Multi-objective Programming Optimization Research Articles

On the transformation of lexicographic nonlinear multiobjective programs to single objective programs

This paper deals with multiobjective optimization programs in which the objective functions are ordered by their degree of priority. A number of approaches have been proposed (and several implemented) for the solution of lexicographic (preemptive priority) multiobjective optimization programs. These approaches may be divided into two classes. The first encompasses the development of algorithms specifically designed to deal directly with the initial model. Considered only for linear multiobjective programs and multiobjective programs with a finite discrete feasible region, the second one attempts to transform, efficiently, the lexicographic multiobjective model into an equvivalent model, i.e. a single objective programming problem. In this paper, we deal with the second approach for lexicographic nonlinear multiobjective programs.

Multi-objective optimization using MS Excel with an application to design of a falling-film evaporator system

There are a number of multi-objective optimization (MOO) methods and programs, as well as many applications of MOO in food engineering. However, almost all these applications have been done using programs/platforms that are not readily used in the industry. On the other hand, engineers are familiar with MS Excel and use it in both research and industrial practice. Hence, in this work, an Excel-based MOO (EMOO) program is developed based on the elitist non-dominated sorting genetic algorithm (NSGA-II) and tested on benchmark problems. It is then applied for MOO of design of a falling-film evaporator system, consisting of a pre-heater, evaporator, vapor condenser and steam jet ejector, for milk concentration. The EMOO program gave well-distributed Pareto-optimal solutions for the MOO problems tested. Design equations and results for two bi-objective optimization problems are presented and discussed.

Gravity-assisted maneuvers applied in the multi-objective optimization of interplanetary trajectories

In this work, the problem of optimization of interplanetary trajectories with minimum fuel consumption, but with a time limit is studied. It was used a methodology known as the Patched Conics, where the trajectory is divided into three parts: (1) departure phase, inside of the sphere of influence of the departure planet; (2) heliocentric phase, during the journey between the planets; and (3) arrival phase, inside of the sphere of influence of the arrival planet. Furthermore, the possibility of gravitational assisted maneuvers (swing-by) was considered to reduce fuel consumption. In this case the full trajectory would be divided into more parts, depending on the number of maneuvers. Therefore, the goal of this work is to find a combination of conical trajectories, using gravitational assisted maneuvers, which perform the transfer close to the departure planet to the vicinity of the arrival planet, spending minimal fuel with minimal time for the journey. Considering the minimization of time, the solution cannot be the solution of minimum fuel consumption, because the minimization of time and the minimization of fuel are conflicting objectives. Thus, a multi-objective problem must be solved. Hence, a methodology based on the Non Inferiority Criterion (Pareto, 1909 [2]) and the Smallest Loss Criterion (Rocco et al., 2002 [6]) was used, capable of considering multiple objectives simultaneously, without reducing the problem to the case of optimizing a single objective as occur in most methods found in the literature. A mission to Pluto, similar to NASA’s New Horizons Mission, was studied considering gravitational assisted maneuvers in Mars, Jupiter and Saturn. Simulating the trajectories and the maneuvers using the Transfer Trajectory Design Programs (Sukhanov, 2004 [13]), several possibilities were analyzed for many combinations of fuel consumption, time of departure, time of arrival and planet used for the swing-by. Then, using the Multi-objective Optimization Program (Rocco et al., 2002 [6]) the problem was solved seeking the best combination. The results can provide good assistance for mission analysis reducing the cost and time.

Quest for appropriate overcapacity in the fisheries industry

The effective management of natural resources is a critical issue that concerns many people with differing interests. This paper examines aspects of overcapacity and optimal capacity within fisheries by accounting for multiple objectives. Overcapacity arises when a fishing fleet is capable of producing more than what is demanded at the industry level, or allowed by a regulatory framework. The presence of multiple objectives within fisheries management is most often an unavoidable reality, where the objectives determine what level of overcapacity is considered optimal. A two-stage model is suggested that can produce information for management in terms of tradeoffs, policy frontiers, objective values and optimal fleet structure. In the first stage, an output-based Data Envelopment Analysis (DEA) model is applied. Efficiency is evaluated and production units transformed such that they use technologically efficient inputs and produce at their full potential. In the second stage, these transformed units are included in an aggregate industry model formulated as a multi-objective optimization program. The model provides information for managers in terms of tradeoffs, policy frontiers, objective values, and optimal fleet structure (by generating Pareto optimal solutions). The proposed model has then been applied to the Danish commercial fishing fleet.

On second-order Fritz John type optimality conditions in nonsmooth multiobjective programming

We study a multiobjective optimization program with a feasible set defined by equality constraints and a generalized inequality constraint. We suppose that the functions involved are Frechet differentiable and their Frechet derivatives are continuous or stable at the point considered. We provide necessary second order optimality conditions and also sufficient conditions via a Fritz John type Lagrange multiplier rule and a set-valued second order directional derivative, in such a way that our sufficient conditions are close to the necessary conditions. Some consequences are obtained for parabolic directionally differentiable functions and C1,1 functions, in this last case, expressed by means of the second order Clarke subdifferential. Some illustrative examples are also given.

