Some Methods for Nonlinear Multi-objective Optimization

Miettinen, Kaisa

doi:10.1007/3-540-44719-9_1

Cited by 155 publications

(204 citation statements)

References 27 publications

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“…A function : that represents the preference of the decision maker among all the objective function is called "Value Function". In MOP the value function is assumed to be implicitly known [1]. A decision maker is needed to reach to a single solution for the problem.…”

Section: Multi-objective Optimization Solution Methodsmentioning

confidence: 99%

“…In Priori methods, the preference and opinion of the decision maker is considered before the solving of the problem. In interactive methods, the decision maker is involved in every iteration of the optimization, and based on the new information will decide [1]. There are several methods for solving a MOP; here we explain three methods in detail.…”

Section: Multi-objective Optimization Solution Methodsmentioning

confidence: 99%

“…There are many algorithms that can solve a convex MOP but they face difficulty in solving non-convex MOP [1].…”

Section: Convex Modeling Of Power and Delaymentioning

confidence: 99%

“…We are thus looking for a non-dominated solution in the sense that if we try to optimize one of the objective functions any further, the other objective function value(s) will degrade. This kind of optimality is called Pareto optimality [1]. Definition ( Mathematically a MOP is solved when the Pareto optimal set is reached.…”

Section: Pareto Optimal Solutionmentioning

confidence: 99%

“…There are many tutorials, review papers, and even text books written on this subject. Different aspects of nonlinear multi-objective optimization are defined in [1]. In [2] some advanced method for solving a MOP e.g., Fuzzy methods, interactive methods, and evolutionary algorithms are explained in details.…”

Section: Introductionmentioning

confidence: 99%

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Multi-objective optimization techniques for VLSI circuits

Kashfi

Hatami

Pedram

2011

2011 12th International Symposium on Quality Electronic Design

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The EDA design flows must be retooled to cope with the rapid increase in the number of operational modes and process corners for a VLSI circuit, which in turn results in different and sometimes conflicting design goals and requirements. Single-objective solutions to various design optimization problems, ranging from sizing and fanout optimization to technology mapping and cell placement, must hence be augmented to deal with this changing landscape. This paper starts off by presenting a variety of methods for providing analytical models for power and delay to be used in the optimization algorithms. The modeling includes non-convex and convex functional forms. Next, a class of robust and scalable methods for solving multi-objective optimization problems (MOP) in a digital circuit is presented. We present the results of a multiobjective (i.e., power dissipation and delay) gate (transistor) sizing optimization algorithm to demonstrate the effectiveness of our method. We set up the problem as a simultaneous, multi-objective optimization problem and solve it by using the Weighted Sum and Compromise Programming methods. After comparing these two methods, we present the Satisficing Trade-off Method (STOM) to find the most desirable operating point of a circuit.

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Section: Multi-objective Optimization Solution Methodsmentioning

confidence: 99%

Section: Multi-objective Optimization Solution Methodsmentioning

confidence: 99%

“…There are many algorithms that can solve a convex MOP but they face difficulty in solving non-convex MOP [1].…”

Section: Convex Modeling Of Power and Delaymentioning

confidence: 99%

Section: Pareto Optimal Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multi-objective optimization techniques for VLSI circuits

Kashfi

Hatami

Pedram

2011

2011 12th International Symposium on Quality Electronic Design

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Utilizing a projection neural network to convex quadratic multi‐objective programming problems

Jahangiri

Nazemi

2023

Adaptive Control & Signal

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Summary In this paper, we propose a projection neural network model for solving convex quadratic multi‐objective optimization problem (CQMOP). The CQMOP is first converted into an equivalent convex nonlinear programming problem by the means of the weighted sum method, where the Pareto optimal solutions are calculated via different values of weights. A neural network model is then constructed for solving the obtained convex problem. It is shown that the presented neural network is stable in the sense of Lyapunov and is globally convergent. Simulation results are given to illustrate the global convergence and performance of the suggested model. Both theoretical and numerical approaches are studied. Numerical results are in good agreement with the proved theoretical concepts.

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Optimization of both operating costs and energy efficiency in the alumina evaporation process by a multi‐objective state transition algorithm

Wang

Zhou

et al. 2015

Can J Chem Eng

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The alumina evaporation process (AEP) is an indispensable step for the reuse of sodium aluminate solution by evaporating excess water contained in the solution. The selection of optimal operating parameters is a complicated task because the process is influenced by many nonlinear factors when both the quality and quantity of the product are concerned. In this paper, we formulate a multi‐objective optimization model to maintain the balance of operating costs and energy efficiency in AEP, and a multi‐objective state transition algorithm (MOSTA) is proposed for solving this problem. With the aim of solving the constrained multi‐objective problem, a search archive strategy of elite populations and a novel infeasible solution replacement mechanism are integrated into STA. Some infeasible solutions with better performances are allowed to be saved and participate randomly in the evolution to select optimal solutions from all possible directions. A mutation operator is introduced into the evolutionary process to enhance the global search ability. Simulation results from some benchmark test problems show that the proposed method tends to converge quickly and effectively to the true Pareto frontier with better distribution. The proposed algorithm is successfully applied to solve the multi‐objective optimization problem arising in AEP. The optimal results show that operating costs and energy loss are considerably reduced, by approximately 13.63 % and 13.39 %, respectively.

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Some Methods for Nonlinear Multi-objective Optimization

Cited by 155 publications

References 27 publications

Multi-objective optimization techniques for VLSI circuits

Multi-objective optimization techniques for VLSI circuits

Utilizing a projection neural network to convex quadratic multi‐objective programming problems

Optimization of both operating costs and energy efficiency in the alumina evaporation process by a multi‐objective state transition algorithm

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