In this paper we investigate multiplicative noise models in the context of continuous optimization. We illustrate how some intrinsic properties of the noise model imply the failure of reasonable search algorithms for locating the optimum of the noiseless part of the objective function. Those findings are rigorously investigated on the (1 + 1)-ES for the minimization of the noisy sphere function...

In metaheuristic optimization, understanding the relationship between problems and algorithms is important but non-trivial. There has been a growing interest in the literature on techniques for analysing problems, however previous work has mainly been developed for discrete problems. In this paper, we develop a novel framework for characterising continuous optimization problems based on the con...

Discrete convex analysis [18, 40, 43, 47] aims to establish a general theoretical framework for solvable discrete optimization problems by means of a combination of the ideas in continuous optimization and combinatorial optimization. The framework of convex analysis is adapted to discrete settings and the mathematical results in matroid/submodular function theory are generalized. Viewed from th...

This paper presents an hybrid algorithm based on genetic algorithm and ant colony optimization for continuous optimization, which combines the global exploration ability of the former with the local exploiting ability of the later. The proposed algorithm is evaluated on several benchmark functions. The simulation results show that the proposed algorithm performs quite well and outperforms class...

Several general benchmark generators (BGs) are available for the dynamic continuous optimization domain, in which generators use functions with adjustable parameters to simulate shifting landscapes. In the combinatorial domain the work is still on early stages. Many attempts of dynamic BGs are limited to the range of algorithms and combinatorial optimization problems (COPs) they are compatible ...

The pupose of this paper is modeling of Partial Digest Problem (PDP) as a mathematical programming problem. In this paper we present a new viewpoint of PDP. We formulate the PDP as a continuous optimization problem and develope a method to solve this problem. Finally we constract a linear programming model for the problem with an additional constraint. This later model can be solved by the simp...

Modern optimization has in its disposal an immense variety of heuristic algorithms which can effectively deal with both continuous and combinatorial optimization problems. Recent years brought in this area fast development of unconventional methods inspired by phenomena found in nature. Flower Pollination Algorithm based on pollination mechanisms of flowering plants constitutes an example of su...

Search-based methods like Branch and Bound and Branch and Cut are essential tools in solving diicult problems to optimality in the eld of combinatorial optimization, and much experience has been gathered regarding the design and implementation of parallel methods in this eld. Search-based methods appear, however, also in connection with certain continuous optimization problems and problems in A...

We consider stochastic discrete optimization problems where the decision variables are non-negative integers. We propose and analyze an on-line control scheme which transforms the problem into a “surrogate” continuous optimization problem and proceeds to solve the latter using standard gradient-based approaches while simultaneously updating both actual and surrogate system states. Convergence o...

In this paper we present an extension of ant colony optimization (ACO) to continuous domains. We show how ACO, which was initially developed to be a metaheuristic for combinatorial optimization, can be adapted to continuous optimization without any major conceptual change to its structure. We present the general idea, implementation, and results obtained. We compare the results with those repor...