract This chapter presents an introduction to the single objective and

multi-objective optimization problems and the optimization techniques to solve the

same. The a priori and a posteriori approaches of solving the multi-objective

optimization problems are explained. The importance of algorithm-speciﬁc

parameter-less concept is emphasized.

1.1 Introduction to Optimization

Optimization may be deﬁned as ﬁnding of solution of a problem where it is nec-

essary to maximize or minimize a single or set of objective functions within a

domain which contai ns the acceptable values of variables while some restrictions

are to be satisﬁed. There might be a large number of sets of variables in the domain

that maximi ze or minimize the objective function(s) while satisfying the described

restrictions. They are called as the accept able solutions and the solution which is the

best among them is called the optimum solution of the problem. An objective

function expresses the main aim of the model which is either to be minimized or

maximized. For example, in a manufacturing process, the aim may be to maximize

the proﬁt or minimize the cost. In designing a structure, the aim may be to maxi-

mize the strength or minimize the deﬂection or a combination of many objectives.

The use of optimization techniques for design of engine ering systems helps the

designers in improving the system’s performance, utilization, reliability and cost.

A typical engineering system is deﬁned by a number of parameters and it is the

designer’s task to specify appropriate values for these variables. Skilled designers

utilize their knowledge, experience, and judgment to specify these variables and

design effective engineering systems. Because of the size and complexity of the

typical desig n task, however, even the most skilled designers are unable to take into

account all of the variables simultaneously. Optimization methodologies can be

applied during the product development stage to ensure that the ﬁnished design will

have high performance, high reliability, low weight, and/or low cost. Alternatively,

R. Venkata Rao, Jaya: An Advanced Optimization Algorithm and its Engineering

Applications, https://doi.org/10.1007/978-3-319-78922-4_1

optimization methods can be applied to existing products to identify potential

design improvements.

Thermal system design includes an optimization process in which the designer

considers certain objectives such as heat transfer rate, thermal resistance, total cost,

friction factor, pressure amplitude, effectiveness, cooling capacity, pressure drop,

etc. depending on the requirements. Whil e achieving the mentioned objectives, it is

also desirable to minimize the total cost of the system. However, the design opti-

mization for a whole thermal syste m assembly may be having a complex objective

function with a large number of design variables. So, it is a good practice to apply

optimization techniques for individual component or intermediate system than to a

whole system. For example, in a thermal power plant, individual optimization of

cooling tower, heat pipe and heat sink is computationally and mathematically

simpler than the optimization of whole power plant.

In the case of manufacturing of products, in order to survive in a competitive

market scenario, industries are required to manufacture products with highest

quality at a lowest possible cost, fulﬁll the fast-changing customer desires, consider

signiﬁcance of aesthetics and conform to environmental norms, adopt ﬂexibili ty in

the production system and minimize time-to market of their products. Industries

employ a numbe r of manufacturing processes to transform raw materials into ﬁn-

ishing goods and efﬁcient utilization of these manufacturing processes is important

to achieve the above goals. Manufacturing processes are characterized by a number

of input parameters which signi ﬁcantly inﬂuence their performances. Therefore,

determining best combination of the input parameters is an important task for the

success of any manufacturing process.

A human process planner may select proper combination of process parameters

for a manufacturing process using his own experience or machine catalog. The

selected parameters are usually conservative and far from optimum. Selecting a

proper combination of process parameters through experimentation is costly, time

consuming and requires a number of experimental trials. Therefore researchers have

opted to use optimization techniques for process parameter optimization of man-

ufacturing processes. Researchers have used a number of traditional optimization

techniques like geometric programming, nonlinear programming, sequential pro-

gramming, goal programming, dynamic programming, etc. for process parameter

optimization of manufacturing processes. Although the traditional optimization

methods had performed well in many practical cases, but they have certain limi-

tations which are mainly related to their inherent search mechanisms. Search

strategies of these traditional optimization methods are generally depended on the

type of objective and constraint functions (linear, non-linear, etc.) and the type of

variables used in the problem modeling (integer, binary, continuous, etc.), their

efﬁciency is also very much dependent on the size of the solution space, number of

variables and constraints used in the problem modeling and the structure of the

solution space (convex, non-convex, etc.), the solutions obtained largely depends

upon the selected initial solution. They also do not provide generic solution

approaches that can be used to solve problems where different types of variables,

objective and constraint functions are used. In real world optimization problems the

