scholarly journals A Brief Look at Multi-Criteria Problems: Multi-Threshold Optimization versus Pareto-Optimization

2020 ◽  
Author(s):  
Nodari Vakhania ◽  
Frank Werner
Keyword(s):  
Optimization Problems ◽  
Optimality Criteria ◽  
General Notion ◽  
Objective Functions ◽  
Objective Criterion ◽  
Solution Quality ◽  
Pareto Optimal Set ◽  
Threshold Optimization ◽  
Feasible Solutions

Multi-objective optimization problems are important as they arise in many practical circumstances. In such problems, there is no general notion of optimality, as there are different objective criteria which can be contradictory. In practice, often there is no unique optimality criterion for measuring the solution quality. The latter is rather determined by the value of the solution for each objective criterion. In fact, a practitioner seeks for a solution that has an acceptable value of each of the objective functions and, in practice, there may be different tolerances to the quality of the delivered solution for different objective functions: for some objective criteria, solutions that are far away from an optimal one can be acceptable. Traditional Pareto-optimality approach aims to create all non-dominated feasible solutions in respect to all the optimality criteria. This often requires an inadmissible time. Besides, it is not evident how to choose an appropriate solution from the Pareto-optimal set of feasible solutions, which can be very large. Here we propose a new approach and call it multi-threshold optimization setting that takes into account different requirements for different objective criteria and so is more flexible and can often be solved in a more efficient way.

Multiobjective Programming

2014 ◽  
pp. 1585-1604
Author(s):  
Minghe Sun
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Objective Functions ◽  
Solution Quality ◽  
Solution Methods ◽  
Multiobjective Programming Problem ◽  
Feasible Solutions ◽  
Multiobjective Programming Problems

Optimization problems with multiple criteria measuring solution quality can be modeled as multiobjective programming problems. Because the objective functions are usually in conflict, there is not a single feasible solution that can optimize all objective functions simultaneously. An optimal solution is one that is most preferred by the decision maker (DM) among all feasible solutions. An optimal solution must be nondominated but a multiobjective programming problem may have, possibly infinitely, many nondominated solutions. Therefore, tradeoffs must be made in searching for an optimal solution. Hence, the DM's preference information is elicited and used when a multiobjective programming problem is solved. The model, concepts and definitions of multiobjective programming are presented and solution methods are briefly discussed. Examples are used to demonstrate the concepts and solution methods. Graphics are used in these examples to facilitate understanding.

scholarly journals A New “Doctor and Patient” Optimization Algorithm: An Application to Energy Commitment Problem

2020 ◽  
Vol 10 (17) ◽  
pp. 5791 ◽  
Author(s):  
Mohammad Dehghani ◽  
Mohammad Mardaneh ◽  
Josep M. Guerrero ◽  
Om Parkash Malik ◽  
Ricardo A. Ramirez-Mendoza ◽  
...  
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Standard Test ◽  
Objective Functions ◽  
Test Function ◽  
Commitment Problem ◽  
New Ideas ◽  
Patient Optimization ◽  
Research World

Regular assessments of events taking place around the globe can be a conduit for the development of new ideas, contributing to the research world. In this study, the authors present a new optimization algorithm named doctor and patient optimization (DPO). DPO is designed by simulating the process of treating patients by a physician. The treatment process has three phases, including vaccination, drug administration, and surgery. The efficiency of the proposed algorithm in solving optimization problems compared to eight other optimization algorithms on a benchmark standard test function with 23 objective functions is been evaluated. The results obtained from this comparison indicate the superiority and quality of DPO in solving optimization problems in various sciences. The proposed algorithm is successfully applied to solve the energy commitment problem for a power system supplied by a multiple energy carriers system.

scholarly journals A time-predefined approach to course timetabling

2003 ◽  
Vol 13 (2) ◽  
pp. 139-151 ◽  
Author(s):  
Edmund Burke ◽  
Yuri Bykov ◽  
James Newall ◽  
Sanja Petrovic
Keyword(s):  
Local Search ◽  
Optimization Problems ◽  
Search Time ◽  
Test Problems ◽  
Solution Quality ◽  
Course Timetabling ◽  
Combinatorial Optimization Problems ◽  
University Course Timetabling ◽  
High Level

