Generation and optimisation of real-world static and dynamic location-allocation problems with application to the telecommunications industry.

The location-allocation (LA) problem concerns the location of facilities and the allocation of demand, to minimise or maximise a particular function such as cost, profit or a measure of distance. Many formulations of LA problems have been presented in the literature to capture and study the unique aspects of real-world problems. However, some real-world aspects, such as resilience, are still lacking in the literature. Resilience ensures uninterrupted supply of demand and enhances the quality of service. Due to changes in population shift, market size, and the economic and labour markets - which often cause demand to be stochastic - a reasonable LA problem formulation should consider some aspect of future uncertainties. Almost all LA problem formulations in the literature that capture some aspect of future uncertainties fall in the domain of dynamic optimisation problems, where new facilities are located every time the environment changes. However, considering the substantial cost associated with locating a new facility, it becomes infeasible to locate facilities each time the environment changes. In this study, we propose and investigate variations of LA problem formulations. Firstly, we develop and study new LA formulations, which extend the location of facilities and the allocation of demand to add a layer of resilience. We apply the population-based incremental learning algorithm for the first time in the literature to solve the new novel LA formulations. Secondly, we propose and study a new dynamic formulation of the LA problem where facilities are opened once at the start of a defined period and are expected to be satisfactory in servicing customers' demands irrespective of changes in customer distribution. The problem is based on the idea that customers will change locations over a defined period and that these changes have to be taken into account when establishing facilities to service changing customers' distributions. Thirdly, we employ a simulation-based optimisation approach to tackle the new dynamic formulation. Owing to the high computational costs associated with simulation-based optimisation, we investigate the concept of Racing, an approach used in model selection, to reduce the high computational cost by employing the minimum number of simulations for solution selection

Performance analysis of GA and PBIL variants for real-world location-allocation problems.

The Uncapacitated Location-Allocation problem (ULAP) is a major optimisation problem concerning the determination of the optimal location of facilities and the allocation of demand to them. In this paper, we present two novel problem variants of Non-Linear ULAP motivated by a real-world problem from the telecommunication industry: Uncapacitated Location-Allocation Resilience problem (ULARP) and Uncapacitated Location-Allocation Resilience problem with Restrictions (ULARPR). Problem sizes ranging from 16 to 100 facilities by 50 to 10000 demand points are considered. To solve the problems, we explore the components and configurations of four Genetic Algorithms [1], [2], [3] and [4] selected from the ULAP literature. We aim to understand the contribution each choice makes to the GA performance and so hope to design an Optimal GA configuration for the novel problems.We also conduct comparative experiments with Population-Based Incremental Learning (PBIL) Algorithm on ULAP. We show the effectiveness of PBIL and GA with parameter set: random and heuristic initialisation, tournament and fined grained tournament selection, uniform crossover and bitflip mutation in solving the proposed problems

Racing strategy for the dynamic-customer location-allocation problem.

In previous work, we proposed and studied a new dynamic formulation of the Location-allocation (LA) problem called the Dynamic-Customer Location-allocation (DC-LA) prob­lem. DC-LA is based on the idea of changes in customer distribution over a defined period, and these changes have to be taken into account when establishing facilities to service changing customers distributions. This necessitated a dynamic stochastic evaluation function which came with a high computational cost due to a large number of simulations required in the evaluation process. In this paper, we investigate the use of racing, an approach used in model selection, to reduce the high computational cost by employing the minimum number of simulations for solution selection. Our adaptation of racing uses the Friedman test to compare solutions statistically. Racing allows simulations to be performed iteratively, ensuring that the minimum number of simulations is performed to detect a statistical difference. We present experiments using Population-Based Incremental Learning (PBIL) to explore the savings achievable from using racing in this way. Our results show that racing achieves improved cost savings over the dynamic stochastic evaluation function. We also observed that on average, the computational cost of racing was about 4.5 times lower than the computational cost of the full dynamic stochastic evaluation

Introducing the dynamic customer location-allocation problem.

In this paper, we introduce a new stochastic Location-Allocation Problem which assumes the movement of customers over time. We call this new problem Dynamic Customer Location-Allocation Problem (DC-LAP). The problem is based on the idea that customers will change locations over a defined horizon and these changes have to be taken into account when establishing facilities to service customers demands. We generate 1440 problem instances by varying the problem parameters of movement rate which determines the possible number of times a customer will change locations over the defined period, the number of facilities and the number of customers. We propose to analyse the characteristics of the instances generated by testing a search algorithm using the stochastic dynamic evaluation (based on the replication of customer movement scenarios) and a deterministic static evaluation (based on the assumption that customer will not move over time). We show that the dynamic approach obtains globally better results, but the performances are highly related to the parameters of the problem. Moreover, the dynamic approach involves a significantly high computational overhead