Showing papers on "Multi-objective optimization published in 1987"

Optimization of Chemical Processes

Abstract: I Problem Formulation 1 The Nature and Organization of Optimization Problems 2 Developing Models for Optimization 3 Formulation of the Objective Function II Optimization Theory and Methods 4 Basic Concepts of Optimization 5 Optimization for Unconstrained Functions: One- Dimensional Search 6 Unconstrained Multivariable Optimization 7 Linear Programming and Applications 8 Nonlinear Programming with Constraints 9 Mixed-Integer Programming 10 Global Optimization for Problems Containing Continuous and Discrete Variables IIIApplications of Optimization 11 Heat Transfer and Energy Conservation 12 Separation Processes 13 Fluid Flow Systems 14 Chemical Reactor Design and Operation 15 Optimization in Large-Scale Plant Design and Operations 16 Integrated Planning, Scheduling, and Control in the Process Industries Appendixes

On the mathematical foundations of nondifferentiable optimization in engineering design

Abstract: It is shown by example that a large class of engineering design problems can be transcribed into the form of a canonical optimization problem with inequality constraints involving mar functions. Such problems are commonly referred to as semi-infinite optimization problems. The bulk of this paper is devoted to the development of a mathematical theory for the construction of first order nondifferentiable optimization algorithms, related to phase I - phase II methods of feasible directions, which solve these semi-infinite optimization problems. The applicability of the theory is illustrated with examples that are relevant to engineering design.

The envelope approach for multiobjeetive optimization problems

Abstract: A multiobjective optimization problem is usually solved by finding the set of all noninferior solutions to the problem. A methodology termed the envelope approach is presented for generating the set of noninferior solutions. The relationship between the envelope approach and multiobjective optimization is explored. Investigation of the use of the envelope approach in multiobjective dynamic programming and in the parametric decomposition method shows that this approach is very suitable for solving certain classes of multiobjective optimization problems by decomposition and coordination.

Concurrent function evaluations in local and global optimization

Abstract: This paper discusses some basic opportunities for the use of multiprocessing in the solution of optimization problems. We consider two fundamental optimization problems, unconstrained optimization and global optimization, in the important case when function evaluation is expensive and gradients are evaluated by finite differences. First we discuss some simple parallel strategies based upon the use of concurrent function evaluations to evaluate the finite difference gradient. These include the speculative evaluation of the gradient concurrently with the evaluation of the function before it is known whether the gradient value at this point will be required. We present examples that indicate the effectiveness of these parallel strategies for unconstrained optimization. We also give experimental results that show the effect of using these strategies to parallelize each of the multiple local minimizations within a recently proposed concurrent global optimization algorithm. We briefly discuss several parallel optimization strategies that are related to these approaches but make more fundamental changes to standard sequential optimization algorithms.

A convergent interactive cutting-plane algorithm for multiobjective optimization

Abstract: This paper presents an interactive cutting-plane algorithm for determining a best-compromise solution to a multiobjective optimization problem in situations with an implicitly defined utility function. We derive cutting planes that are based on suitable pairwise trade-offs between the objective functions, as prescribed by the decision maker at each iterate generated by the algorithm. The proposed algorithm requires no line searches, and generates iterates that are all contained in the efficient frontier. This feature facilitates the preference judgment of the decision maker, and permits an analyst to terminate short of optimality with an efficient near-optimal solution. A convergence analysis establishes that any accumulation point generated by the algorithm is a best-compromise solution. We also conduct an error analysis to point out the effect of inconsistencies in trade-off information provided by the decision maker. The algorithm may be extended to situations involving nonconvex feasible regions, as well as nonconcave for a max problem objective functions. We offer remarks for such cases, and describe an application to an urban runoff control-design problem.

Combinatorial Optimization Problems with Soft and Hard Requirements

Abstract: In this paper, the authors describe a heuristic principle for the solution of an important class of problems. Using real-world examples, it is then shown how some difficult combinatorial problems are modelled and solved by the suggested principle. In one case, a detailed discussion of the implementation of the solution is also provided.

Interactive solution to multiobjective optimization problems

Abstract: Sensitivity analysis is presented as a natural addition to interactive multiobjective optimization methods based on compromise programming. It is shown that useful information regarding trade-offs in the objectives can be generated effectively by means of an analysis of the sensitivity of solutions to variations in preference structures. An implementation based on sequential quadrative programming is provided and examples are given for illustration.

