The Method of Alternate Formulations, an Automated Strategy for Optimal Design

1988 ◽  
Vol 110 (4) ◽  
pp. 459-463 ◽  
Author(s):  
C. R. Hammond ◽  
G. E. Johnson
Keyword(s):  
Optimal Design ◽  
Trend Analysis ◽  
Optimization Problems ◽  
Optimization Techniques ◽  
Global Information ◽  
Objective Functions ◽  
State Equations ◽  
Complete Set ◽  
Optimum Solution ◽  
Monotonicity Analysis

The Method of Alternate Formulations (MAF) is a new method of global information extraction for constrained, nonlinear optimization problems. MAF automatically generates the complete set of candidate solution points for these optimization problems using a symbolic mathematics computer package. MAF uses ideas and techniques from both the Method of Optimal Design and Monotonicity Analysis to reduce and formulate the problem. The reduced problem is repeatedly reformulated to develop state equations and objective functions in terms of all possible variable partitions. Trend analysis on the decision variables in the objective functions yields global information about constraint activity at possible solution points. Trend analysis on all of the possible formulations of the objective functions yields the complete set of candidate solutions. The state equations in each partition of the variables are used to test the feasibility of these candidate solutions, and the best feasible point is selected as the optimum solution. MAF can be used as a preprocessor for standard numerical optimization techniques and can be extended to nonmonotonic problems.

scholarly journals Investigation of the iCC Framework Performance for Solving Constrained LSGO Problems

Algorithms ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 108
Author(s):  
Alexey Vakhnin ◽  
Evgenii Sopov
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Optimization Techniques ◽  
Objective Functions ◽  
Parameter Adaptation ◽  
New Approach ◽  
Scientific Papers ◽  
Evolution Algorithms ◽  
Low Dimensional ◽  
Modern Optimization

Many modern real-valued optimization tasks use “black-box” (BB) models for evaluating objective functions and they are high-dimensional and constrained. Using common classifications, we can identify them as constrained large-scale global optimization (cLSGO) tasks. Today, the IEEE Congress of Evolutionary Computation provides a special session and several benchmarks for LSGO. At the same time, cLSGO problems are not well studied yet. The majority of modern optimization techniques demonstrate insufficient performance when confronted with cLSGO tasks. The effectiveness of evolution algorithms (EAs) in solving constrained low-dimensional optimization problems has been proven in many scientific papers and studies. Moreover, the cooperative coevolution (CC) framework has been successfully applied for EA used to solve LSGO problems. In this paper, a new approach for solving cLSGO has been proposed. This approach is based on CC and a method that increases the size of groups of variables at the decomposition stage (iCC) when solving cLSGO tasks. A new algorithm has been proposed, which combined the success-history based parameter adaptation for differential evolution (SHADE) optimizer, iCC, and the ε-constrained method (namely ε-iCC-SHADE). We investigated the performance of the ε-iCC-SHADE and compared it with the previously proposed ε-CC-SHADE algorithm on scalable problems from the IEEE CEC 2017 Competition on constrained real-parameter optimization.

Economic Dispatch Problems Using Backtracking Search Optimization

2018 ◽  
Vol 7 (2) ◽  
pp. 39-60
Author(s):  
Kuntal Bhattacharjee
Keyword(s):  
Large Scale ◽  
Transmission Loss ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Inequality Constraints ◽  
Optimization Techniques ◽  
Backtracking Search ◽  
Search Optimization ◽  
Set Up ◽  
Optimum Solution

The purpose of this article is to present a backtracking search optimization technique (BSA) to determine the feasible optimum solution of the economic load dispatch (ELD) problems involving different realistic equality and inequality constraints, such as power balance, ramp rate limits, and prohibited operating zone constraints. Effects of valve-point loading, multi-fuel option of large-scale thermal plants, system transmission loss are also taken into consideration for more realistic application. Two effective operations, mutation and crossover, help BSA algorithms to find the global solution for different optimization problems. BSA has the capability to deal with multimodal problems due to its powerful exploration and exploitation capability. BSA is free from sensitive parameter control operations. Simulation results set up the proposed approach in a better stage compared to several other existing optimization techniques in terms quality of solution and computational efficiency. Results also reveal the robustness of the proposed methodology.

scholarly journals Optimal Design of Plated/Shell Structures under Flutter Constraints—A Literature Review

Materials ◽  
2019 ◽  
Vol 12 (24) ◽  
pp. 4215 ◽  
Author(s):  
Aleksander Muc ◽  
Justyna Flis ◽  
Marcin Augustyn
Keyword(s):  
Composite Materials ◽  
Optimal Design ◽  
Composite Structures ◽  
Optimization Problems ◽  
Piezoelectric Actuators ◽  
Functionally Graded ◽  
Shell Structures ◽  
Objective Functions ◽  
Graded Materials ◽  
Definition Of

Aeroelastic optimization has become an indispensable component in the evaluation of divergence and flutter characteristics for plated/shell structures. The present paper intends to review the fundamental trends and dominant approaches in the optimal design of engineering constructions. A special attention is focused on the formulation of objective functions/functional and the definition of physical (material) variables, particularly in view of composite materials understood in the broader sense as not only multilayered laminates but also as sandwich structures, nanocomposites, functionally graded materials, and materials with piezoelectric actuators/sensors. Moreover, various original aspects of optimization problems of composite structures are demonstrated, discussed, and reviewed in depth.