Evaluating Environmental Impact in Water Distribution System Design

An index-based method for the evaluation of the environmental impact of water distribution systems is introduced. The method is developed according to a set of methodological criteria to assess the environmental effect of water networks. A number of environmental measures are incorporated into the index-based method to account for nonrenewable resource consumption, greenhouse gas emissions, and emissions to air, land, and water. The index-based method can be included into a multiobjective optimization program to find design solutions that minimize cost and environmental impact. The index-based method was applied to the design of a water transmission system over a 20-year design horizon. Design alternatives were compared on the basis of the environmental impact index and cost. For the system analyzed, results indicated that of the hydraulically feasible alternatives, the five most environmentally acceptable alternatives were the five most cost-effective alternatives. Results also showed that the environmental impact index is mainly influenced by pumping energy and partially influenced by pipe diameter selection.

Mental Contents in Interacting with a Multiobjective Optimization Program

User psychology aims at understanding human-machine interaction from a psychological point of view. Its ultimate goal is to provide knowledge about human psychological properties for interaction designers. In this article, we are particularly interested in applying the theoretical concepts of mental contents (i.e., the information contents of users’ mental representations), in studying interaction with professional software. The immediate motivation for adopting such an approach arises from problems met in designing interaction processes in multiobjective optimization software. These types of software are meant to support complex thought and decision-making processes and this is why interaction design has to meet a number of theoretical problems, which do seldom arise in simpler interaction types. In four experiments, we investigated the types of knowledge required when developing ones’ capability of working with such a thought tool. We observed that in interaction design it is essential to take into account domain, professional and software specific mental content structures.

Optimality conditions and duality in multiobjective programming with invexity

(', ?)-invexity has recently been introduced with the intent of generalizing invex functions in mathematical programming. Using such conditions we obtain new sufficiency results for optimality in multiobjective programming and extend some classical duality properties.

Green supply chain management, reverse logistics and nuclear power generation

Built on the concepts of green supply chain management (G-SCM), this paper presents a multi-objective optimization programming approach to address the issue of nuclear power generation. In this study, a linear multi-objective optimization model is formulated to optimize the operations of both the nuclear power generation and the corresponding induced-waste reverse logistics. Factors such as the operational risks induced in both the power generation and reverse logistics processes are considered in the model formulation. Numerical results indicate that using the proposed approach, the induced environmental impact including the corresponding costs and risks can be improved up to 37.8%.

A hybrid fuzzy-optimization approach to customer grouping-based logistics distribution operations

This paper presents an integrated fuzzy-optimization customer grouping based logistics distribution methodology for quickly responding to a variety of customer demands. The proposed methodology involves three main mechanisms: (1) pre-route customer classification using fuzzy clustering techniques, (2) determination of customer group-based delivery service priority and (3) en-route goods delivery using multi-objective optimization programming methods. In the process of pre-route customer classification, the proposed method groups customers’ orders primarily based on the multiple attributes of customer demands, rather than by static geographic attributes, which are mainly considered in classical vehicle routing algorithms. Numerical studies including a real-world application are conducted to illustrate the applicability of the proposed method and its potential advantages over existing operational strategies. Using the proposed method, it is shown that the overall performance of a logistics distribution system can be improved by more than 20%, according to the numerical results from the case studied.

An inexact optimization approach for river water-quality management

A previously developed fuzzy waste load allocation model (FWLAM) for a river system is extended to address uncertainty involved in fixing the membership functions for the fuzzy goals of the pollution control agency (PCA) and the dischargers using the concept of grey systems. The model provides flexibility for the PCA and the dischargers to specify their goals independently, as the parameters for membership functions are considered as interval grey numbers instead of deterministic real numbers. An inexact or a grey fuzzy optimization model is developed in a multiobjective framework, to maximize the width of the interval valued fractional removal levels for providing latitude in decision-making and to minimize the width of the goal fulfillment level for reducing the system uncertainty. The concept of an acceptability index for order relation between two partially or fully overlapping intervals is used to get a deterministic equivalent of the grey fuzzy optimization model developed. The improvement of the optimal solutions over a previously developed grey fuzzy waste load allocation model (GFWLAM) is shown through an application to a hypothetical river system. The fuzzy multiobjective optimization and fuzzy goal programming techniques are used to solve the deterministic equivalent of the GFWLAM.

ENTRAINER SELECTION AND SOLVENT RECYCLING IN COMPLEX BATCH DISTILLATION

This article presents a simultaneous integration of entrainer selection and solvent recycling for the batch distillation synthesis problem for the first time. The industrial case study used here is to separate acetonitrile from an aqueous acetonitrile waste mixture, a challenging problem because of the thermodynamic complexity of the mixture. Two batch distillation campaigns have been designed using coupled heuristics and optimization approaches and investigated with complex batch column configurations. The first campaign for fast removal of highly pure water identified batch stripper and middle vessel column as the optimal column configurations. In the second campaign, effective entrainer molecules were generated by a computer-aided molecular design approach, and the proposed entrainer was continuously charged at a specified fraction into the middle vessel column to obtain pure acetonitrile and water. Two candidate entrainers, propyl amine, having high relative volatility, and acetone, having low relative volatility, were proposed and compared. A multiobjective optimization programming framework and trade-off are also presented for further complete analysis.