A common weakness of local search metaheuristics, such as Simulated Annealing, in solving combinatorial optimization problems, is the necessity of setting a certain number of parameters. This tends to generate a significant increase in the total amount of time required to solve the problem and often requires a high level of experience from the user. This paper is motivated by the goal of overcoming this drawback by employing "parameter-free" techniques in the context of automatically solving course timetabling problems. We employ local search techniques with "straightforward" parameters, i.e. ones that an inexperienced user can easily understand. In particular, we present an extended variant of the "Great Deluge" algorithm, which requires only two parameters (which can be interpreted as search time and an estimation of the required level of solution quality). These parameters affect the performance of the algorithm so that a longer search provides a better result - as long as we can intelligently stop the approach from converging too early. Hence, a user can choose a balance between processing time and the quality of the solution. The proposed method has been tested on a range of university course timetabling problems and the results were evaluated within an International Timetabling Competition. The effectiveness of the proposed technique has been confirmed by a high level of quality of results. These results represented the third overall average rating among 21 participants and the best solutions on 8 of the 23 test problems. .

A Multiobjective Particle Swarm Optimizer for Constrained Optimization

2013 ◽  
pp. 71-95
Author(s):  
Gary G. Yen ◽  
Wen-Fung Leong
Keyword(s):  
Optimization Problems ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Constraint Handling ◽  
Benchmark Problems ◽  
Particle Swarm Optimizer ◽  
Multiobjective Optimization Problems ◽  
Feasible Solutions ◽  
Constrained Multiobjective Optimization

Constraint handling techniques are mainly designed for evolutionary algorithms to solve constrained multiobjective optimization problems (CMOPs). Most multiojective particle swarm optimization (MOPSO) designs adopt these existing constraint handling techniques to deal with CMOPs. In the proposed constrained MOPSO, information related to particles’ infeasibility and feasibility status is utilized effectively to guide the particles to search for feasible solutions and improve the quality of the optimal solution. This information is incorporated into the four main procedures of a standard MOPSO algorithm. The involved procedures include the updating of personal best archive based on the particles’ Pareto ranks and their constraint violation values; the adoption of infeasible global best archives to store infeasible nondominated solutions; the adjustment of acceleration constants that depend on the personal bests’ and selected global best’s infeasibility and feasibility status; and the integration of personal bests’ feasibility status to estimate the mutation rate in the mutation procedure. Simulation to investigate the proposed constrained MOPSO in solving the selected benchmark problems is conducted. The simulation results indicate that the proposed constrained MOPSO is highly competitive in solving most of the selected benchmark problems.

A New Hybrid Algorithm for Multi-Objective Robust Optimization With Interval Uncertainty

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Shuo Cheng ◽  
Jianhua Zhou ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Hybrid Approach ◽  
Interval Uncertainty ◽  
Engineering Optimization ◽  
Objective Functions ◽  
Robust Solutions ◽  
Multi Objective ◽  
And Performance

Uncertainty is a very critical but inevitable issue in design optimization. Compared to single-objective optimization problems, the situation becomes more difficult for multi-objective engineering optimization problems under uncertainty. Multi-objective robust optimization (MORO) approaches have been developed to find Pareto robust solutions. While the literature reports on many techniques in MORO, few papers focus on using multi-objective differential evolution (MODE) for robust optimization (RO) and performance improvement of its solutions. In this article, MODE is first modified and developed for RO problems with interval uncertainty, formulating a new MODE-RO algorithm. To improve the solutions’ quality of MODE-RO, a new hybrid (MODE-sequential quadratic programming (SQP)-RO) algorithm is proposed further, where SQP is incorporated into the procedure to enhance the local search. The proposed hybrid approach takes the advantage of MODE for its capability of handling not-well behaved robust constraint functions and SQP for its fast local convergence. Two numerical and one engineering examples, with two or three objective functions, are tested to demonstrate the applicability and performance of the proposed algorithms. The results show that MODE-RO is effective in solving MORO problems while, on the average, MODE-SQP-RO improves the quality of robust solutions obtained by MODE-RO with comparable numbers of function evaluations.

scholarly journals Adaptive Plant Propagation Algorithm for Solving Economic Load Dispatch Problem

2017 ◽  
Author(s):  
Sayan Nag
Keyword(s):  
Optimization Problems ◽  
State Of The Art ◽  
Economic Load Dispatch ◽  
Objective Functions ◽  
Plant Propagation ◽  
Propagation Algorithm ◽  
Highly Nonlinear ◽  
Plant Intelligence ◽  
Classical Optimization

