Heidi A. Taboada

MOMS-GA: A Multi-Objective Multi-State Genetic Algorithm for System Reliability Optimization Design Problems

A custom genetic algorithm was developed and implemented to solve multiple objective multi-state reliability optimization design problems. Many real-world engineering design problems are multi-objective in nature, and among those, several of them have various levels of system performance ranging from perfectly functioning to completely failed. This multi-objective genetic algorithm uses the universal moment generating function approach to evaluate the different reliability or availability indices of the system. The components are characterized by having different performance levels, cost, weight, and reliability. The solution to the multi-objective multi-state problem is a set of solutions, known as the Pareto-front, from which the analyst may choose one solution for system implementation. Two illustrative examples are presented to show the performance of the algorithm; and the multi-objective formulation considered for both of them is the maximization of system availability, and the minimization of both system cost, and weight.

Practical solutions for multi-objective optimization: An application to system reliability design problems

For multiple-objective optimization problems, a common solution methodology is to determine a Pareto optimal set. Unfortunately, these sets are often large and can become difficult to comprehend and consider. Two methods are presented as practical approaches to reduce the size of the Pareto optimal set for multiple-objective system reliability design problems. The first method is a pseudo-ranking scheme that helps the decision maker select solutions that reflect his/her objective function priorities. In the second approach, we used data mining clustering techniques to group the data by using the k-means algorithm to find clusters of similar solutions. This provides the decision maker with just k general solutions to choose from. With this second method, from the clustered Pareto optimal set, we attempted to find solutions which are likely to be more relevant to the decision maker. These are solutions where a small improvement in one objective would lead to a large deterioration in at least one other objective. To demonstrate how these methods work, the well-known redundancy allocation problem was solved as a multiple objective problem by using the NSGA genetic algorithm to initially find the Pareto optimal solutions, and then, the two proposed methods are applied to prune the Pareto set.

Data Clustering of Solutions for Multiple Objective System Reliability Optimization Problems

Abstract This paper proposes a practical methodology for the solution of multi-objective system reliability optimization problems. The new method is based on the sequential combination of multi-objective evolutionary algorithms and data clustering on the prospective solutions to yield a smaller, more manageable sets of prospective solutions. Existing methods for multiple objective problems involve either the consolidation of all objectives into a single objective, or the determination of a Pareto-optimal set. In this paper, a new approach, involving post-Pareto clustering is proposed, offering a compromise between the two traditional approaches. In many real-life multi-objective optimization problems, the Pareto-optimal set can be extremely large or even contain an infinite number of solutions. Broad and detailed knowledge of the system is required during the decision making process in discriminating among the solutions contained in the Pareto-optimal set to eliminate the less satisfactory trade-offs and to select the most promising solution(s) for system implementation. The well-known reliability optimization problem, the redundancy allocation problem (RAP), was formulated as a multi-objective problem with the system reliability to be maximized, and cost and weight of the system to be minimized. A multiple stage process was performed to identify promising solutions. A Pareto-optimal set was initially obtained using the fast elitist nondominated sorting genetic algorithm (NSGA-II). The decision-making stage was then performed with the aid of data clustering techniques to prune the size of the Pareto-optimal set and obtain a smaller representation of the multi-objective design space; thereby making it easier for the decision-maker to find satisfactory and meaningful trade-offs, and to select a preferred final design solution.

Multi-objective scheduling problems: Determination of pruned Pareto sets

There are often multiple competing objectives for industrial scheduling and production planning problems. Two practical methods are presented to efficiently identify promising solutions from among a Pareto optimal set for multi-objective scheduling problems. Generally, multi-objective optimization problems can be solved by combining the objectives into a single objective using equivalent cost conversions, utility theory, etc., or by determination of a Pareto optimal set. Pareto optimal sets or representative subsets can be found by using a multi-objective genetic algorithm or by other means. Then, in practice, the decision maker ultimately has to select one solution from this set for system implementation. However, the Pareto optimal set is often large and cumbersome, making the post-Pareto analysis phase potentially difficult, especially as the number of objectives increase. Our research involves the post Pareto analysis phase, and two methods are presented to filter the Pareto optimal set to determine a subset of promising or desirable solutions. The first method is pruning using non-numerical objective function ranking preferences. The second approach involves pruning by using data clustering. The k-means algorithm is used to find clusters of similar solutions in the Pareto optimal set. The clustered data allows the decision maker to have just k general solutions from which to choose. These methods are general, and they are demonstrated using two multi-objective problems involving the scheduling of the bottleneck operation of a printed wiring board manufacturing line and a more general scheduling problem.

