An Efficient and Accurate Solution Methodology for Bilevel Multi-Objective Programming Problems Using a Hybrid Evolutionary-Local-Search Algorithm

2010 ◽  
Vol 18 (3) ◽  
pp. 403-449 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Ankur Sinha
Keyword(s):  
Problem Solving ◽  
Local Search ◽  
Bilevel Programming ◽  
Optimization Problem ◽  
Practical Importance ◽  
Test Problems ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Bilevel Programming Problems ◽  
Solution Methodology

Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

Creativity in Multi Objective Problem Solving

2012 ◽  
Author(s):  
Mohamed E. M. El-Sayed ◽  
Jacqueline A. J. El-Sayed
Keyword(s):  
Problem Solving ◽  
Modeling And Simulation ◽  
Design Research ◽  
Engineering Problem ◽  
Research Projects ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Research Goal ◽  
Engineering Problem Solving

Problem solving is one of the main activities in achieving design and research goal. While problem solving in general is an activity aiming at transforming unacceptable state of reality to acceptable state of reality, problem solving in engineering is usually a means for tackling other activities such as design and research. By breaking down design and research into a set of engineering problem solving activities, the goals of complicated design and research projects can be achieved. For this reason, the transitions from design or research to problem solving in some cases are unidentifiable. The identification of the problem solving activity goals and the transition between the three activities, however, are essentials for creativity and achieving the desired objectives especially when dealing with conflicting objectives and constraints. In this paper, design, research, and problem solving are distinguished as realization activities performed in different reality domains with different beginning and ending states. These three activities use modeling and simulation as basic elements of mapping between realities to perform analysis and integration. While analysis and simulation are mainly the analytical actions, modeling and integration are mainly the creative actions. With these distinctions, the identification of problem solving activity goals, and transitions between activities, can be easily realized. Also, creativity and dealing with conflicting objectives can be greatly facilitated. To demonstrate these concepts and their implications some illustrative examples are discussed.

Multi-Objective Optimization of Piezoelectric Actuator Placement for Shape Control of Plates Using Genetic Algorithms

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
Rajesh Kudikala ◽  
Deb Kalyanmoy ◽  
Bishakh Bhattacharya
Keyword(s):  
Optimization Algorithm ◽  
Shape Control ◽  
Optimization Problem ◽  
Piezoelectric Actuators ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Input Control ◽  
Wide Range ◽  
Conflicting Objectives ◽  
Lag Model

Shape control of adaptive structures using piezoelectric actuators has found a wide range of applications in recent years. In this paper, the problem of finding optimal distribution of piezoelectric actuators and corresponding actuation voltages for static shape control of a plate is formulated as a multi-objective optimization problem. The two conflicting objectives considered are minimization of input control energy and minimization of mean square deviation between the desired and actuated shapes with constraints on the maximum number of actuators and maximum induced stresses. A shear lag model of the smart plate structure is created, and the optimization problem is solved using an evolutionary multi-objective optimization algorithm: nondominated sorting genetic algorithm-II. Pareto-optimal solutions are obtained for different case studies. Further, the obtained solutions are verified by comparing them with the single-objective optimization solutions. Attainment surface based performance evaluation of the proposed optimization algorithm has been carried out.

A Lion’s Pride Inspired Algorithm for VLSI Floorplanning

2019 ◽  
Vol 29 (01) ◽  
pp. 2050003
Author(s):  
Lalin L. Laudis ◽  
N. Ramadass
Keyword(s):  
Design Process ◽  
Integrated Circuit ◽  
Large Scale ◽  
Optimization Problem ◽  
Standard Test ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Scale Integration ◽  
Vlsi Floorplanning