2 1 Introduction

number of variables can be very large and the inﬂuence on objective function to be

optimized can be very complicated. The objective function may have many local

optima, whereas the designer or process planner (or the decision maker) is inter-

ested in the global opti mum. Such problems cannot be effectively handled by

classical methods or traditional methods that compute only local optima. So there

remains a need for efﬁcient and effective optimization methods for design problems.

Continuous resear ch is being conducted in this ﬁeld and nature inspired heuristic

optimization methods are proving to be better than deterministic methods and are

widely used.

Therefore, keeping in view of the limitations of the traditional optimization

techniques, the researchers have developed a number of advanced optimization

algorithms popularly known as metaheuristics. The population-based metaheuristic

algorithms have two important groups: evolutionary algorithms (EA) and swarm

intelligence (SI) based algorithms. Some of the recognized evolutionary algorithms

are: Genetic Algorithm (GA), Evolutionary Strategy (ES), Evolutionary

Programming (EP), Differential Evolution (DE), etc. Some of the well-known

swarm intelligence based algorithms are: Particle Swarm Optimization (PSO), Ant

Colony Optimization (ACO), Artiﬁcial Bee Colony (ABC), Fire Fly (FF) algorithm,

Cuckoo search algorithm (CSA), etc. Besides the evolutionary and swarm intelli-

gence based algorithms, there are some other algorithms which work on the prin-

ciples of different natural phenomena and some of them are: Harmony Search

(HS) algorithm, Gravitational Search Algori thm (GSA), Biogeography-Based

Optimization (BBO) algorithm, etc.

The optimization problem may contain only a single objective function or a

number of objective functions. A problem containing only one objective function is

called the single objective optimization problem. A problem containing more than

one objective function is called the multiple or multi-objective optimization prob-

lem. An example of a constrained single objective optimization problem is given

below.

Maximize Proﬁt,

¼ f ðx

; x

Þ¼2x

þ 3x

þ 1:5x

þ 0:8x

ð1:1Þ

Subject to the constraints:

þ 2x

þ x

 150 ð1:2Þ

þ x

þ 0:3x

 170 ð1:3Þ

þ 1:5x

 128 ð1:4Þ

1.1 Introduction to Optimization 3

The ranges of the variables:

0  x

 50 ð1:5Þ

0  x

 32 ð1:6Þ

0  x

 44 ð1:7Þ

0  x

 18 ð1:8Þ

In this optimization problem the objective function and the constraints are

expressed as linear equations. However, in practical applications, these may be in

the form of non-linear equations. From the considered ranges of the variables given

by Eqs. (1.5)– (1.8), it can be observed that the variables can assume any value

within the given ranges. For example, x

can assume any value betw een 0 and 50

(including 0 and 50), x

can assume any value between 0 and 32 (including 0 and

32), x

can assume any value between 0 and 44 (including 0 and 44) and x

can

assume any value between 0 and 18 (including 0 and 18). The problem is to ﬁnd out

the best combination of x

, x

and x

to obtain the maximum value of Y

. We can

solve the above single objective optimization problem by using traditional (such as

simplex method, dynamic programming, separable programming, etc.) and

advanced optimization methods such as genetic algorithm (GA), simulated

annealing (SA), particle swarm optimization (PSO), ant colony optimization

(ACO), artiﬁcial bee colony algorithm (ABC), etc. Then which method will give us

the best solution (i.e. maximum value of Y

)? We do not know! We can know only

after applying these methods to the same problem and whichever method gives the

best solution is called the best optimization method for the given problem.

