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Faced with the challenge of solving hard optimization problems that abound in the real world, classical methods often encounter great difficulty - even when equipped with a theoretical guarantee of finding an optimal solution. Vitally important applications in business, engineering, economics and science cannot be tackled with any reasonable hope of success, within practical time horizons, by solution methods that have been the predominant focus of academic research throughout the past three decades (and which are still the focus of many textbooks). The impact of technology and the advent of the computer age have presented us with the need (and opportunity) to solve a range of problems that could scarcely have been envisioned in the past. Weare confronted with applications that span the realms of resource planning, telecommunications, VLSI design, fmancial analysis, scheduling, space planning, energy distribution, molecular engineering, logistics, pattern classification, flexible manufacturing, waste management, mineral exploration, biomedical analysis, environmental conservation and scores of others.