Data survivability vs. security in information systems

A multiple objective problem formulation and solution methodology is presented to select optimal information and data storage configurations considering both data survivability and data security, as well as cost. This paper considers a situation where the information is divided into several separately stored blocks in order to mitigate the risk of unauthorized access or theft. The information can be used only if all of the blocks are accessed. To impede the information theft, the defender prefers to maximize the number of blocks. On the other hand the destruction of any block destroys the integrity of information and makes it impossible to use. To impede the information destruction, the defender prefers to maximize the number of parallel (reserve) copies of each block, regardless how many blocks in series there are. Given the set of available information storage resources, the defender must consider a multi-objective optimization problem to determine how many blocks and their copies to create, and how to distribute them among available resources in order to minimize information vulnerability, insecurity, and storage cost. Non-dominated solutions to this problem are determined using a multiple objective genetic algorithm (MOGA). This methodology is demonstrated with two general examples.

A Multi-Objective Decision and Analysis Approach for the Berth Scheduling Problem

Berth scheduling can be described as the resource allocation problem of berth space to vessels in a container terminal. When defining the allocation of berths to vessels container terminal operators set several objectives which ideally need to be optimized simultaneously. These multiple objectives are often non-commensurable and gaining an improvement on one objective often causes degrading performance on the other objectives. In this paper, the authors present the application of a multi-objective decision and analysis approach to the berth scheduling problem, a resource allocation problem at container terminals. The proposed approach allows the port operator to efficiently select a subset of solutions over the entire solution space of berth schedules when multiple and conflicting objectives are involved. Results from extensive computational examples using real-world data show that the proposed approach is able to construct and select efficient berth schedules, is consistent, and can be used with confidence.

A Post-Pareto Approach for Multi-Objective Decision Making Using a Non-Uniform Weight Generator Method

Abstract There exist two general approaches to solve multiple objective problems. The first approach involves the aggregation of all the objective functions into a single composite objective function. Mathematical methods such as the weighted sum method, goal programming, or utility functions are methods that pertain to this general approach. The output of this method is a single solution. On the other hand, we have the multiple objective evolutionary algorithms that offer the decision maker a set of trade off solutions usually called non dominated solutions or, Pareto-optimal solutions. This set is usually very large and the decision maker faces the problem of reducing the size of this set to have a manageable number of solutions to analyze. This paper presents a post- Pareto approach to prune the non-dominated set of solutions obtained by multiple objective evolutionary algorithms. The proposed approach uses a non-uniform weight generator method to reduce the size of the Pareto-optimal set. A pair of examples is presented to show the performance of the method.

Exploring a solar photovoltaic-based energy solution for green manufacturing industry

A large amount of electricity is required to support the operation of large manufacturing facilities. Integrating renewable energy into the manufacturing industry reduces the carbon footprint and ensures the long-term sustainability. A key challenge in deploying renewable technology is the power volatility. We propose a solar photovoltaic-based co-generation system to accommodate the electricity needs of semiconductor wafer fabs. The problem is formulated as a stochastic programming model with the goal to minimize the system cost subject to the loss-of-load probability constraint. We compare the renewable energy yield and the system cost at five different wafer fabs in the U.S. Given appropriate tax incentives or equipment subsidies, the study shows that the solar-based energy solution is economically competitive in regions where the overcast days are less than 35% of the year.

A New Multiple Objective Evolutionary Algorithm for Reliability Optimization of Series-Parallel Systems

A new multiple objective evolutionary algorithm is proposed for reliability optimization of series-parallel systems. This algorithm uses a genetic algorithm based on rank selection and elitist reinsertion and a modified constraint handling method. Because genetic algorithms are appropriate for high-dimensional stochastic problems with many nonlinearities or discontinuities, they are suited for solving reliability design problems. The developed algorithm mainly differs from other multiple objective evolutionary algorithms in the crossover operation performed and in the fitness assignment. In the crossover step, several offspring are created through multi-parent recombination. Thus, the mating pool contains a great amount of diverse solutions. The disruptive nature of the proposed type of crossover, called subsystem rotation crossover, encourages the exploration of the search space. The paper presents a multiple objective formulation of the redundancy allocation problem. The three objective functions that are simultaneously optimized are the maximization of system reliability, the minimization of system cost, and the minimization of system weight. The proposed algorithm was thoroughly tested and a performance comparison of the proposed algorithm against one well-known multiple objective evolutionary algorithms that currently exists shows that the algorithm has a better performance when solving multiple objective redundant allocation problems.

Applications and performance of the non-numerical ranking preferences method for post-Pareto optimality

Abstract Most real-world engineering optimization problems are implicitly or explicitly multi-objective, and approaches to find the best feasible solution to be implemented can be quite challenging for the decision-maker. In this kind of problem, either the analyst determines a single solution or identifies a set of nondominated solutions, often referred to as Pareto-optimal set. Although, several methods for solving multi-objective optimization problems have been developed and studied, little prior work has been done on the evaluation of results obtained in multi-objective optimization. This selection stage is often referred as post-Pareto optimality. This paper presents a method based on preferences rankings provided from the decision-maker. The method is clearly advantageous because there is no need to provide specific weight values; the only requirement is to provide a non-nominal ranking. Several examples are used to show the performance of the algorithm.