An Evolutionary Strategy based on Partial Imitation for Solving Optimization Problems

In this work we introduce an evolutionary strategy to solve combinatorial optimization tasks, i.e. problems characterized by a discrete search space. In particular, we focus on the Traveling Salesman Problem (TSP), i.e. a famous problem whose search space grows exponentially, increasing the number of cities, up to becoming NP-hard. The solutions of the TSP can be codified by arrays of cities, and can be evaluated by fitness, computed according to a cost function (e.g. the length of a path). Our method is based on the evolution of an agent population by means of an imitative mechanism, we define `partial imitation'. In particular, agents receive a random solution and then, interacting among themselves, may imitate the solutions of agents with a higher fitness. Since the imitation mechanism is only partial, agents copy only one entry (randomly chosen) of another array (i.e. solution). In doing so, the population converges towards a shared solution, behaving like a spin system undergoing a cooling process, i.e. driven towards an ordered phase. We highlight that the adopted `partial imitation' mechanism allows the population to generate solutions over time, before reaching the final equilibrium. Results of numerical simulations show that our method is able to find, in a finite time, both optimal and suboptimal solutions, depending on the size of the considered search space.Comment: 18 pages, 6 figure

Deriving the Normalized Min-Sum Algorithm from Cooperative Optimization

The normalized min-sum algorithm can achieve near-optimal performance at decoding LDPC codes. However, it is a critical question to understand the mathematical principle underlying the algorithm. Traditionally, people thought that the normalized min-sum algorithm is a good approximation to the sum-product algorithm, the best known algorithm for decoding LDPC codes and Turbo codes. This paper offers an alternative approach to understand the normalized min-sum algorithm. The algorithm is derived directly from cooperative optimization, a newly discovered general method for global/combinatorial optimization. This approach provides us another theoretical basis for the algorithm and offers new insights on its power and limitation. It also gives us a general framework for designing new decoding algorithms.Comment: Accepted by IEEE Information Theory Workshop, Chengdu, China, 200

Centralized versus market-based approaches to mobile task allocation problem: State-of-the-art

Centralized approach has been adopted for finding solutions to resource allocation problems (RAPs) in many real-life applications. On the other hand, market-based approach has been proposed as an alternative to solve the problem due to recent advancement in ICT technologies. In spite of the existence of some efforts to review the pros and cons of each approach in RAPs, the studies cannot be directly applied to specific problem domains like mobile task allocation problem which is characterised with high level of uncertainty on the availability of resources (workers). This paper aims to review existing studies on task allocation problems(TAPs) focusing on those two approaches and their comparison and identify major issues that need to be resolved for comparing the two approaches in mobile task allocation problems. Mobile Task Allocation Problem (MTAP) is defined and its problematic structures are explained in relation with task allocation to mobile workers. Solutions produced by each approach to some applications and variations of MTAP are also discussed and compared. Finally, some future research directions are identified in order to compare both approaches in function of uncertainty emerging from the mobile nature of the MTAP