Optimizing Chance-Constrained Submodular Problems with Variable Uncertainties

Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems, which capture a wide range of optimization problems with stochastic constraints. Previous studies considered submodular problems with stochastic knapsack constraints in the case where uncertainties are the same for each item that can be selected. However, uncertainty levels are usually variable with respect to the different stochastic components in real-world scenarios, and rigorous analysis for this setting is missing in the context of submodular optimization. This paper provides the first such analysis for this case, where the weights of items have the same expectation but different dispersion. We present greedy algorithms that can obtain a high-quality solution, i.e., a constant approximation ratio to the given optimal solution from the deterministic setting. In the experiments, we demonstrate that the algorithms perform effectively on several chance-constrained instances of the maximum coverage problem and the influence maximization problem

Analysis of the (1+1) EA on LeadingOnes with Constraints

Understanding how evolutionary algorithms perform on constrained problems has gained increasing attention in recent years. In this paper, we study how evolutionary algorithms optimize constrained versions of the classical LeadingOnes problem. We first provide a run time analysis for the classical (1+1) EA on the LeadingOnes problem with a deterministic cardinality constraint, giving $\Theta(n (n-B)\log(B) + n^2)$ as the tight bound. Our results show that the behaviour of the algorithm is highly dependent on the constraint bound of the uniform constraint. Afterwards, we consider the problem in the context of stochastic constraints and provide insights using experimental studies on how the ($\mu$+1) EA is able to deal with these constraints in a sampling-based setting

3-Objective Pareto Optimization for Problems with Chance Constraints

Evolutionary multi-objective algorithms have successfully been used in the context of Pareto optimization where a given constraint is relaxed into an additional objective. In this paper, we explore the use of 3-objective formulations for problems with chance constraints. Our formulation trades off the expected cost and variance of the stochastic component as well as the given deterministic constraint. We point out benefits that this 3-objective formulation has compared to a bi-objective one recently investigated for chance constraints with Normally distributed stochastic components. Our analysis shows that the 3-objective formulation allows to compute all required trade-offs using 1-bit flips only, when dealing with a deterministic cardinality constraint. Furthermore, we carry out experimental investigations for the chance constrained dominating set problem and show the benefit for this classical NP-hard problem

On the Impact of Operators and Populations within Evolutionary Algorithms for the Dynamic Weighted Traveling Salesperson Problem

Evolutionary algorithms have been shown to obtain good solutions for complex optimization problems in static and dynamic environments. It is important to understand the behaviour of evolutionary algorithms for complex optimization problems that also involve dynamic and/or stochastic components in a systematic way in order to further increase their applicability to real-world problems. We investigate the node weighted traveling salesperson problem (W-TSP), which provides an abstraction of a wide range of weighted TSP problems, in dynamic settings. In the dynamic setting of the problem, items that have to be collected as part of a TSP tour change over time. We first present a dynamic setup for the dynamic W-TSP parameterized by different types of changes that are applied to the set of items to be collected when traversing the tour. Our first experimental investigations study the impact of such changes on resulting optimized tours in order to provide structural insights of optimization solutions. Afterwards, we investigate simple mutation-based evolutionary algorithms and study the impact of the mutation operators and the use of populations with dealing with the dynamic changes to the node weights of the problem

An adaptive evolutionary multi-objective approach based on simulated annealing

A multi-objective optimization problem can be solved by decomposing it into one or more single objective subproblems in some multi-objective metaheuristic algorithms. Each subproblem corresponds to one weighted aggregation function. For example, MOEA/D is an evolutionary multi-objective optimization (EMO) algorithm that attempts to optimize multiple subproblems simultaneously by evolving a population of solutions. However, the performance of MOEA/D highly depends on the initial setting and diversity of the weight vectors. In this paper, we present an improved version of MOEA/D, called EMOSA, which incorporates an advanced local search technique (simulated annealing) and adapts the search directions (weight vectors) corresponding to various subproblems. In EMOSA, the weight vector of each subproblem is adaptively modified at the lowest temperature in order to diversify the search towards the unexplored parts of the Pareto-optimal front. Our computational results show that EMOSA outperforms six other well-established multi-objective metaheuristic algorithms on both the (constrained)multi-objective knapsack problemand the (unconstrained) multi-objective traveling salesman problem. Moreover, the effects of the main algorithmic components and parameter sensitivities on the search performance of EMOSA are experimentally investigated