Optimization problems in design engineering are complex by nature, often because of the involvement of critical objective functions accompanied by a number of rigid constraints associated with the products involved. One such problem is Economic Load Dispatch (ED) problem which focuses on the optimization of the fuel cost while satisfying some system constraints. Classical optimization algorithms are not sufficient and also inefficient for the ED problem involving highly nonlinear, and non-convex functions both in the objective and in the constraints. This led to the development of metaheuristic optimization approaches which can solve the ED problem almost efficiently. This paper presents a novel robust plant intelligence based Adaptive Plant Propagation Algorithm (APPA) which is used to solve the classical ED problem. The application of the proposed method to the 3-generator and 6-generator systems shows the efficiency and robustness of the proposed algorithm. A comparative study with another state-of-the-art algorithm (APSO) demonstrates the quality of the solution achieved by the proposed method along with the convergence characteristics of the proposed approach.

scholarly journals Separating Design Optimization Problems Into Decision-Based Design Processes

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Peyman Karimian ◽  
Jeffrey W. Herrmann
Keyword(s):  
Exact Solution ◽  
Design Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Objective Functions ◽  
Surrogate Constraints ◽  
Solution Quality ◽  
Design Processes ◽  
Motor Design ◽  
Decision Based Design

This paper introduces the technique of separation, which replaces a design optimization problem with a set of subproblems. This separation is similar to decomposition but does not require a second-level coordination. We identify conditions under which this separation yields an exact solution and other conditions under which the error can be bounded. We show that the decision-based design framework, which seeks to find the most profitable design, can be separated into a sequence of subproblems. We also apply separation to a motor design problem and demonstrate how the surrogate constraints and objective functions affect the solution quality. These results indicate a way to apply the principles of decision-based design to design processes.

Hybrid Mean-Variance Mapping Optimization for Non-Convex Economic Dispatch Problems

2017 ◽  
Vol 8 (4) ◽  
pp. 34-59
Author(s):  
Truong H. Khoa ◽  
Pandian M. Vasant ◽  
Balbir Singh Mahinder Singh ◽  
V. N. Dieu
Keyword(s):  
Cost Saving ◽  
Power Systems ◽  
Optimization Problems ◽  
Economic Dispatch ◽  
Objective Functions ◽  
Fuel Cost ◽  
Solution Quality ◽  
Prohibited Operating Zones ◽  
System Generation ◽  
Mean Variance

The economic dispatch (ED) is one of the important optimization problems in power system generation for fuel cost saving. This paper proposes a hybrid variant of mean-variance mapping optimization (MVMO-SH) for solving such problem considering the non-convex objective functions. The new proposed method is a hybrid variant of the original mean-variance mapping optimization algorithm (MVMO) with the embedded local search and multi-parent crossover to enhance its global search ability and improve solution quality for optimization problems. The proposed MVMO-SH is tested on different non-convex ED problem including valve point effects, multiple fuels and prohibited operating zones characteristics. The result comparisons from the proposed method with other methods in the literature have indicated that the proposed method is more robust and provides better solution quality than the others. Therefore, the proposed MVMO-SH is a promising method for solving the complex ED problems in power systems.

scholarly journals Fusing Swarm Intelligence and Self-Assembly for Optimizing Echo State Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Charles E. Martin ◽  
James A. Reggia
Keyword(s):  
Self Assembly ◽  
Effective Means ◽  
Optimality Criteria ◽  
Difficult Problem ◽  
Benchmark Problems ◽  
Objective Functions ◽  
Echo State Networks ◽  
And Topology ◽  
Interacting Networks

Optimizing a neural network’s topology is a difficult problem for at least two reasons: the topology space is discrete, and the quality of any given topology must be assessed by assigning many different sets of weights to its connections. These two characteristics tend to cause very “rough.” objective functions. Here we demonstrate how self-assembly (SA) and particle swarm optimization (PSO) can be integrated to provide a novel and effective means ofconcurrentlyoptimizing a neural network’s weights and topology. Combining SA and PSO addresses two key challenges. First, it creates a more integrated representation of neural network weights and topology so that we have just a single, continuous search domain that permits “smoother” objective functions. Second, it extends the traditional focus of self-assembly, from the growth of predefinedtarget structures, to functional self-assembly, in which growth is driven by optimality criteria defined in terms of the performance of emerging structures on predefinedcomputational problems. Our model incorporates a new way of viewing PSO that involves a population of growing, interacting networks, as opposed to particles. The effectiveness of our method for optimizing echo state network weights and topologies is demonstrated through its performance on a number of challenging benchmark problems.

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