An evolutionary multiobjective approach to sparse reconstruction

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 at-tempts 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) cor-responding to various subproblems. In EMOSA, the weight vector of each subprob-lem 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 metaheuris-tic algorithms on both the (constrained) multi-objective knapsack problem and the (un-constrained) 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