Multi-objective optimization of environmentally conscious chemical supply chains under demand uncertainty

In this work, we analyze the effect of demand uncertainty on the multi-objective optimization of chemical supply chains (SC) considering simultaneously their economic and environmental performance. To this end, we present a stochastic multi-scenario mixed-integer linear program (MILP) with the unique feature of incorporating explicitly the demand uncertainty using scenarios with given probability of occurrence. The environmental performance is quantified following life cycle assessment (LCA) principles, which are represented in the model formulation through standard algebraic equations. The capabilities of our approach are illustrated through a case study. We show that the stochastic solution improves the economic performance of the SC in comparison with the deterministic one at any level of the environmental impact.

Fault tolerant embedded systems design by multi-objective optimization

The design of fault tolerant systems is gaining importance in large domains of embedded applications where design constrains are as important as reliability. New software techniques, based on selective application of redundancy, have shown remarkable fault coverage with reduced costs and overheads. However, the large number of different solutions provided by these techniques, and the costly process to assess their reliability, make the design space exploration a very difficult and time-consuming task. This paper proposes the integration of a multi-objective optimization tool with a software hardening environment to perform an automatic design space exploration in the search for the best trade-offs between reliability, cost, and performance. The first tool is commanded by a genetic algorithm which can simultaneously fulfill many design goals thanks to the use of the NSGA-II multi-objective algorithm. The second is a compiler-based infrastructure that automatically produces selective protected (hardened) versions of the software and generates accurate overhead reports and fault coverage estimations. The advantages of our proposal are illustrated by means of a complex and detailed case study involving a typical embedded application, the AES (Advanced Encryption Standard).

Tuning compilations by multi-objective optimization: Application to Apache web server

Modern compilers present a great and ever increasing number of options which can modify the features and behavior of a compiled program. Many of these options are often wasted due to the required comprehensive knowledge about both the underlying architecture and the internal processes of the compiler. In this context, it is usual, not having a single design goal but a more complex set of objectives. In addition, the dependencies between different goals are difficult to be a priori inferred. This paper proposes a strategy for tuning the compilation of any given application. This is accomplished by using an automatic variation of the compilation options by means of multi-objective optimization and evolutionary computation commanded by the NSGA-II algorithm. This allows finding compilation options that simultaneously optimize different objectives. The advantages of our proposal are illustrated by means of a case study based on the well-known Apache web server. Our strategy has demonstrated an ability to find improvements up to 7.5% and up to 27% in context switches and L2 cache misses, respectively, and also discovers the most important bottlenecks involved in the application performance.

Multi-objective adaptive evolutionary strategy for tuning compilations

Tuning compilations is the process of adjusting the values of a compiler options to improve some features of the final application. In this paper, a strategy based on the use of a genetic algorithm and a multi-objective scheme is proposed to deal with this task. Unlike previous works, we try to take advantage of the knowledge of this domain to provide a problem-specific genetic operation that improves both the speed of convergence and the quality of the results. The evaluation of the strategy is carried out by means of a case of study aimed to improve the performance of the well-known web server Apache. Experimental results show that a 7.5% of overall improvement can be achieved. Furthermore, the adaptive approach has shown an ability to markedly speed-up the convergence of the original strategy.

Feature selection by multi-objective optimisation: Application to network anomaly detection by hierarchical self-organising maps