Acquiring expert knowledge from characterized designs

Abstract: The expertise of designers consists, primarily, of information about the relationship between goals or performance criteria and the attributes of the desired artifact that will result in performances that will satisfy these criteria. The designer like experts in other fields is typically better at applying the knowledge that constitutes his expertise than he is at articulating this knowledge. Generation and simulation models are discussed as a means of generating a set of designs for which the set of attributes defining these designs and the performance of these designs in terms of the criteria considered are explicitly defined. Pareto optimization is discussed as a means of structuring these designs on the basis of their performance. The induction algorithm ID3 is used as a means of inferring general statements about the nature of solutions which exhibit Pareto optimal performance in terms of a set of performance criteria. The rules inferred in building design domain are compared with those extracted using a heuristic based learning system.

Parametric approximation problems arising in vector optimization

Abstract: In this paper, a known scalarization result of vector optimization theory is reviewed and stated in a different form and a new short proof is presented. Moreover, it is shown how to apply this result to multi-objective optimization problems and to special problems in statistics and optimal control theory.

A knowledge-based approach to mathematical design modeling and optimization

Abstract: Optimization is a well understood process in design domains. Designers formulate their design problems as single criterion or multicriteria optimization problems and then select an appropriate optimization algorithm to search for the optimal values for the design variables. The formulation and algorithm selection procedures have been considered to be activities which relied on substantive human knowledge. This paper describes a computer system, OPTIMA, which formulates design optimization problems from a pseudo-English description into canonical algebraic expressions. It then recognizes the formulation and selects appropriate algorithm(s) for its solution. Finally, it runs the selected algorithm(s) and sends the results back to the original descriptions. Areas of expert knowledge involved in carrying out the above tasks are identified. Such knowledge is explicitly encoded in the system. The basic philosophy and key features of the system are described and are illustrated with examples.

About duality and alternative in multiobjective optimization

Abstract: McLinden's result on the equivalence between a theorem of the alternative and a duality theorem for constrained optimization problems is extended to the multiobjective case. We then discuss some existing results on that topic and present an alternative approach to duality relations in conditionally complete lattices.

Survey of input optimization 1

Abstract: Input optimization is a conceptually new level of optimization, at which the mathematical programming model, rather than a usual program, is optimized. This is achieved by optimizing the optimal value function by stable perturbations of the parameters (input). This paper is a survey of the basic ideas in finite-dimensional input optimization for both single- and multi-objective linear and convex models. The theory is general enough not to require extraneous assumptions, such as linear independence of the gradients or Slater's Condition. On the other hand, it is of a constructive nature that takes it possible to formulate numerical methods for computing an “optimal input”and the corresponding “optimal realization” of the mathematical model. Many results from the “usual” mathematical programming and sensitivity analysis follow as special cases. The paper contains many illustrative examples and lists a wide range of (potential) applications of input optimization from long-range planning for an economic syste...

Priority-Based Interactive Multicriteria Optimization Algorithm

Abstract: The algorithm presented in this paper describes an interactive approach for generating search directions in multiobjective linear programming problems (MOLP). The approach is based on using the AHP to assign priorities to vertices adjacent to those that are in the basis, as generated by the simplex method. Using these priorities, an approximate gradient is found that is used to weigh the objective functions during the next iteration. The novel feature of the algorithm is that the decision-maker (DM) is not required to provide interactive inputs to implicit preference questions concerning his objectives, but instead consider explicit evaluation of adjacent possible improvements and generates his next step in this most preferred direction.

A Flexible Model for Multi-Objective Optimization

Abstract: Decision problems often involve a multitude of objectives (or decision criteria) which are incommensurable and possibly conflicting with one another. At times, a decision-maker may not be able to express an explicit preference ordering for the various objectives. In fact, he may find it difficult to state the objectives, or to distinguish between objectives and constraints. For example, in designing a new car model, the resistance to impact may be viewed as an objective to be maximized, or as a constraint fixed by law.