The multi-objective optimization problems require the simultaneous optimiza-

tion of multiple (often conﬂicting) objectives over a given space of candidate

solutions. These problems occur in many practical applications, rather often as

bi-objective problems, with typical pairs of objectives as quality vs cost, strength vs

weight, or accuracy vs complexity. Suppose, we include another objective function

of minimizing the cost to the above single objective optimization problem.

Minimize Cost,

¼ fx

; x

ðÞ¼0:75x

þ 8x

þ x

þ 1:2x

ð1:9Þ

Then the problem is to ﬁnd out the best combination of x

, x

and x

to obtain

the maximum value of Y

and minimum value of Y

. Now let us assum e a set of

values (0, 0, 0, 0) of x

, x

and x

. These values satisfy the constraints and hence

substituting these values in the objective function Y

leads to the value of cost of 0.

This value is highly appreciable but at the same time if the same set of values (0, 0,

0, 0) is substit uted in the ﬁrst objective function Y

then it leads to the value of proﬁt

of 0. This is highly undesirable and hence we can say that the set of values (0, 0, 0,

0) of x

, x

and x

do not give the optimum solution. Now let us assume another

4 1 Introduction

set of values (0, 5, 40, 10) of x

, x

and x

. These values also satisfy the

constraints and hence substituting these values in the objective functions Y

and Y

lead to the values of 342 and 83 respectively. The set of values (0, 5, 40, 10) of x

, x

and x

can be said as a feasible solution but not the optimum solution. Let us

further assume another set of values (15, 18, 7, 24) of x

, x

and x

. These values

also satisfy the constraints and hence substituting these values in the objective

functions Y

and Y

lead to the values of 191.05 and 113.7 respectively. Thus, the

set of values (15, 18, 7, 24) of x

, x

and x

can be said as another feasible

solution but not the optimum solution. Thus, how many feasible solutions are

possible for the considered problem? Various combinations of x

, x

and x

are

possible and hence we can say that a large number (or almost inﬁnite number) of

feasible solutions may be possible for the considered problem. The two objectives

are of con ﬂicting type and optimal solution of o ne objective does not meet the

optimal solution of the other and there exist a large number (or almost inﬁnite

number) of solutions (as variables can take any value within their bounds). In

general, the multi-objective optimization problems have decision variable values

which are determined in a continuous or integer domain with either an inﬁnite or a

large number of solutions, the best of which should sati sfy the designer or decision

maker’s constraints and preference priorities.

Here also we can apply different optimization methods to solve the same

bi-objective optimization problem and whichever method gives the best combina-

tion of solution (i.e. most maximum value of Y

and most minimum value of Y

)is

called the best optimization method for the given problem. In fact, the solution to

the multi-objective optimization problem involves ﬁnding not one, but a set of

solutions that represent the best possible trade-offs among the objective functions

being optimized. Such trade-offs constitute the so called Pareto optimal set, and

their corresponding objective function values form the so called Pareto front. The

multi-objective opti mization problem may contain any number of objectives more

than one. The example described by Eqs. (1.1)–(1.9) is only for giving an idea to

the readers about the concepts of single objective and multi-objective optimization

problems.

1.2 A Priori and a Posteriori Approaches of Solving

the Multi-objective Optimization Problems

There are basically two approaches to solve a multi-objective optimization problem

and these are: a priori approach and a poste riori approach. In a priori approach,

multi-objective optimization problem is transformed into a single objective opti-

mization problem by assigning an appropriate weight to each objective. This ulti-

mately leads to a unique optimum solution. In the a priori approach, the preferences

of the decision maker are asked and the best solution according to the given

preferences is found. The preferences of the decision maker are in the form of

1.1 Introduction to Optimization 5

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