A General Approach to Constrained Optimal Design Based on Symbolic Mathematics

1987 ◽  
Author(s):  
C. R. Hammond ◽  
G. E. Johnson
Keyword(s):  
Optimal Design ◽  
Optimal Solution ◽  
New Method ◽  
Candidate Solution ◽  
Complete Set ◽  
Monotonicity Analysis ◽  
Develop State ◽  
Constraint Sets ◽  
Reduced Problem

Abstract This paper presents a new method of optimal design that combines ideas and techniques from both the Method of Optimal Design (MOD) and monotonicity analysis. This new method, while presently limited to constrained monotonic problems, has been automated. The problem is first reduced in size and reformulated using ideas from MOD. The reduced problem is then repeatedly reformulated to develop state and design equations in terms of all possible variable partitions. The complete set of candidate optimal solution points is extracted by monotonicity analysis applied to the trivial constraint sets on the design equations from every possible formulation of the problem. These candidate solution points can then be numerically sorted to determine the optimal solution for a particular numerical case. The new method and its automation are illustrated with two example problems from the literature.

Different Meta-Heuristic Optimization Techniques and Their Application in Solar Photovoltaic Field

2022 ◽  
pp. 1-37
Author(s):  
Krupali Devendra Kanekar ◽  
Rahul Agrawal ◽  
Dhiraj Magare
Keyword(s):  
Optimization Problems ◽  
Optimization Techniques ◽  
Heuristic Optimization ◽  
Solar Photovoltaic ◽  
Multimodal Approach ◽  
Objective Functions ◽  
Linear Type ◽  
Intelligent Technique

A method of optimization is used to resolve issues smartly by selecting the better option from various existing possibilities. Many optimization problems are possessing characteristics, namely nonlinearity, complexity, multimodal approach, and incompatible objective functions. Sometimes even for individual simple and linear type objective functions, a solution that is optimal and does not exist, there is uncertainness of obtaining the best solution. The aim of finding methods that can resolve various issues in a defined manner potentially has found the concentration of different researchers responsible for performing the advancement of a new “intelligent” technique called meta-heuristics technique. In the last few years, there is an advancement of various meta-heuristics techniques in different areas or various fields. Meta-heuristics are a demanded thrust stream of research that showed important advancement in finding the answer to problems that are optimized. The chapter gives the guidance for enhancing research more meaningfully.

Scalable Computing Architecture for Time-Dependent Transportation Optimization Problems Based on High-Performance Computing Techniques

2019 ◽  
Vol 2673 (4) ◽  
pp. 205-216 ◽  
Author(s):  
Pengfei (Taylor) Li ◽  
Peirong (Slade) Wang ◽  
Farzana Chowdhury ◽  
Li Zhang
Keyword(s):  
Objective Function ◽  
High Performance Computing ◽  
High Performance ◽  
Optimization Problems ◽  
Dynamic Network ◽  
Alternative Formulation ◽  
High Fidelity ◽  
Objective Functions ◽  
Performance Computing ◽  
Transportation Optimization

Traditional formulations for transportation optimization problems mostly build complicating attributes into constraints while keeping the succinctness of objective functions. A popular solution is the Lagrangian decomposition by relaxing complicating constraints and then solving iteratively. Although this approach is effective for many problems, it generates intractability in other problems. To address this issue, this paper presents an alternative formulation for transportation optimization problems in which the complicating attributes of target problems are partially or entirely built into the objective function instead of into the constraints. Many mathematical complicating constraints in transportation problems can be efficiently modeled in dynamic network loading (DNL) models based on the demand–supply equilibrium, such as the various road or vehicle capacity constraints or “IF–THEN” type constraints. After “pre-building” complicating constraints into the objective functions, the objective function can be approximated well with customized high-fidelity DNL models. Three types of computing benefits can be achieved in the alternative formulation: ( a) the original problem will be kept the same; ( b) computing complexity of the new formulation may be significantly reduced because of the disappearance of hard constraints; ( c) efficiency loss on the objective function side can be mitigated via multiple high-performance computing techniques. Under this new framework, high-fidelity and problem-specific DNL models will be critical to maintain the attributes of original problems. Therefore, the authors’ recent efforts in enhancing the DNL’s fidelity and computing efficiency are also described in the second part of this paper. Finally, a demonstration case study is conducted to validate the new approach.

scholarly journals A Multi-Objective Approach toward Optimal Design of Sustainable Integrated Biodiesel/Diesel Supply Chain Based on First- and Second-Generation Feedstock with Solid Waste Use