The complexity of any integrated circuit pushes the researchers to optimize the various parameters in the design process. Usually, the Nondeterministic Polynomial problems in the design process of Very Large Scale Integration (VLSI) are considered as a Single Objective Optimization Problem (SOOP). However, due to the increasing demand for the multi-criterion optimization, researchers delve up on Multi-Objective Optimization methodologies to solve a problem with multiple objectives. Moreover, it is evident from the literature that biologically inspired algorithm works very well in optimizing a Multi-Objective Optimization Problem (MOOP). This paper proposes a new Lion’s pride inspired algorithm to solve any MOOP. The methodologies mimic the traits of a Lion which always strives to become the Pride Lion. The Algorithm was tested with VLSI floorplanning problem wherein the area and dead space are the objectives. The algorithm was also tested with several standard test problems. The tabulated results justify the ruggedness of the proposed algorithm in solving any MOOP.

scholarly journals A Novel Multi-Objective Artificial Bee Colony Algorithm for the QoS Based Wireless Route Optimization Problem

2012 ◽  
Vol 6-7 ◽  
pp. 445-451
Author(s):  
Chang Sheng Zhang ◽  
Ming Kang Ren ◽  
Bin Zhang
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problem ◽  
Artificial Bee Colony ◽  
Route Optimization ◽  
Test Problems ◽  
Nsga Ii ◽  
Solution Quality ◽  
Artificial Bee Colony Optimization ◽  
Multi Objective ◽  
Bee Colony

In this paper, an efficient multi-objective artificial bee colony optimization algorithm based on Pareto dominance called PC_MOABC is proposed to tackle the QoS based route optimization problem. The concepts of Pareto strength and crowding distance are introduced into this algorithm, and are combined together effectively to improve the algorithm’s efficiency and generate a set of evenly distributed solutions. The proposed algorithm was evaluated on a set of different scale test problems and compared with the recently proposed popular NSGA-II based multi-objective optimization algorithm. The experimental results reveal very encouraging results in terms of the solution quality and the processing time required.

scholarly journals Comparison of Approaches for Irrigation Scheduling Using AquaCrop and NSGA-III Models under Climate Uncertainty

2020 ◽  
Vol 12 (18) ◽  
pp. 7694
Author(s):  
Richwell Mubita Mwiya ◽  
Zhanyu Zhang ◽  
Chengxin Zheng ◽  
Ce Wang
Keyword(s):  
Optimization Problem ◽  
Irrigation Scheduling ◽  
Irrigated Agriculture ◽  
Climate Data ◽  
Maize Crop ◽  
Maize Production ◽  
Multi Objective ◽  
Study Approach ◽  
Aquacrop Model ◽  
Conflicting Objectives

In the face of increased competition for water resources, optimal irrigation scheduling is necessary for sustainable development of irrigated agriculture. However, optimal irrigation scheduling is a nonlinear problem with many competing and conflicting objectives and constraints, and deals with an environment in which conditions are uncertain. In this study, a multi-objective optimization problem for irrigation scheduling was presented in which maximization of net benefits and water use efficiency and minimization of risk were the objectives. The presented optimization problem was solved using four different approaches, all of which used the AquaCrop model and nondominated sorting genetic algorithm III. Approach 1 used dynamic climate data without adaption; Approach 2 used dynamic climate data with adaption; Approach 3 used static climate data without adaption; and Approach 4 used static climate data with adaption. The dynamic climate data were generated using the bootstrap resampling of original climate data. A case study of maize production in north Jiangsu Province of China was used to evaluate the proposed approaches. Under the multi-objective scenario presented and other conditions of the study, Approach 4 gave the best results, and showed that irrigation depths of 400, 325, and 200 mm were required to produce a maize crop in a dry, normal, and wet year, respectively.

scholarly journals Optimization of a Power Line Communication System to Manage Electric Vehicle Charging Stations in a Smart Grid

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1767 ◽  
Author(s):  
Sara Carcangiu ◽  
Alessandra Fanni ◽  
Augusto Montisci
Keyword(s):  
Frequency Response ◽  
Optimization Problem ◽  
Power Line ◽  
Power Line Communication ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Charging Station ◽  
Conflicting Objectives ◽  
Charging Stations ◽  
Line Design

