This article presents an overview of recent work on ant algorithms, that is, algorithms for discrete optimization that took inspiration from the observation of ant colonies' foraging behavior, and introduces the ant colony optimization (ACO) metaheuristic. In the first part of the article the basic biological findings on real ants are reviewed and their artificial counterparts as well as the AC...

The primary benefit of fuzzy systems theory is to approximate system behavior where analytic functions or numerical relations do not exist. In this paper, heuristic fuzzy rules were used with the intention of improving the performance of optimization models, introducing experiential rules acquired from experts and utilizing recommendations. The aim of this paper was to define soft constraints u...

We show ways in which differential evolution, a member of the genetic/evolutionary family of global optimization methods, can be used for the purpose of discrete optimization. We consider several nontrivial problems arising from actual practice, using differential evolution as our primary tool to obtain good results. We indicate why methods more commonly seen in discrete optimization, such as i...

The new voting system of the Council of the European Union cannot be represented as the intersection of six or fewer weighted games, i.e., its dimension is at least 7. This sets a new record for real-world voting bodies. A heuristic combination of different discrete optimization methods yields a representation as the intersection of 13 368 weighted games. Determination of the exact dimension is...

‎In this paper‎, ‎first we study the weak and strong convergence of solutions to the‎ ‎following first order nonhomogeneous gradient system‎ ‎$$begin{cases}-x'(t)=nablaphi(x(t))+f(t), text{a.e. on} (0,infty)\‎‎x(0)=x_0in Hend{cases}$$ to a critical point of $phi$‎, ‎where‎ ‎$phi$ is a $C^1$ quasi-convex function on a real Hilbert space‎ ‎$H$ with ${rm Argmin}phineqvarnothing$ and $fin L^1(0...

1. Abstract In structural sizing optimization problems the aim is to minimize an objective function under certain constraints. The design variables of the optimization problem are generally discrete and belong to certain discrete sets. In the context of the present work the design set is implemented and efficiently treated as a database that contains the required geometric properties for all de...

We consider methods for aggregating preferences that are based on the resolution of discrete optimization problems. The preferences are represented by arbitrary binary relations (possibly weighted) or incomplete paired comparison matrices. This incomplete case remains practically unexplored so far. We examine the properties of several known methods and propose one new method. In particular, we ...

Combinatorial optimization problems arise in situations where discrete choices must be made and solving them amounts to finding an optimal solution among a finite or countably infinite number of alternatives. Optimality relates to some cost criterion, which provides a quantitative measure of the quality of each solution. This area of discrete mathematics is of great practical use and has attrac...

It is a common feature of many real-life design optimization problems that some design components can only be selected from a finite set of choices. Each choice corresponds to a possibly multidimensional design point representing the specifications of the chosen design component. In this paper we present a method to explore the resulting discrete search space for design optimization. We use the...

We propose a general branch-and-bound algorithm for discrete optimization in which binary decision diagrams (BDDs) play the role of the traditional linear programming relaxation. In particular, relaxed BDD representations of the problem provide bounds and guidance for branching, while restricted BDDs supply a primal heuristic. Each problem is given a dynamic programming model that allows one to...