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2261
Author(s):  
Evgeniy Ganev ◽  
Boyan Ivanov ◽  
Natasha Vaklieva-Bancheva ◽  
Elisaveta Kirilova ◽  
Yunzile Dzhelil
Keyword(s):  
Supply Chain ◽  
Optimal Design ◽  
Solid Waste ◽  
Second Generation ◽  
Agricultural Land ◽  
Optimization Problems ◽  
Biodiesel Production ◽  
Mixed Integer ◽  
Economic Criterion ◽  
Multi Objective

This study proposes a multi-objective approach for the optimal design of a sustainable Integrated Biodiesel/Diesel Supply Chain (IBDSC) based on first- (sunflower and rapeseed) and second-generation (waste cooking oil and animal fat) feedstocks with solid waste use. It includes mixed-integer linear programming (MILP) models of the economic, environmental and social impact of IBDSC, and respective criteria defined in terms of costs. The purpose is to obtain the optimal number, sizes and locations of bio-refineries and solid waste plants; the areas and amounts of feedstocks needed for biodiesel production; and the transportation mode. The approach is applied on a real case study in which the territory of Bulgaria with its 27 districts is considered. Optimization problems are formulated for a 5-year period using either environmental or economic criteria and the remainder are defined as constraints. The obtained results show that in the case of the economic criterion, 14% of the agricultural land should be used for sunflower and 2% for rapeseed cultivation, while for the environmental case, 12% should be used for rapeseed and 3% for sunflower. In this case, the price of biodiesel is 14% higher, and the generated pollutants are 6.6% lower. The optimal transport for both cases is rail.

scholarly journals A Method for Integration of Preferences to a Multi-Objective Evolutionary Algorithm Using Ordinal Multi-Criteria Classification

2021 ◽  
Vol 26 (2) ◽  
pp. 27
Author(s):  
Alejandro Castellanos-Alvarez ◽  
Laura Cruz-Reyes ◽  
Eduardo Fernandez ◽  
Nelson Rangel-Valdez ◽  
Claudia Gómez-Santillán ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Selective Pressure ◽  
Optimization Problems ◽  
Region Of Interest ◽  
Decision Makers ◽  
Multiple Objective ◽  
Objective Functions ◽  
Multi Objective ◽  
Imperfect Knowledge ◽  
Real World Problems

Most real-world problems require the optimization of multiple objective functions simultaneously, which can conflict with each other. The environment of these problems usually involves imprecise information derived from inaccurate measurements or the variability in decision-makers’ (DMs’) judgments and beliefs, which can lead to unsatisfactory solutions. The imperfect knowledge can be present either in objective functions, restrictions, or decision-maker’s preferences. These optimization problems have been solved using various techniques such as multi-objective evolutionary algorithms (MOEAs). This paper proposes a new MOEA called NSGA-III-P (non-nominated sorting genetic algorithm III with preferences). The main characteristic of NSGA-III-P is an ordinal multi-criteria classification method for preference integration to guide the algorithm to the region of interest given by the decision-maker’s preferences. Besides, the use of interval analysis allows the expression of preferences with imprecision. The experiments contrasted several versions of the proposed method with the original NSGA-III to analyze different selective pressure induced by the DM’s preferences. In these experiments, the algorithms solved three-objectives instances of the DTLZ problem. The obtained results showed a better approximation to the region of interest for a DM when its preferences are considered.

scholarly journals Joint Optimization on Trajectory, Cache Placement, and Transmission Power for Minimum Mission Time in UAV-Aided Wireless Networks

2021 ◽  
Vol 10 (7) ◽  
pp. 426
Author(s):  
Tingting Lan ◽  
Danyang Qin ◽  
Guanyu Sun
Keyword(s):  
Wireless Communication ◽  
Power Allocation ◽  
Optimization Problems ◽  
Base Station ◽  
Optimization Techniques ◽  
Joint Optimization ◽  
Transmission Power ◽  
Wireless Backhaul ◽  
Mission Time ◽  
Cache Placement

In recent years, due to the strong mobility, easy deployment, and low cost of unmanned aerial vehicles (UAV), great interest has arisen in utilizing UAVs to assist in wireless communication, especially for on-demand deployment in emergency situations and temporary events. However, UAVs can only provide users with data transmission services through wireless backhaul links established with a ground base station, and the limited capacity of the wireless backhaul link would limit the transmission speed of UAVs. Therefore, this paper designed a UAV-assisted wireless communication system that used cache technology and realized the transmission of multi-user data by using the mobility of UAVs and wireless cache technology. Considering the limited storage space and energy of UAVs, the joint optimization problem of the UAV’s trajectory, cache placement, and transmission power was established to minimize the mission time of the UAV. Since this problem was a non-convex problem, it was decomposed into three sub-problems: trajectory optimization, cache placement optimization, and power allocation optimization. An iterative algorithm based on the successive convex approximation and alternate optimization techniques was proposed to solve these three optimization problems. Finally, in the power allocation optimization, the proposed algorithm was improved by changing the optimization objective function. Numerical results showed that the algorithm had good performance and could effectively reduce the task completion time of the UAV.

Sign in / Sign up

Export Citation Format

Share Document