Feature selection is an important and active issue in clustering and classification problems. By choosing an adequate feature subset, a dataset dimensionality reduction is allowed, thus contributing to decreasing the classification computational complexity, and to improving the classifier performance by avoiding redundant or irrelevant features. Although feature selection can be formally defined as an optimisation problem with only one objective, that is, the classification accuracy obtained by using the selected feature subset, in recent years, some multi-objective approaches to this problem have been proposed. These either select features that not only improve the classification accuracy, but also the generalisation capability in case of supervised classifiers, or counterbalance the bias toward lower or higher numbers of features that present some methods used to validate the clustering/classification in case of unsupervised classifiers. The main contribution of this paper is a multi-objective approach for feature selection and its application to an unsupervised clustering procedure based on Growing Hierarchical Self-Organising Maps (GHSOMs) that includes a new method for unit labelling and efficient determination of the winning unit. In the network anomaly detection problem here considered, this multi-objective approach makes it possible not only to differentiate between normal and anomalous traffic but also among different anomalies. The efficiency of our proposals has been evaluated by using the well-known DARPA/NSL-KDD datasets that contain extracted features and labelled attacks from around 2 million connections. The selected feature sets computed in our experiments provide detection rates up to 99.8% with normal traffic and up to 99.6% with anomalous traffic, as well as accuracy values up to 99.12%.

Robust solutions to multi-objective linear programs with uncertain data

In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for the radius of robust feasibility guaranteeing constraint feasibility for all possible scenarios within a specified uncertainty set under affine data parametrization. We then present numerically tractable optimality conditions for minmax robust weakly efficient solutions, i.e., the weakly efficient solutions of the robust counterpart. We also consider highly robust weakly efficient solutions, i.e., robust feasible solutions which are weakly efficient for any possible instance of the objective matrix within a specified uncertainty set, providing lower bounds for the radius of highly robust efficiency guaranteeing the existence of this type of solutions under affine and rank-1 objective data uncertainty. Finally, we provide numerically tractable optimality conditions for highly robust weakly efficient solutions.

Optimization of test and maintenance of ageing components consisting of multiple items and addressing effectiveness

There are many models in the literature that have been proposed in the last decades aimed at assessing the reliability, availability and maintainability (RAM) of safety equipment, many of them with a focus on their use to assess the risk level of a technological system or to search for appropriate design and/or surveillance and maintenance policies in order to assure that an optimum level of RAM of safety systems is kept during all the plant operational life. This paper proposes a new approach for RAM modelling that accounts for equipment ageing and maintenance and testing effectiveness of equipment consisting of multiple items in an integrated manner. This model is then used to perform the simultaneous optimization of testing and maintenance for ageing equipment consisting of multiple items. An example of application is provided, which considers a simplified High Pressure Injection System (HPIS) of a typical Power Water Reactor (PWR). Basically, this system consists of motor driven pumps (MDP) and motor operated valves (MOV), where both types of components consists of two items each. These components present different failure and cause modes and behaviours, and they also undertake complex test and maintenance activities depending on the item involved. The results of the example of application demonstrate that the optimization algorithm provide the best solutions when the optimization problem is formulated and solved considering full flexibility in the implementation of testing and maintenance activities taking part of such an integrated RAM model.

Combined simulation-optimization methodology for the design of environmental conscious absorption systems

This work addresses the optimization of ammonia–water absorption cycles for cooling and refrigeration applications with economic and environmental concerns. Our approach combines the capabilities of process simulation, multi-objective optimization (MOO), cost analysis and life cycle assessment (LCA). The optimization task is posed in mathematical terms as a multi-objective mixed-integer nonlinear program (moMINLP) that seeks to minimize the total annualized cost and environmental impact of the cycle. This moMINLP is solved by an outer-approximation strategy that iterates between primal nonlinear programming (NLP) subproblems with fixed binaries and a tailored mixed-integer linear programming (MILP) model. The capabilities of our approach are illustrated through its application to an ammonia–water absorption cycle used in cooling and refrigeration applications.

Handling of Uncertainty in Life Cycle Inventory by Correlated Multivariate Lognormal Distributions: Application to the Design of Supply Chain Networks

Poster presented in the 24th European Symposium on Computer Aided Process Engineering (ESCAPE 24), Budapest, Hungary, June 15-18, 2014.

