In many engineering problems, we face multi-objective optimization, with several objective functions f1, . . . , fn. We want to provide the user with the Pareto set – set of all possible solutions x which cannot be improved in all categories (i.e., for which fj(x′) ≥ fj(x) for all j and fj(x′) > fj(x) for some j is impossible). The user should be able to select an appropriate trade-off between,...

We investigate the problem of approximating the Pareto set of biobjective optimization problems with a given number of solutions. This task is relevant for two reasons: (i) Pareto sets are often computationally hard so approximation is a necessary tradeoff to allow polynomial time algorithms; (ii) limiting explicitly the size of the approximation allows the decision maker to control the expecte...

Different implementation possibilities of an algorithm into hardware offer a variety of design solutions. Only best solutions so called pareto optimal solutions are for design decision of interest. Heuristic methods are preferred for the generation of these pareto optimal solutions, because exhaustive search methods cannot efficiently cope with this problem. This paper describes the mapping of ...

This article reports an experimental analysis on stochastic local search for approximating the Pareto set of bi-objective unconstrained binary quadratic programming problems. First, we investigate two scalarizing strategies that iteratively identify a high-quality solution for a sequence of sub-problems. Each sub-problem is based on a static or adaptive definition of weighted-sum aggregation co...

where x is an n-dimensional vector of variables, A is an m × n matrix, b is the RHS vector and the vectors ci (i = 1, ...,m) represent the coefficients of the objective functions (criteria). Let’s denote yi = fi(x), i = 1, ...,m, and let y = (y1, ..., ym) be a vector in the criteria space. The set Y ⊂ Rm composed by all possible criterion vectors y = f(x) when x ∈ X, is known as Feasible Criter...

Many studies are performed by researchers about Shell and Tube Heat Exchanger but the Multi-Objective Big Bang-Big Crunch algorithm (MOBBA) technique has never been used in such studies. This paper presents application of Thermal-Economic Multi-Objective Optimization of Shell and Tube Heat Exchanger Using MOBBA. For optimal design of a shell and tube heat exchanger, it was first thermally model...

There are currently three different game strategies to solve multi-criteria design problems: 1) Cooperative Games (Pareto Front), 2) Competitive Games (Nash Game) and 3) Hierarchical Games (Stackelberg Game). Nowadays EAs and Pareto front concept are more and more in solving practical design problems in industry, but this process is time consuming. Here, deterministic optimization method and Pa...

We propose a general-purpose algorithm APS (Adaptive Pareto-Sampling) for determining the set of Pareto-optimal solutions of bicriteria combinatorial optimization (CO) problems under uncertainty, where the objective functions are expectations of random variables depending on a decision from a finite feasible set. APS is iterative and population-based and combines random sampling with the soluti...

Multiobjective (or multicriteria) optimization is a research area with rich history and under heavy investigation within Operations Research and Economics in the last 60 years [1,2]. Its object of study is to investigate solutions to combinatorial optimization problems that are evaluated under several objective functions – typically defined on multidimensional attribute (cost) vectors. In multi...

This paper presents a new multiobjective evolutionary algorithm for Environmental/Economic power Dispatch (EED) problem. The EED problem is formulated as a nonlinear constrained multiobjective optimization problem. A new Strength Pareto Evolutionary Algorithm (SPEA) based approach is proposed to handle the problem as a true multiobjective problem with competing and non-commensurable objectives....