Multicriteria Optimization Procedures in Application on Structural Mechanics Systems

Abstract: This paper reports on investigations carried out in the field of vector optimization and its practical application on a structural mechanics system. The main reason is that in addition to the minimization of costs for developing and manufacturing machines and plants, some other objectives such as shape accuracy, reliability and others are playing an important role as well. These problems can be formulated as “Optimization Problems with Multiple Objectives” (Vector-Optimization, PARETO-Optimization). Most of the objectives are non-linear and besides that competing. Thus, they do not lead to one or several solutions for the optimum but rather to a “functional-efficient” solution set, i.e. the decision maker is able to select out of this set the most efficient compromise solution. Moreover, the vector optimization problem is transformed into a scalar substitute problem by means of a preference function. This so-called optimization strategy is an important part of the modelling. For carrying out the transformation, several preference functions, e.g. objective weighting, distance functions, constraint oriented transformation (Trade-off Method), and Min-Max-Formulation have been analysed and tested. The investigations showed that the efficiency of the single preference function is problem-dependent and furthermore dependent on the adapting on special optimization algorithms (Methods of Mathematical Programming). Within the scope of this contribution the application of multicriteria optimization techniques in structural mechanics systems is shown, e.g. the shape optimization of a special shell structure (conveyer belt drum).

Sensitivity information in multiobjective optimization

Abstract: The analysis of sensitivity of efficient solutions to changes in the preference structure of the designer is presented as a way to improve the efficiency of interactive multiobjective optimization problems. Sensitivity analysis is used to predict new efficient solutions and to generate information that can guide the designer in the search for more satisfactory designs in the efficient set. This information is generated without additional function or gradient evaluations, making the method particularly suited to problems involving a lengthy analysis. The procedure can be implemented effectively when the optimization is performed by sequential quadratic programming algorithms. Examples of this implementation are provided for illustration.

An Interactive Modification of the Decision Set to Attain a Target Point in Vector Optimization Problems

Abstract: We propose a systematic way to achieve the target set in multicriteria optimization problems by relaxing the constraints in the primary problem formulation. We assume that a change of constraints from a preliminarily disposed set U0 to a new one V bears the cost v(U0,V). The values of the cost function v and of the distance from the target set Q serve as auxiliary objectives which are taken into account by the decision-maker during a decision making procedure. We give a theoretical background for the analysis of this kind of problems in the case where the admissible decision subsets are convex sets defined by m-parameter inequality constraints, the criteria are monotonic functions and the target set is convex. An interactive procedure involving a visualisation of the attainable and target sets is outlined in the final part of the paper.

A Coupled Algorithmic-Heuristic Approach for Design Optimization

Abstract: An optimization strategy is presented that provides a frame-work in which optimization algorithms and heuristic procedures can be coupled to solve nonlinearly constrained design optimization problems These problems cannot be efficiently solved by either approach independently The approach is based on an optimization algorithm dealing with local monotonicity and sequential quadratic programming techniques with heuristic procedures which are statistically derived from observations obtained by applying the optimization algorithm to different classes of test problems

An Application of Fuzzy Linear and Nonlinear Programming to Structural Optimization

Abstract: General structural optimization in civil engineering has been done that only one objective function is to be maximized or minimized under constraints of crisp condition(1)But many civil engineering structures have high public utilities or serviceabilities like highway or railway bridges,tunnel, airport, marine structure,etcThen they are required multi level objectives,generallyFurthermore these objectives may have competitive or conflicting needs,utilities or serviceabilities,among themselves Therefore,to satisfy the needs, the planning or design of types,locations or sizes of these structures should be required the multi objective decision making sense,essentially(2),In this sense,the multi objective optimization approach may be useful for the decision making of the problem

Multicriteria dynamic linear optimization methods applied in HYBRID package

Abstract: Many optimization problems in economic planning over time, production scheduling, inventory, transportation, control dynamic systems, can be formulated as dynamic linear programming problems. In actual application it is often necessary to use multicriteria optimization for a choice of a solution. In the presented paper methods that can be used to handle such problems are described as well as the HYBRID package, which is an application of the presented methods.

Multicriteria Optimization Problems in Statistics

Abstract: Many statistical procedures can be viewed as solutions of optimization problems. A careful and detailed analysis of these procedures reveals that many of these problems are essentially multiobjective optimization problems. Further, most of the standard statistical procedures aim at finding an efficient (nondominated) solution.