Multiobjective Optimization for Safety-related Decision Making in Chemical Processes

This paper proposes a novel decision making procedure based on multiobjective optimization programming (MOOP) to find the investment priority to reduce plant accidents. The new method rank the accident scenarios in order among many possible accident scenarios in a plant to decide the invest priority as considering safety and cost simultaneously. The method is explained by taking an example, which includes 30 accident scenario data (Kim et al., 2001) consisting of accident consequence, accident frequency, safety activity cost, and non-operating time. In this example, four goals are considered: (1) minimization of total safety activity cost, (2) minimization of total accident consequence, (3) minimization of the number of accident scenarios for unreasonable frequency, and (41 minimization of non-operating time. To analyze this optimization problem in terms of process safety and cost, this study obtained the noninferior solution curve (Pareto curve) by using the Goal programming (GP) methods. We found the ideal compromise solution set based on the Pareto curve. This result assists the business decision maker to select the best compromise in improving process safety as well as reducing investment cost.

Optimal suspension design for femto sliders

This paper describes a process on how to optimize the suspension for femto sliders in the design process by using multiobjective topology optimization. The design objectives are defined to maximize the resonant frequency of sway mode subject to inequality constraints on the spring rate and frequencies of first bending and first torsion modes of the suspension. Then the optimization problem is solved with the self-developed multiobjective topology optimization program. Finally, an optimal design of the suspension assembly for femto sliders is presented with much better dynamic characteristics.

Multiobjective Optimization of Cyclic Adsorption Processes

This paper focuses on the development of a multiobjective optimization approach and the first application to highly nonlinear cyclic adsorption processes such as thermal swing adsorption (TSA) and rapid pressure swing adsorption (RPSA). The new method was modified from the conventional summation of a weighted objective function (SWOF) method, which is one of the most traditional and the simplest way of multiobjective optimization programming. The new modified SWOF technique eliminates the main drawbacks of the conventional SWOF and approximates the Pareto curve efficiently with several Pareto points as explained by the two examples (TSA and RPSA). The sensitivity of these processes was also analyzed.

Multiobjective Optimization in Terms of Economics and Potential Environment Impact for Process Design and Analysis in a Chemical Process Simulator

This paper is devoted to an application of the MOOP (multiobjective optimization programming) concept to the practical field of chemical engineering to take into account the trade-off between economics and pollution with appropriate analysis methods. Optimization of the process is performed along an infeasible path with the SQP (successive quadratic programming) algorithm. One of the objective functions, the global pollution index function, is based on potential environmental impact indexes calculated by using the hazard value (HV). The other is the cost−benefit function. To analyze the biobjective optimization system in terms of economics and potential environmental impact, the noninferior solution curve (Pareto curve) is formed using SWOF (summation of weighted objective functions), GP (goal programming), and PSI (parameter space investigation) methods within a chemical process simulator. We can find the ideal compromise solution set based on the Pareto curve. The multiobjective problem is then interpreted by sensitivity and elasticity analyses of the Pareto curve that give the decision basis between the conflicting objectives.

Robust automatic steering control for look-down reference systems with front and rear sensors

This paper describes a robust control design for automatic steering of passenger cars. Previous studies showed that reliable automatic driving at highway speed may not be achieved under practical conditions with look-down reference systems which use only one sensor at the front bumper to measure the lateral displacement of the vehicle from the lane reference. An additional lateral displacement sensor is added here at the tail bumper to solve the automatic steering control problem. The control design is performed stepwise: an initial controller is determined using the parameter space approach in an invariance plane; and this controller is then refined to accommodate practical constraints and finally optimized using the multiobjective optimization program. The performance and robustness of the final controller was verified experimentally at California PATH in a series of test runs.

Optimality Conditions for Multiobjective Programming with Generalized ([formula omitted], ρ, θ)-Convex Set Functions

Necessary conditions for Pareto optimality in multiobjective programming with subdifferentiable set functions are established in Theorem 12 of H. C. Lai and L. J. Lin (J. Math. Anal. Appl.132,1988, 558–571). In this paper, we establish some sufficient conditions under which a feasible solution of such a problem will be Pareto optimal provided that a weaker convexity requirement is satisfied; for instance (I,ρ,θ)-convexity is assumed for both objective and constraint set functions. Some duality models are also discussed. Wolfe-type and Mond–Weir-type duality theorems are proved.

Optimality and duality for multiobjective programming involving subdifferentiable set functions

Necessary conditions for optimality in multiobjective programming involving subdifferentiable set functions are shown to be suficient under the assumption of a particular form of ρ-convexity or ρ-pseudoconvexity. Duality results are thus extended for a Wolfe-type or a Mond-Weir type dual.