In this paper, a procedure is proposed to design a power line communication (PLC) system to perform the digital transmission in a distributed energy storage system consisting of fleets of electric cars. PLC uses existing power cables or wires as data communication multicarrier channels. For each vehicle, the information to be transmitted can be, for example: the models of the batteries, the level of the charge state, and the schedule of charging/discharging. Orthogonal frequency division multiplexing modulation (OFDM) is used for the bit loading, whose parameters are optimized to find the best compromise between the communication conflicting objectives of minimizing the signal power, maximizing the bit rate, and minimizing the bit error rate. The off-line design is modeled as a multi-objective optimization problem, whose solution supplies a set of Pareto optimal solutions. At the same time, as many charging stations share part of the transmission line, the optimization problem includes also the assignment of the sub-carriers to the single charging stations. Each connection between the control node and a charging station has its own frequency response and is affected by a noise spectrum. In this paper, a procedure is presented, called Chimera, which allows one to solve the multi-objective optimization problem with respect to a unique frequency response, representing the whole set of lines connecting each charging station with the central node. Among the provided Pareto solutions, the designer will make the final decision based on the control system requirements and/or the hardware constraints.

scholarly journals An Entropy-Based Multiobjective Evolutionary Algorithm with an Enhanced Elite Mechanism

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yufang Qin ◽  
Junzhong Ji ◽  
Chunnian Liu
Keyword(s):  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Optimization Problem ◽  
State Of The Art ◽  
Early Stage ◽  
Test Problems ◽  
Multiobjective Optimization Problem ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective

Multiobjective optimization problem (MOP) is an important and challenging topic in the fields of industrial design and scientific research. Multi-objective evolutionary algorithm (MOEA) has proved to be one of the most efficient algorithms solving the multi-objective optimization. In this paper, we propose an entropy-based multi-objective evolutionary algorithm with an enhanced elite mechanism (E-MOEA), which improves the convergence and diversity of solution set in MOPs effectively. In this algorithm, an enhanced elite mechanism is applied to guide the direction of the evolution of the population. Specifically, it accelerates the population to approach the true Pareto front at the early stage of the evolution process. A strategy based on entropy is used to maintain the diversity of population when the population is near to the Pareto front. The proposed algorithm is executed on widely used test problems, and the simulated results show that the algorithm has better or comparative performances in convergence and diversity of solutions compared with two state-of-the-art evolutionary algorithms: NSGA-II, SPEA2 and the MOSADE.

An Efficient Framework Using Normalized Dominance Operator for Multi-Objective Evolutionary Algorithms

2019 ◽  
Vol 10 (1) ◽  
pp. 15-37 ◽  
Author(s):  
Muneendra Ojha ◽  
Krishna Pratap Singh ◽  
Pavan Chakraborty ◽  
Shekhar Verma
Keyword(s):  
Evolutionary Algorithms ◽  
Pareto Front ◽  
Optimization Problem ◽  
Computational Cost ◽  
Optimization Methods ◽  
Objective Test ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Pareto Dominance ◽  
Multi Objective

Multi-objective optimization algorithms using evolutionary optimization methods have shown strength in solving various problems using several techniques for producing uniformly distributed set of solutions. In this article, a framework is presented to solve the multi-objective optimization problem which implements a novel normalized dominance operator (ND) with the Pareto dominance concept. The proposed method has a lesser computational cost as compared to crowding-distance-based algorithms and better convergence. A parallel external elitist archive is used which enhances spread of solutions across the Pareto front. The proposed algorithm is applied to a number of benchmark multi-objective test problems with up to 10 objectives and compared with widely accepted aggregation-based techniques. Experiments produce a consistently good performance when applied to different recombination operators. Results have further been compared with other established methods to prove effective convergence and scalability.

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