Duc-Cuong Dang

An effective PSO-inspired algorithm for the team orienteering problem

The Team Orienteering Problem (TOP) is a particular vehicle routing problem in which the aim is to maximize the profit gained from visiting customers without exceeding a travel cost/time limit. This paper proposes a new and fast evaluation process for TOP based on an interval graph model and a Particle Swarm Optimization inspired Algorithm (PSOiA) to solve the problem. Experiments conducted on the standard benchmark of TOP clearly show that our algorithm outperforms the existing solving methods. PSOiA reached a relative error of 0.0005% whereas the best known relative error in the literature is 0.0394%. Our algorithm detects all but one of the best known solutions. Moreover, a strict improvement was found for one instance of the benchmark and a new set of larger instances was introduced.

A Branch-and-Cut Algorithm for Solving the Team Orienteering Problem

This paper describes a branch-and-cut algorithm to solve the Team Orienteering Problem (TOP). TOP is a variant of the Vehicle Routing Problem (VRP) in which the aim is to maximize the total amount of collected profits from visiting customers while not exceeding the predefined travel time limit of each vehicle. In contrast to the exact solving methods in the literature, our algorithm is based on a linear formulation with a polynomial number of binary variables. The algorithm features a new set of useful dominance properties and valid inequalities. The set includes symmetric breaking inequalities, boundaries on profits, generalized subtour eliminations and clique cuts from graphs of incompatibilities. Experiments conducted on the standard benchmark for TOP clearly show that our branch-and-cut is competitive with the other methods in the literature and allows us to close 29 open instances.

Heuristic solutions for the vehicle routing problem with time windows and synchronized visits

We present a simulated annealing based algorithm for a variant of the vehicle routing problem (VRP), in which a time window is associated with each client service and some services require simultaneous visits from different vehicles to be accomplished. The problem is called the VRP with time windows and synchronized visits. The algorithm features a set of local improvement methods to deal with various objectives of the problem. Experiments conducted on the benchmark instances from the literature clearly show that our method is fast and outperforms the existing approaches. It produces all known optimal solutions of the benchmark in very short computational times, and improves the best results for the rest of the instances.

Simplified Runtime Analysis of Estimation of Distribution Algorithms

Estimation of distribution algorithms (EDA) are stochastic search methods that look for optimal solutions by learning and sampling from probabilistic models. Despite their popularity, there are only few rigorous theoretical analyses of their performance. Even for the simplest EDAs, such as the Univariate Marginal Distribution Algorithm (UMDA) which assumes independence between decision variables, there are only a handful of results about its runtime, and results for simple functions such as Onemax are still missing. In this paper, we show that the recently developed level-based theorem for non-elitist populations is directly applicable to runtime analysis of EDAs. To demonstrate this approach, we derive easily upper bounds on the expected runtime of the UMDA.

Efficient Optimisation of Noisy Fitness Functions with Population-based Evolutionary Algorithms

Population-based EAs can optimise pseudo-Boolean functions in expected polynomial time, even when only partial information about the problem is available [7]. In this paper, we show that the approach used to analyse optimisation with partial information extends naturally to optimisation under noise. We consider pseudo-Boolean problems with an additive noise term. Very general conditions on the noise term is derived, under which the EA optimises the noisy function in expected polynomial time. In the case of the Onemax and Leadingones problems, efficient optimisation is even possible when the variance of the noise distribution grows quickly with the problem size.

A Simulated Annealing Algorithm for the Vehicle Routing Problem with Time Windows and Synchronization Constraints

This paper focuses on solving a variant of the vehicle routing problem VRP in which a time window is associated with each customer service and some services require simultaneous visits from different vehicles to be accomplished. The problem is therefore called the VRP with time windows and synchronization constraints VRPTWSyn. We present a simulated annealing algorithm SA that incorporates several local search techniques to deal with this problem. Experiments on the instances from the literature show that our SA is fast and outperforms the existing approaches. To the best of our knowledge, this is the first time that dedicated local search methods have been proposed and evaluated on this variant of VRP.

Runtime Analysis of Non-elitist Populations: From Classical Optimisation to Partial Information

Although widely applied in optimisation, relatively little has been proven rigorously about the role and behaviour of populations in randomised search processes. This paper presents a new method to prove upper bounds on the expected optimisation time of population-based randomised search heuristics that use non-elitist selection mechanisms and unary variation operators. Our results follow from a detailed drift analysis of the population dynamics in these heuristics. This analysis shows that the optimisation time depends on the relationship between the strength of the selective pressure and the degree of variation introduced by the variation operator. Given limited variation, a surprisingly weak selective pressure suffices to optimise many functions in expected polynomial time. We derive upper bounds on the expected optimisation time of non-elitist evolutionary algorithms (EA) using various selection mechanisms, including fitness proportionate selection. We show that EAs using fitness proportionate selection can optimise standard benchmark functions in expected polynomial time given a sufficiently low mutation rate. As a second contribution, we consider an optimisation scenario with partial information, where fitness values of solutions are only partially available. We prove that non-elitist EAs under a set of specific conditions can optimise benchmark functions in expected polynomial time, even when vanishingly little information about the fitness values of individual solutions or populations is available. To our knowledge, this is the first runtime analysis of randomised search heuristics under partial information.

Escaping Local Optima with Diversity Mechanisms and Crossover

Population diversity is essential for the effective use of any crossover operator. We compare seven commonly used diversity mechanisms and prove rigorous run time bounds for the (μ+1) GA using uniform crossover on the fitness function Jumpk. All previous results in this context only hold for unrealistically low crossover probability pc=O(k/n), while we give analyses for the setting of constant pc < 1 in all but one case. Our bounds show a dependence on the problem size~

Refined upper bounds on the expected runtime of non-elitist populations from fitness-levels

n

Self-adaptation of Mutation Rates in Non-elitist Populations

, the jump length k, the population size μ, and the crossover probability pc. For the typical case of constant k > 2 and constant pc, we can compare the resulting expected optimisation times for different diversity mechanisms assuming an optimal choice of μ: O}(nk-1) for duplicate elimination/minimisation, O}(n2 log n) for maximising the convex hull, O(n log n) for det. crowding (assuming pc = k/n), O(n log n) for maximising the Hamming distance, O(n log n) for fitness sharing, O(n log n) for the single-receiver island model. This proves a sizeable advantage of all variants of the (μ+1) GA compared to the (1+1) EA, which requires θ(nk). In a short empirical study we confirm that the asymptotic differences can also be observed experimentally.