Disjunctive programming for multiobjective discrete optimisation

In this paper, I view and present the multiobjective discrete optimisation problem as a particular case of disjunctive programming where one seeks to identify efficient solutions from within a disjunction formed by a set of systems. The proposed approach lends itself to a simple yet effective iterative algorithm that is able to yield the set of all nondominated points, both supported and nonsupported, for a multiobjective discrete optimisation problem. Each iteration of the algorithm is a series of feasibility checks and requires only one formulation to be solved to optimality that has the same number of integer variables as that of the single objective formulation of the problem. The application of the algorithm show that it is particularly effective, and superior to the state-of-the-art, when solving constrained multiobjective discrete optimisation problem instances

Disjunctive Programming for Multiobjective Discrete Optimisation

In this paper, I view and present the multiobjective discrete optimisation problem as a particular case of disjunctive programming where one seeks to identify efficient solutions from within a disjunction formed by a set of systems. The proposed approach lends itself to a simple yet effective iterative algorithm that is able to yield the set of all nondominated points, both supported and nonsupported, for a multiobjective discrete optimisation problem. Each iteration of the algorithm is a series of feasibility checks and requires only one formulation to be solved to optimality that has the same number of integer variables as that of the single objective formulation of the problem. The application of the algorithm show that it is particularly effective, and superior to the state-of-the-art, when solving constrained multiobjective discrete optimisation problem instances

Computer-aided design of optimal environmentally benign solvent-based adhesive products

The manufacture of improved adhesive products that meet specified target properties has attracted increasing interest over the last decades. In this work, a general systematic methodology for the design of optimal adhesive products with low environmental impact is presented. The proposed approach integrates computer-aided design tools and Generalised Disjunctive Programming (GDP), a logic-based framework, to formulate and solve the product design problem. Key design decisions in product design (i.e., how many components should be included in the final product, which active ingredients and solvent compounds should be used and in what proportions) are optimised simultaneously. This methodology is applied to the design of solvent-based acrylic adhesives, which are commonly used in construction. First, optimal product formulations are determined with the aim to minimize toxicity. This reveals that number of components in the product formulation does not correlate with performance and that high performance can be achieved by investigating different number of components as well as by optimising all ingredients simultaneously rather than sequentially. The relation between two competing objectives (product toxicity and concentration of the active ingredient) is then explored by obtaining a set of Pareto optimal solutions. This leads to significant trade-offs and large areas of discontinuity driven by discrete changes in the list of optimal ingredients in the product

Integration of different models in the design of chemical processes: Application to the design of a power plant

With advances in the synthesis and design of chemical processes there is an increasing need for more complex mathematical models with which to screen the alternatives that constitute accurate and reliable process models. Despite the wide availability of sophisticated tools for simulation, optimization and synthesis of chemical processes, the user is frequently interested in using the ‘best available model’. However, in practice, these models are usually little more than a black box with a rigid input–output structure. In this paper we propose to tackle all these models using generalized disjunctive programming to capture the numerical characteristics of each model (in equation form, modular, noisy, etc.) and to deal with each of them according to their individual characteristics. The result is a hybrid modular–equation based approach that allows synthesizing complex processes using different models in a robust and reliable way. The capabilities of the proposed approach are discussed with a case study: the design of a utility system power plant that has been decomposed into its constitutive elements, each treated differently numerically. And finally, numerical results and conclusions are presented.Spanish Ministry of Science and Innovation (CTQ2012-37039-C02-02)

A survey on portfolio optimisation with metaheuristics.

A portfolio optimisation problem involves allocation of investment to a number of different assets to maximize return and minimize risk in a given investment period. The selected assets in a portfolio not only collectively contribute to its return but also interactively define its risk as usually measured by a portfolio variance. This presents a combinatorial optimisation problem that involves selection of both a number of assets as well as its quantity (weight or proportion or units). The problem is extremely complex due to a large number of selectable assets. Furthermore, the problem is dynamic and stochastic in nature with a number of constraints presenting a complex model which is difficult to solve for exact solution. In the last decade research publications have reported the applications of metaheuristic-based optimisation methods with some success., This paper presents a review of these reported models, optimisation problem formulations and metaheuristic approaches for portfolio optimisation

Simultaneous environmental and economic process synthesis of Isobutane Alkylation

This multidisciplinary study concerns the optimal design of processes with a view to both maximizing profit and minimizing environmental impacts. This can be achieved by a combination of traditional chemical process design methods, measurements of environmental impacts and advanced mathematical optimization techniques. More to the point, this paper presents a hybrid simulation-multiobjective optimization approach that at once optimizes the production cost and minimizes the associated environmental impacts of isobutane alkylation. This approach has also made it possible to obtain the flowsheet configurations and process variables that are needed to manufacture isooctane in a way that satisfies the above-stated double aim. The problem is formulated as a Generalized Disjunctive Programming problem and solved using state-of-the-art logic-based algorithms. It is shown, starting from existing alternatives for the process, that it is possible to systematically generate a superstructure that includes alternatives not previously considered. The optimal solution, in the form a Pareto curve, includes different structural alternatives from which the most suitable design can be selected. To evaluate the environmental impact, Life Cycle Assessment based on two different indicators is employed: Ecoindicator 99 and Global Warming Potential.Spanish Ministry of Science and Innovation (CTQ2012-37039-C02-02)

Multi-objective enhanced memetic algorithm for green job shop scheduling with uncertain times

The quest for sustainability has arrived to the manufacturing world, with the emergence of a research field known as green scheduling. Traditional performance objectives now co-exist with energy-saving ones. In this work, we tackle a job shop scheduling problem with the double goal of minimising energy consumption during machine idle time and minimising the project’s makespan. We also consider uncertainty in processing times, modelled with fuzzy numbers. We present a multi-objective optimisation model of the problem and we propose a new enhanced memetic algorithm that combines a multiobjective evolutionary algorithm with three procedures that exploit the problem-specific available knowledge. Experimental results validate the proposed method with respect to hypervolume, -indicator and empirical attaintment functions

From conceptual design to process design optimization: a review on flowsheet synthesis

International audienceThis paper presents the authors’ perspectives on some of the open questions and opportunities in Process Systems Engineering (PSE) focusing on process synthesis. A general overview of process synthesis is given, and the difference between Conceptual Design (CD) and Process Design (PD) is presented using an original ternary diagram. Then, a bibliometric analysis is performed to place major research team activities in the latter. An analysis of ongoing work is conducted and some perspectives are provided based on the analysis. This analysis includes symbolic knowledge representation concepts and inference techniques, i.e., ontology, that is believed to become useful in the future. Future research challenges that process synthesis will have to face, such as biomass transformation, shale production, response to spaceflight demand, modular plant design, and intermittent production of energy, are also discussed

Mixed-Integer Nonlinear Programming Optimization Strategies for Batch Plant Design Problems

Due to their large variety of applications, complex optimisation problems induced a great effort to develop efficient solution techniques, dealing with both continuous and discrete variables involved in non-linear functions. But among the diversity of those optimisation methods, the choice of the relevant technique for the treatment of a given problem keeps being a thorny issue. Within the Process Engineering context, batch plant design problems provide a good framework to test the performances of various optimisation methods : on the one hand, two Mathematical Programming techniques – DICOPT++ and SBB, implemented in the GAMS environment – and, on the other hand, one stochastic method, i.e. a genetic algorithm. Seven examples, showing an increasing complexity, were solved with these three techniques. The result comparison enables to evaluate their efficiency in order to highlight the most appropriate method for a given problem instance. It was proved that the best performing method is SBB, even if the GA also provides interesting solutions, in terms of quality as well as of computational time