Handling of Uncertainty in Life Cycle Inventory by Correlated Multivariate Lognormal Distributions: Application to the Design of Supply Chain Networks

In this work, we analyze the effect of incorporating life cycle inventory (LCI) uncertainty on the multi-objective optimization of chemical supply chains (SC) considering simultaneously their economic and environmental performance. To this end, we present a stochastic multi-scenario mixed-integer linear programming (MILP) coupled with a two-step transformation scenario generation algorithm with the unique feature of providing scenarios where the LCI random variables are correlated and each one of them has the desired lognormal marginal distribution. The environmental performance is quantified following life cycle assessment (LCA) principles, which are represented in the model formulation through standard algebraic equations. The capabilities of our approach are illustrated through a case study of a petrochemical supply chain. We show that the stochastic solution improves the economic performance of the SC in comparison with the deterministic one at any level of the environmental impact, and moreover the correlation among environmental burdens provides more realistic scenarios for the decision making process.

Constraint qualifications in convex vector semi-infinite optimization

Convex vector (or multi-objective) semi-infinite optimization deals with the simultaneous minimization of finitely many convex scalar functions subject to infinitely many convex constraints. This paper provides characterizations of the weakly efficient, efficient and properly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The results in this paper generalize those obtained by the same authors on linear vector semi-infinite optimization problems.

Sensitivity Analysis in Convex Optimization through the Circatangent Derivative

The main goal of this paper is to analyse the sensitivity of a vector convex optimization problem according to variations in the right-hand side. We measure the quantitative behavior of a certain set of Pareto optimal points characterized to become minimum when the objective function is composed with a positive function. Its behavior is analysed quantitatively using the circatangent derivative for set-valued maps. Particularly, it is shown that the sensitivity is closely related to a Lagrange multiplier solution of a dual program.

Hybrid simulation-optimization based approach for the optimal design of single-product biotechnological processes

In this work, we present a systematic method for the optimal development of bioprocesses that relies on the combined use of simulation packages and optimization tools. One of the main advantages of our method is that it allows for the simultaneous optimization of all the individual components of a bioprocess, including the main upstream and downstream units. The design task is mathematically formulated as a mixed-integer dynamic optimization (MIDO) problem, which is solved by a decomposition method that iterates between primal and master sub-problems. The primal dynamic optimization problem optimizes the operating conditions, bioreactor kinetics and equipment sizes, whereas the master levels entails the solution of a tailored mixed-integer linear programming (MILP) model that decides on the values of the integer variables (i.e., number of equipments in parallel and topological decisions). The dynamic optimization primal sub-problems are solved via a sequential approach that integrates the process simulator SuperPro Designer® with an external NLP solver implemented in Matlab®. The capabilities of the proposed methodology are illustrated through its application to a typical fermentation process and to the production of the amino acid L-lysine.

Integration of modular process simulators under the Generalized Disjunctive Programming framework for the structural flowsheet optimization

The optimization of chemical processes where the flowsheet topology is not kept fixed is a challenging discrete-continuous optimization problem. Usually, this task has been performed through equation based models. This approach presents several problems, as tedious and complicated component properties estimation or the handling of huge problems (with thousands of equations and variables). We propose a GDP approach as an alternative to the MINLP models coupled with a flowsheet program. The novelty of this approach relies on using a commercial modular process simulator where the superstructure is drawn directly on the graphical use interface of the simulator. This methodology takes advantage of modular process simulators (specially tailored numerical methods, reliability, and robustness) and the flexibility of the GDP formulation for the modeling and solution. The optimization tool proposed is successfully applied to the synthesis of a methanol plant where different alternatives are available for the streams, equipment and process conditions.

Primal Attainment in Convex Infinite Optimization Duality

This article provides results guarateeing that the optimal value of a given convex infinite optimization problem and its corresponding surrogate Lagrangian dual coincide and the primal optimal value is attainable. The conditions ensuring converse strong Lagrangian (in short, minsup) duality involve the weakly-inf-(locally) compactness of suitable functions and the linearity or relative closedness of some sets depending on the data. Applications are given to different areas of convex optimization, including an extension of the Clark-Duffin Theorem for ordinary convex programs.