Structural design using multi-objective metaheuristics. Comparative study and application to a real-world problem

Many structural design problems in the field of civil engineering are naturally multi-criteria, i.e., they have several conflicting objectives that have to be optimized simultaneously. An example is when we aim to reduce the weight of a structure while enhancing its robustness. There is no a single solution to these types of problems, but rather a set of designs representing trade-offs among the conflicting objectives. This paper focuses on the application of multi-objective metaheuristics to solve two variants of a real-world structural design problem. The goal is to compare a representative set of state-of-the-art multi-objective metaheuristic algorithms aiming to provide civil engineers with hints as to what optimization techniques to use when facing similar problems as those selected in the study presented in this paper. Accordingly, our study reveals that MOCell, a cellular genetic algorithm, provides the best overall performance, while NSGA-II, the de facto standard multi-objective metaheuristic technique, also demonstrates a competitive behavior.     

Differential Evolution performances for the solution of mixed-integer constrained process engineering problems

An important number of publications deal with the computational efficiency of a novel Evolutionary Algorithm called Differential Evolution (DE). However, there is still a noticeable lack of studies on DE's performance on engineering problems, which combine large-size instances, constraint-handling and mixed-integer variables issues. This paper proposes the solution by DE of process engineering problems and compares its computational performance with an exact optimization method (Branch-and-Bound) and with a Genetic Algorithm. Two analytical formulations are used to model the batch plant design problem and a set of examples gathering the three above-mentioned issues are also provided.The computational results obtained highlight the clear superiority of DE since its best found solutions always lie very close to the Branch-and-Bound optima. Moreover, for an equal number of objective function evaluations, the results repeatability was found to be much better for the DE method than for the Genetic Algorithm.     

DEMORS: A hybrid multi-objective optimization algorithm using differential evolution and rough set theory for constrained problems

The aim of this paper is to show how the hybridization of a multi-objective evolutionary algorithm (MOEA) and a local search method based on the use of rough set theory is a viable alternative to obtain a robust algorithm able to solve difficult constrained multi-objective optimization problems at a moderate computational cost. This paper extends a previously published MOEA [Hernández-Díaz AG, Santana-Quintero LV, Coello Coello C, Caballero R, Molina J. A new proposal for multi-objective optimization using differential evolution and rough set theory. In: 2006 genetic and evolutionary computation conference (GECCO’2006). Seattle, Washington, USA: ACM Press; July 2006], which was limited to unconstrained multi-objective optimization problems. Here, the main idea is to use this sort of hybrid approach to approximate the Pareto front of a constrained multi-objective optimization problem while performing a relatively low number of fitness function evaluations. Since in real-world problems the cost of evaluating the objective functions is the most significant, our underlying assumption is that, by aiming to minimize the number of such evaluations, our MOEA can be considered efficient. As in its previous version, our hybrid approach operates in two stages: in the first one, a multi-objective version of differential evolution is used to generate an initial approximation of the Pareto front. Then, in the second stage, rough set theory is used to improve the spread and quality of this initial approximation. To assess the performance of our proposed approach, we adopt, on the one hand, a set of standard bi-objective constrained test problems and, on the other hand, a large real-world problem with eight objective functions and 160 decision variables. The first set of problems are solved performing 10,000 fitness function evaluations, which is a competitive value compared to the number of evaluations previously reported in the specialized literature for such problems. The real-world problem is solved performing 250,000 fitness function evaluations, mainly because of its high dimensionality. Our results are compared with respect to those generated by NSGA-II, which is a MOEA representative of the state-of-the-art in the area.     

Increasing selective pressure towards the best compromise in evolutionary multiobjective optimization: The extended NOSGA method

Most current approaches in the evolutionary multiobjective optimization literature concentrate on adapting an evolutionary algorithm to generate an approximation of the Pareto frontier. However, finding this set does not solve the problem. The decision-maker still has to choose the best compromise solution out of that set. Here, we introduce a new characterization of the best compromise solution of a multiobjective optimization problem. By using a relational system of preferences based on a multicriteria decision aid way of thinking, and an outranked-based dominance generalization, we derive some necessary and sufficient conditions which describe satisfactory approximations to the best compromise. Such conditions define a lexicographic minimum of a bi-objective optimization problem, which is a map of the original one. The NOSGA-II method is a NSGA-II inspired efficient way of solving the resulting mapped problem.     

Handling multiple objectives with particle swarm optimization

This paper presents an approach in which Pareto dominance is incorporated into particle swarm optimization (PSO) in order to allow this heuristic to handle problems with several objective functions. Unlike other current proposals to extend PSO to solve multiobjective optimization problems, our algorithm uses a secondary (i.e., external) repository of particles that is later used by other particles to guide their own flight. We also incorporate a special mutation operator that enriches the exploratory capabilities of our algorithm. The proposed approach is validated using several test functions and metrics taken from the standard literature on evolutionary multiobjective optimization. Results indicate that the approach is highly competitive and that can be considered a viable alternative to solve multiobjective optimization problems.     

A new approach for evaluating sheet metal forming based on sheet drawing test. Application to TRIP 700 steel

Sheet formability has usually been evaluated by experimental tests that act under different conditions to those the material is subjected to during industrial processing. The different variables acting on the process are not split up sufficiently to be separately analysed. In this work, a new approach to evaluate formability in pure shear deformation has been developed. For this purpose, a new apparatus has been devised to do drawing tests to thin sheets which permits the calculation of deformation work as a function of the drawing strain. Moreover, the coefficient of friction under high pressure values can be modelled. One application to TRIP 700 steel and the friction results have been considered up to an apparent pressure of 1900 MPa. Deformation work has been analysed and inhomogeneity deformation has been evaluated in terms of redundant work as a function of the geometry of the die. The obtained results agree with the theory of plasticity and demonstrate the utility of the methodology presented herein.     

An optimal power flow plus transmission costs solution

This paper is aimed at the solution of the optimal power flow (OPF) problem with embedded security constraints (OPF-SC) by the particle swarm optimizer. The major objective is to minimize the overall operating cost while satisfying the power flow equations, system security, and equipment operating limits. The overall operating cost is composed by the generation cost, transmission cost, and the consumer benefit. A modification of the conventional particle swarm optimizer (PSO) has been used as the optimization tool, which uses reconstruction operators and dynamic penalization for handling constraints. The reconstruction operators allow the increase of the number of particles within the feasible region. The power equations mismatch, loss active power transmission, and voltages are calculated by the Newton–Raphson method. To demonstrate its robustness, the proposed algorithm was tested on systems from the open literature. Several cases have been studied to test and validate the proposed approach.     

Multiobjective structural optimization using a microgenetic algorithm

In this paper, we present a genetic algorithm with a very small population and a reinitialization process (a microgenetic algorithm) for solving multiobjective optimization problems. Our approach uses three forms of elitism, including an external memory (or secondary population) to keep the nondominated solutions found along the evolutionary process. We validate our proposal using several engineering optimization problems taken from the specialized literature and compare our results with respect to two other algorithms (NSGA-II and PAES) using three different metrics. Our results indicate that our approach is very efficient (computationally speaking) and performs very well in problems with different degrees of complexity.     

A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques

This paper presents a critical review of the most important evolutionary-based multiobjective optimization techniques developed over the years, emphasizing the importance of analyzing their Operations Research roots as a way to motivate the development of new approaches that exploit the search capabilities of evolutionary algorithms. Each technique is briefly described with its advantages and disadvantages, its degree of applicability and some of its known applications. Finally, the future trends in this discipline and some of the open areas of research are also addressed.